T H E U N I V.E R S I T Y 0 F M I C HI G A N COLLEGE OF ENGINEERING Department of Chemical and Metallurgical Engineering Final Report PIPELINE CALCULATIONS FOR GAS-LIQUID SYSTEMS Donald L. Katz Ao Prakash Sikri Dale E, Briggs ORA Projeedt 06922 supported byo AMERICAN NATURAL GAS SERVICE COMPANY COLUMBIA GAS SYSTEM SERVICE COMPANY NATURAL GAS PIPELINE COMPANY OF AMERICA administered through: OFFICE OF RESEARCH ADMINISTRATION ANN ARBOR August 1965

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TABLE OF CONTENTS Page SUMMARY AND CONCLUSIONS...................................... v LIST OF APPENDIXES........................................... xi LIST OF FIGURES.............................................. xiii LIST OF TABLES............................................... xiv INTRODUCTION................................................. 1 PHASE BEHAVIOR OF HYDROCARBON SYSTEMS........................ 2 Behavior of a Binary Mixture............................ 3 Region of Interest for Pipeline Flow.................... 9 MIXTURES CONSIDERED IN STUDY................................. ll Permissible Pressures................................. 12 THE DENSITY OF SINGLE PHASE HYDROCARBON FLUIDS............... 18 VISCOSITY.................................................... 22 PIPELINE FLOW CALCULATIONS.................................. 28 Flow Formula............................................ 28 Calculation of Supercompressibility Factor.............. 30 Calculation of Moody Friction Factor and Transmission Factor (Ft)...............*...e..... 30 Drag Factor (Ff)... 30 WORK OF COMPRESSION.......................................... 1 ECONOMICS OF SINGLE PHASE PIPELINE FLOW FOR MIXTURES OF NATURAL GAS AND LIQUID HYDROCARBONS........................ 3 CALCULATION OF TRANSPORTATION COSTS.......................... 41 Effect of Temperature................................... 50 Cost of Hauling Liquids................................. 50 CONCLUSIONS.................................................. 55 BIBLIOGRAPHY,................................................. 58 iii

SUMMARY AND CONCLUSIONS This study has considered the transporting of light hydrocarbon liquids by dissolving them in high pressure natural gases. The presence of the higher molecular weight material increases the deviation of the gas mixture from ideal gas behavior and increases the gas density in the pipeline but with only minor viscosity increases. Thus, the addition of liquids like propane to natural gases increases the flow capacity of the line and thereby reduces the cost of transportation. A computer program was written to solve the pipeline flow equation, to calculate the horsepower of compression of the gas, and to determine the cost of building and operating the line. This program was capable of finding the minimum cost of transportation for a given pipe strength, line diameter, gas composition, and flow rate. The phase relationships for gas-liquid systems were studiedo The minimum pressure to maintain the mixtures in a single phase was found for various systems of natural gases and light hydrocarbon liquidso The pipeline pressure was always maintained at pressures above this minimum value in the design calculationso The transportation costs were calculated for natural gas and nine mixtures containing condensable liquids for a series of conditionso The parameters studied were Composition and corresponding minimum pressure Steel strength: 65,000 and 100,000 psi Pipe diameter: 16, 24, and 30 inch Pressure: 700 to some 3600 psia Flow rate: 200-1500 million cu. ft./dayo The important factors used in the study and the costs of transportation of the mixtures (single phase) in cents/100 miles/Mcf are given in Tables 5, 6A, and 6B, attachedo V

It was found that the transportation cost decreased with increasing flow rate, increasing pressure level to some 2500 psia, and increasing molecular weight of the gas mixture up to gravities of about 0.9. The costs of transporting propane, butane, and condensates are in the range of 8 to 15 cents per barrel per 1000 miles. The cost of separating the condensates from the natural gas at the market terminal has not been included in these figures. Costs for specific mixtures are attached in Table 9. The above costs for hauling liquids in large quantities appear to be from 35-50% of the tariff for product pipelines. The study indicates that further work is justified in considering the transportation of light hydrocarbons in large quantities along with natural gas in long distance pipelines. vi

TABLE 5 Economic and Other Factors Used in Study Length of line (Lt) 1000 miles Flowing temperature (T ) 60~F Pipe strength (S) 65,000 psi and 100,000 psi Pipe diameter OD) 16 inch, 24 inch and 30 inch (OD) Pipe roughness EE = 250 micro-inches Bend Index 2000 per mile Longitudinal joint factor for pipe (E) 1.0 Pipe design factor (F) 0.72 Compressor efficiency, EFF, 80% Pipe cost (Y) 65,000 psi strength, $265 per ton 100,000 psi strength, $384 per ton Cost of laying pipe (N) $1200 per inch OD per mile Communication system cost (H) $3000 per mile Compression station cost (X1 + X) $270,000 + $165 per horsepower Cost of fuel (CF) 20 cents/Mcf Fuel consumption (FHPHR) 8.7 X 10-3 Mcf per horsepower - hour Cost of labor and maintenance for pipeline (CLML) $850/mile/yr Cost of labor and maintenance for compressor stations (CLMS) $19/hp/yr Gas loss (LG) = 0.005 fraction of flow at 20 cents/Mcf Administration expenses (AD) 1 cents/100 miles/Mcf 3650 Annual investment charge, 15% per year Line assumed to flow at 100% capacity 365 days/yr vii

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LIST OF APPENDIXES Appendix Page A Formula for Cost of Pipe 61 B Computer Program and Nomenclature 65 C Example Hand Calculation 107 D Kurata Phase Diagrams for Mixtures Not Studied 121 E Charts Giving Results of Economic Calculations 133 F Example of Sarem's Method for Computing Compressibility Factor 171 G Viscosity Data Used to Represent Correlation 177 H Data for Compressibility Factor of MethanePropane System 181 I Subroutine FNGFRI for Moody Friction Factor 185 xi

LIST OF FIGURES Figure Page 1 Illustration of Phase Behavior for Binary System of Methane-Propane 4 2a Bubble and Dew Point Curves for Methane-Propane System 3 2b Phase Behavior of Methane-Propane System 6 3a Bubble and Dew Point Curves for Methane-n-Butane System 7 3b Phase Behavior of Methane-n-Butane System 8 4 Region of Interest for Pipeline Transportation of Gas-Liquid Systems 10 5 Relationship of Barrels of Liquid Per Day as a Function of Quantity of Gas as Mixture 14 6 Critical Loci of Methane-Propane-Pentane System 16 ~7 Phase Diagram for; Mixture S-2 (Kurata)28 19 8 Phase Diagram for Mixture S-4 (Kurata)28 20 9 PDensity of Gas S-Natural Gasoline Mixtures (S-2 and S-4) 25 10 Viscosity of Propane, Methane and Mixtures 25 11 Viscosity of Paraffin Hydrocarbons (Correlation) at High Reduced Temperatures 26 12 Viscosity of Paraffin Hydrocarbons at Low Reduced Temperatures 27 13 Drag Factor as a Function of Bend Index 32 14 Cost of Transporting Gas as a Function of Number of Stations 42 15 Cost of Transporting Gas as a Function of Flow Rate, 80% Natural Gas-20% Propane 43 16 Effect of Flow Rate on Cost 47 xiii

LIST OF FIGURES (continued) Figure Page 17 Effect of Pressure on Cost of Transportation 48 18 Effect of Pressure on Cost of Transportation 49 19 Effect of Molecular Weight on Cost of Transportation (65,000 psi steel) 51 20 Effect of Molecular Weight on Cost of Transportation (100,000 psi steel) 52 LIST OF TABLES Table Page 1 Compositions and Properties of Mixtures 13 2 Phase Behavior Data Sources for Light Hydrocarbon Systems 17 3 Viscosity Data 24 4 Comparison of Work of Compression Calculations 36 5 Economic and Other Factors Used in Study 40 6A Cost of Transporting Fluids, cents/100 miles/Mcf 45 6B Cost of Transporting Fluids, cents/100 miles/Mcf 46 7 Calculation of Cost of Transporting Liquids in Gas Pipeline for 1000 Miles 55 8 Published Tariff for Product Transportation by Colonial Pipeline Company 56 9 Cost of Hauling Liquids 57 xiv

PIPELINE CALCULATIONS FOR GAS-LIQUID SYSTEMS Introduction The purpose of this project is to investigate the economics of carrying liquids along with natural gases in a single phase in high pressure pipelines. To carry out the investigation, the physical properties of the gas-liquid mixtures, pipeline flow calculations, compression calculations, and economical factors are combined into a single relationship. This relationship was programmed for the computer to permit a quick evaluation of the parameters over a wide range of conditions. The basis of the study is the fact that liquefiable hydrocarbons when added to natural gas increase the density of the system, both because of the increased molecular weight of the mixture and also because the compressibility factor is lower for the mixture due to its lower pseudocritical temperature. At the same time, the increased molecular weight of the mixture does not increase the viscosity of the gas significantlyo This combination of properties was thought to be such that the cost of transporting gases containing propane, butane, and raw natural gasoline could be less than for natural gas itself. To carry out the study, it is necessary to determine the conditions at- which various systems are in a single phase. The density in the form of the compressibility factor and the viscosity are needed for such systems at the pressures and temperatures of the pipelines The pipeline flow calculations for this study are based on the American Gas Association Institute of Gas Technology report. It was deemed necessary to ascertain that the procedure was the equivalent of Weymouth's equation with Moody friction factors2, and this was found to be true for the "partially turbulent case" adopted. 1

In any comparative study, it is necessary to establish a standard. After several trials, it appeared best to compare the cost of transporting natural gas a distance of 1000 miles with included liquids dissolved in a single phase fluid with the cost of transporting the gas alone. For each mixture and pipe diameter, the cheapest transportation cost was sought before comparing the two costs. From these two costs, one can find the cost of hauling the normally liquid constituent and compare it with liquid pipeline rateso The various phases of the study will be described in turn starting with the phase behavior of gas-liquid systemso Phase Behavior of Hydrocarbon Systems Mixtures of natural gas and light hydrocarbons may be transported as a single phase provided the proper temperatures and pressures are maintained. For pipelines buried in the ground, the temperature range is limited to from about 30-150~F or from ground temperature to the compressor outlet temperature. The objective of this study is to find the pressures suitable for pipeline transportation over which gas-liquid mixtures will remain in single phase at temperatures of 40-100 F. As will be illustrated in a general discussion of phase behavior, there are two pressure regions at which mixtures such as methane and propane will remain in single phase. The first is the low pressure region wherein increased pressure causes condensation of liquid to occur. The second region —that of interest in this study —is the high pressure region where two phases occur upon lowering the pressureo The latter is sometimes referred to as the retrograde region since phase changes occur due to an opposite change in pressure to that normally found at low pressure. This behavior will be made clear in a general discussion of the behavior of mixtures 2

Behavior of a Binary Mixture Figure 1 shows the behavior of a binary system such as methane-propane. The curve AC1 is the vapor pressure curve of methane and HC3 is the vapor pressure curve of propaneo At pressures above AC1C2C3, all mixtures of methane and propane are in a single phase. Diagram BDC2EFG represents the border curve between the single phase region outside and the two phase region inside for a specific mixture of 80 methane and 20% propane (molal basis). The areas of interest in the single phase region are pressures above the curves DC2EF or any pressure at temperatures above F. The problem is to find a convenient way of calculating the single phase region for any mixtures of known composition at pipeline temperatures. Although Figure 1 shows the behavior of only one mixture of methane and propane, the two phase region for all mixtures lies within the area of AC1C2C3H and outside this region all mixtures are in single phaseo Figures 2a and 2b show quantitatively the location of the border curves for the methanepropane system. It may be seen that the various mixtures are similar in behavior and so only the 80 methane mixture will be discussedo When viewed from the interest of pipeline flow at 40-100IF, one needs to consider a series of mixtures of increasing propane content. Figures 3a and 3b give experimental data for the methane-butane systemo Studies were made by the writer on phase behavior of hydrocarbon systems in glass windowed cells some 25-30 years ago2 3,4o Consider the behavior of mixture A, Figure lo At the temperature and pressure of I, it is in a single phaseo Upon dropping the pressure isothermally to D, it remains in single phase until reaching pressure D at which pressure bubbles of vapor appear. The curve BDC2 is the bubble point curve for mixture A. Further pressure reductions below D cause various percentages of vapor to form as indicated qualitatively on Figure lo For quantitative percentages of liquid, see Kurata phase diagrams in this report. 3

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2,000'SHOW'ESTIMATED VALUES - 1,800 1,600 1,.400 _ 1,200 iX,00 80 600 400 100 6L 10000.-100 0 0 1 0. 2 0. 3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 100 n-BUTANE MOLE FRACTIONI METHANE METHANE Figure 3a. Bubble and Dew Point Curves for Methane-n-Butane ] L200% n- --— BUTANE MOLE- FRACTION — METHANE —-- METHANE —--- --- -^ —I Figure 3a. Bubble and Dew Pont Cures o^r Methane-n-Butane 2 F - - -- - - ^ 2 ^ ^ - -- - - - -;- - - -- - - - - - — T — - j - -- q --- _- _- _ —--- --- T_ __ __ T_ __ _7-,.:7Vy V'o<< IA_ I - - - IAII _I_-__-11111 — 1 IIH IIH L IIIII H r _ — -_ -- _ - _ - _ -^ - -- J_ ra l - J - ----- ~|:::::: F^ - ^ ^ / ":::::?::::::^:::::::::::::: jp::l::t: *::_ _ ____T_:: /: 1 1111 1 II 111::.:,l|zL IIII11- III*I1 <so 8::: _ _::: tAlls lii-il/ill-^::::::"illiiliill::::::::lliilliil:::::-: -- -4 -r -^: r tl r llll::::: -g 111 11l1.::::::^11111; 0 t1 — I-T- - -2 _ T, s l ff1'4 -^_ 1 1 111 11IX ZT I 11 < 1-i? - - - - - - ( -- - - - 3 - - - -? T —-11 —i 11^ -111 1T 111 Z111 111 ^ 1' l l IFi ur 1 3a,,%. B, b Ln De Po IIIIII nI i ntIII 0 C Ir e Io IMethIIaneI-I III In-B III l Iu t11a 111 nn[z r_ -Zrzi r lrlt xSysteImr nT ~rt ~ l t~ T|urrlI1 4w E ( t jl d 2 E~~7,-II

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Mixture A at J is in a single phase and upon dropping the pressure to E, droplets of liquid or dew form beginning at pressure E. The curve C2EF is the dew point curve for mixture A, sometimes known as the upper or retrograde dew point curve. As the pressure is dropped below E, liquid forms reaching its maximum volume at K. Further pressure reductions below K cause the liquid to vaporize. When the pressure reaches G, all of the liquid has vaporized and point G is the lower or normal dew point. When compressing the mixture from L to G, dew forms in the manner usual for pipelines. Should one have selected a single pressure just above C2 and allowed the pressure to drop, it would have been observed that at C2 the mixture would change from a single phase to about 50 by volume liquid and 50 vapor. Point C2 is the critical temperature and pressure for mixture A; it is the convergence of the bubble point, dew point, and various percentage liquid lines. Region of Interest for Pipeline Flow Any mixture of natural gas and liquid hydrocarbons has a phase diagram generally similar to mixture A. Figure 4 is presented to relate the region of interest relative to the phase behavior of a mixtureo In the past, pipelines have been operated at temperatures above C of Figure 4 to keep the gas in a single phase. A mixture carefully stripped of heavy hydrocarbons, pentanes and heavier, can carry a considerable amount of liquefiable propane or butane at temperatures of 40 F and above. For these mixtures whose maximum two phase temperature (cricondentherm point C of Figure 4) lies below the pipeline temperature, the currently used procedures may be followed in that there is no lower or higher limit of pressure which will cause condensation. This study proposes to handle in pipelines those mixtures for which point C is within or above the pipeline temperature range of 40-100~Fo Therefore, it will be necessary for such 9

e * * ~ a *. ~ * ~ ~ * -'*- *.....** REGION OF,' I.. *J * INTEREST'-, ~ *~*'. v B..; * - -. ~~~ ** ~ ~ ~ ~ PRESSURE ~ / \. ~ o,,'* ~ c. 10 ~ I ~0 ~ ~4~ ~ PRESSURE of Gas-Liquid Systems 10~~~~~~~~~~"e

mixtures to limit the lower pressure at which they may be transported to the conditions corresponding to pressures of ABC of Figure 4. It would seem that the procedure desired is a way of finding the maximum pressure in the temperature range of pipeline flow used here as 40-100~F at which two phases occur. This maximum two phase pressure will then become the minimum pipeline pressure for single phase operation. Thus for methanepropane mixtures, the minimum pressure in pipelines for mixtures rich in propane, one can use the critical loci, curve C1C C3 of Figure 1. The plan is to use a minimum pressure in the pipeline 100 psi above the single phase pressure to give some degree of safety. It does not matter with respect to phase behavior whether the mixture is at condition I or J on Figure 1. For pipeline transportation, it can move over a temperature range including crossing the critical at these pressures and remain in single phase. It is true that the densities of the mixtures in this region are high compared to present values in gas pipelines, and that the density changes rapidly with both temperature and pressure. It is believed that centrifugal compressors should be considered for such fluids in that they are as much like a liquid as a gas. The terms liquid and gas become relatively useless when describing single phase fluids in the region of I and J in Figures 1 and 4. Fluid at I might be called a "compressed liquid", but the nature of the liquid at D, Figure 1, is so unusual, i.e., density, compressibility, etc., that use of the term "liquid" may be misleading. Likewise, application of the term "gas" to fluid at J would not be meaningful. The description of these single phase fluids can be made only by indicating their density and compressibility. Mixtures Considered in Study The liquids which need transportation are propane, butanes, natural gasolines or condensates, and crude oil. Initially, 11

it was intended to consider transporting all of these liquids. However, pipeline calculations have been made only for propane, butanes, natural gasoline, and propane-butane mixtures. Table 1 lists the mixtures which have been studied. One consideration is the volume of liquids which a pipeline can handle for various concentrations. When vaporized, propane represents 35.8 cubic feet at 60~F and 1 atmosphere per gallon and n-butane 30.77 cubic feet per gallon. A pipeline with a 500 million cubic feet per day capacity will carry 1,580,000 gallons (37,700 bbls) of propane per day at a concentration of 10 mole % propane. These quantities of liquids are largeO The State of Louisiana in 1964 produced a total of 350,000 bbls per day of all natural gas liquids, while Texas produced 750.000 bbls per day. The barrels condensate per million cubic feet of gas included all the propane as listed in Table 1. Figure 5 is a plot of barrels of liquid per day versus quantity of gas with lines for various mixtures of gas and liquids. It is helpful in arriving at the quantities of liquid being considered for various concentrations and gas flow rates. This figure does not include the propane present in the natural gas as condensateo Permissible Pressures For each mixture on Table 1, one needs to know the minimum pressure permitted when transporting the fluid in a single phase. For a 0~6 gravity natural gas and the 10% propane-90% natural gas mixture, the 40~F minimum pipeline temperature is above the liquefaction temperature at any pressure. For such mixtures, the minimum pressure put in Table 1 is 600 psia, but this is an arbitrary value to make the lowest pipeline pressure at 700 psia the minimum permitted pressure plus 100 psia safety factor used for all mixtures to avoid condensation in liquid rich mixtures For those mixtures which form two phases at the lowest contemplated pipeline temperature, used here as 40~F, one needs 12

_L (D cO OOOCO COI O GO 0 c O n?- -p O OK -) CO CO Lotn ) 0 r- O KG) -t- E — - oo- ooooooCC) o cu co M ~o ~4.......... 0 C -- LcD 0 -P I CO L N CO rn C H -- C' CYO) O O O0 0 HX7U E' L-00000000- O O O (). CC) CQ^C4 o r= rH l'. H LC 4 K pq CO 0 r -i on 0 C (D O o o 0 O O' — OL C\ 0H 0 L0 0 o 0 H CM CY) OA 0 o0 C —I KON -cO L - - O PO c0 o r 0 -- CCco H......o0 40 0 0 pq r aj oh C 0 g r-i nOH 0 000 CM0 i oo-o o 0000 c d rO1-c -d G O 0O O --- G pG7\2qH c*c^^ Ho oo 00 4-) pq * o o coj oCy ) 04 (D 0r-C mn,cd K Gc -4'-j -- oCC O I>-0 O ~O O oq o O O O cu o 0 U G OK )' -P. CDC)G - rl 0 tO pq?- (D^ O Lnw0C. Ei]-.i 0 0 KG ) - c E- O coO c o -: 0O O GJ L-o.Lh Cy-)1O OGO QO O 0O ~ ~ r4 r 0 co'IQ0 C(C 0K 0 00 0G,d COHOO^ C -G- O14 O^G' Q) 1 0 O -I r-. -- I- n 0 Q0 C'cli 0d CC) 4 CC H 0 4 GO CM 0 0o C O ( K 0 c' o c O0 CQ^ C^H CM H 4 LC\KG) ^O iOr02... n CO 0 r 00D d CD- CM 4I 4KG O CO O O G r-4 0 4co -, o o K) C'- - Cq ~ O O-0 M a ~a 0J c/l ~ C: I D C O cO kO o, ~c' a, -c~3~ 0 o *. CO o C CD>aCl.(CD CQ C C 4 CM 0, 0KG CMQ Lf 0 H. 43 43 c. ~.~.~ 4~ r0 0 0o ^ ed ed -rP ed U2 a^rl.r$ CM GO 0 C7' K 43c CMLC\CM 0o Co G CP KG )r-c ^ e 1 (

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the upper dew point pressure or bubble point pressure should the critical temperature be above 40~F. Calculation of the dew or bubble point pressure could be made for various mixtures 2 using equilibrium constants. However, in this region, the convergence pressure for the equilibrium constants is very sensitive to composition and machine computation with an established program such as the NGPA and Oklahoma State University are devising would be needed. However, even such a program cannot be trusted at critical conditions. A rather fruitless study was made of a correlation of the single phase pressures with molal average boiling point and molecular weight for the mixtures under considerationo From the lack of correlation found in this study, it was decided to rely on experimental phase data with minor adjustments for the mixtures shown in Table 1. References to experimental data for specific systems are given in Table 2. For the natural gas, it was decided to use a 0.6 gravity gas with the composition shown on Table 1. The compositions for streams 2-8 are given on the table after adding the indicated amount of liquids. For the last mixtures, 9 and 10, the compositions are those used for determining the phase behavior. It should be noted that the mixtures in Table 1 are not the pure methane-propane and methane-butane systems, but have intermediate constituents present in the natural gas. The differences in the behavior of mixtures 2, 3 and 4 as compared to the methane-propane mixtures should be considered. Figure 6 shows the critical loci of the methane-propane-pentane system. From the figure, it is observed that adding an intermediate constituent, propane, lowers the critical pressure for any methane-pentane system. In like manner, ethane will lower not only the critical pressure at a given temperature but also the bubble and dew point curves for a specific mixtureo Reference can be made to the methane-ethane-propane systems of Price and Kobayashi, shown in the Handbook, p. 579. At 1100 psia and 50~F, ethane at 3N does not reduce the propane content of a dew point gaso At 800 and 1000 psia and 50~F, the propane content is 1 or 2% less for a dew point whem some 5% of ethane is added to the methane-propane systemo 15

250 L~. _ / __- - _.....'.^ -'ZO -100 0 100 200 300 400 Temperoture, deg F Figure 6. Critical Loci of Methane-Propane-Pentane System 16

TABLE 2 Phase Behavior Data Sources for Light Hydrocarbon Systems Two Phase Tamp. Press. Range System ( F) (psia) Reference Methane-Ethane 0 300-900 5 40 500-900 Methane-Propane 40 511-1469 6 100 180-1355 160 380-890 Methane-n-Butane 70 819-1924 7 100 339-1904 160 435-1810 Methane-Isobutane 100 100-1680 8 160 150-1400 Methane-n-Pentane 100 313-2443 9 160 720-2300 Methane-Propane- 100 1350-2375 10 n-Pentane 160 700-2150 11 Methane-Ethane-Propane 0 100-1300 12 50 100-1200 Ethane-Propane 0 100-400 12 50 100-200 Propane-n-Butane 160 55-172 13 Methane-Butane-Decane 100-460 400-10 000 14 160 400-5000 15 100-460 200-10, 000 16 40 1000-4000 Gas Condensates 0-200 600-2700 4 17

It may be concluded that the differences in minimum pipeline pressures selected from binary systems are not in error enough to influence the cost of pipeline transportation significantlyo Dr. Fred Kurata measured for his doctorate thesis gas-natural gasoline mixtures for which the phase behavior are of interest. Two of these mixtures S-2 and S-4 were selected for this study. Figures 7 to 8 give the phase diagrams from the thesiso At 40~F, mixture S-2 is below the critical temperature of 55 F. In this case, a higher pressure is required to hold the mixture in a single phase at 100~F than at 40~Fo Mixture S-4 has the full. pipeline temperature range below its critical temperature of 109 F. The phase diagrams for nine other mixtures studied by Kurata are given in Appendix D along with the compositions. To obtain 4L2 the critical points for other mixtures, the method of Kurata is suggested since it is based on natural gas-liquid systems. The minimum pressure listed on Table 1 is either the 600 psia when no phase changes occur, or the highest bubble or dew point value found over the temperature range of 40-100~Fo As indicated previously, the ethane in the natural gas was neglected. Likewise, the propane in the gas was neglected in finding the single phase pressure for mixtures 6, 7, and 8. Initially, it was intended to use butanes as 40 mole % isobutane and 60 mole % normal butaneo The composition is indicated in this manner on Table 1 and was used in finding pseudocritical conditions for viscosity and density to be discussed later. Otherwise, the phase behavior is based on methane-n-butane properties. Isobutane generally would provide some safety factoro The 5% propane-5% butane, mixture No. 5, has not been measured experimentally. The value given is an estimate. The Density of Single Phase Hydrocarbon Fluids The method of expressing the density for natural gases is the gas law, including a compressibility factor (Z) 18

2600 ----------------- ^ - o- - ^, ^__" 2400 200 1600 / / 01400-, 41200 -- cn LI oo 800 COMPOSITION COMP MOL % N2 0.579 Ci 7.. O 600 C2 5,900 C3 3,146 C4 2. 660 C5 4.50 C6 2.525 C7- 2, 140 400-.200 0 20 40 60 80 100 120 140 160 180 200 TEMPERATURE DEG. F Figure 7. Phase Diagram for Mixture S-2 (Kurata)28 19

2800 2600 -,,oo 1/ ) 0 - v, T \ 2200 2000 /14 00< / \, W 0^ -^ —.^-,^-^-/* s/ /, / / tat7 20 ) 12 0 6 0 0 2 // ~1200 -- - -/20.800 -- COMPOSITION.000 ~ COMP MOL.., —-oo^ N2 0.538 600 -------- t C 72.80 /^^~~~ C2 5.46.00-01~ ~C3 3.02.0000,'~ C4 3.07 "C5 " 6.88...^ ______ ^ ^'^______________________________ Ce 4.382 540~0 J^ —------------------------- C7+ 3.75 0 200. 20 4p 60 80 100 120 140 160 180 200 2 2C TEMPERATURE DEG. r Figure 8. Phase Diagram for Mixture S-4 (Kurata)2U 20

PV = ZnRT where P = pressure, psia V = volume, cu. ft./lb. mole Z = compressibility factor n = number of pound moles R = gas constant, 10.73 for these units T = ~Rankine, F + 460. A generalized chart of compressibiliity factor versus reduced pressure (pressure over critical pressure) and lines of reduced temperature (absolute temperature over critical temperature) has 2 been devised for natural gases, Figure 4-16, p. 106. This chart 17 has been put in form for computing by Sareml7 and is generally satisfactory, excepting for values of the compressibility factor below 0.50 where errors can become large. At reduced temperatures of 1o15 and below and at pressures of 600 to 2000 psia, the correlation is not reliable. A program (ZFAC) has been prepared using Sarem's method to give the compressibility factor for any temperature and pressure when the gas composition is known. Should the composition be represented only by the gas gravity (G), the program uses the pseudocriticals corresponding to the published relationship of these values with G. The subroutine for computing Z at any temperature (Tr 1o052.95) and pressure (Pr 0.1-14.95) requires the composition of the gas or its gravity. The critical properties and molecular weight of N2, C2, CH4-C7H6, iC4H10, and iC5H12 are already in the program. Three added constituents may be specified along with their Tc, P and molecular weights. Initially, the mole c c fractions of all constituents and properties of the three added constituents are set at zero. This subroutine is incorporated into the pipeline flow program, and it provides the Z when called upon. An example of the use of this program for predicting Z's is given in Appendix F, along with a comparison of computer values with those read from the chart. 21

The AGA supercompressibility factors were not used in this study, and presumably would be an alternate way of expressing density. For mixtures S-2 and S-4, the thesis gives the saturated densities with only a nominal precision. Figure 9 shows the measured saturated densities along with values at 3000 and 4000 psia calculated from the compressibility chart. Viscosity The pipeline flow formula requires the viscosity of the fluid as a function of temperature and pressure. In general, for simplified cases a constant flowing temperature will be used in the pipeline. Therefore, it is more appropriate to say that the viscosity is needed as a function of pressure at a given temperature (60~F) and for a given composition. The viscosity of methane, some natural gases, and of the methane-butane and methane-propane system have been determined. These viscosities also have been correlated as a function of reduced temperature and pressure with a reasonable degree of 18,19 success' Table 3 lists the sources of data which are of interest. Figure 10 gives the reported methane-propane viscosities. It was decided to use the correlation of Bicher and Katz for the viscosity of the fluids. Figures 11 and 12 give the correlation based on reduced temperature, reduced pressure, and molecular weight. The work of Carr et al indicated that Bicher's data had some inaccuracies over some ranges of pressure, since Bicher apparently had some turbulence in his rolling ball viscosimeter. The correlation of Carr et al probably would have been better but would have been more difficult to use. In view of the indirect effect of viscosity on the friction factor, the work of Bicher seemed satisfactory. The viscosity correlations as shown in Figures 11 and 12 were programmed by submitting the points on the curves as data 22

I0.5 IIII I I7 I i - TI 1 I-.II DENSITY OF MIXTURE -4 I 0.4 2150 PSIA E! ".: ^1: 0.3 -! II I:I0.I3 I:1:: 1 1:1ITIIIIII I: I II:I I I rn rr:T 2545 PSIA ~ I l l pp545 PDSIA i,::::,,::::::: —=::Z:,,,,,,,2555 PSIA T 0 20 40 60 80 100 120 140 TEMPERATURE -OF E:::sAT PRESSi PSIA I:E:EEE:EEEE:-Tm..Fg0 9S DS Tur G2400t PSI(A a-n:::::: Z:::::: 2600 PSIA i.20 20 2'.40 20 4I 60 i 80 100 120 1.40 TEMPERATURE - O F S-4) 25 t~~2

TABLE 3 Viscosity Data Temp. Pressure System ( F) (psia) Source Methane 0-150 14.7-4000 18,21 Methane-Propane 0-150 14.7-4000 18 Propane 0-150 14.7-4000 18,22 Methane-n-Butane 70-160 14.7-4000 23 Ethane 59-150 100-4000 22 Pentane 77-150 100-3000 24 Natural Gases 100-4000 21 24

3000 _ -------- tt00 __ w\W>^-__ —---— __ —. 1" _ " 0 100 200 300400 500 > I \ 1N, "^. TEMP~RATURE *. 02p r - 200 - 0 - _! TWO -fHAE \ -0o~ ___-'oo O 100 200 300 400 500 00 TEMPERATURE F. 2^~~~00^^^- _|0200 I5(' -, - -- - - 7- _ e -- 1 - - D 10^^^^^^%'3 -_0- 02 - - - - o _ 2E _ ot> _ __00 300 400 Soo_0 600 u_5 TEMPERATURE - -. 4/ d. - -SQ. B ~ u 200 PHASE LS 0 > REGION'500 ISO 0 0 100 200 300 400 500 600 TEMPERATURE or. 0 Goo 4400` So ~- "0 —\ -.,i 300. -0. - I i ABS. 7TEMPERATUE 2 A. Propane.. D. 64 per cent methane-40 per eent propane I -'4 pe- _.a e....pe na pepm 25 7 too 200 300 400 --- = —. TEMPERATURE er. B. 20 per eent metbune-80 per cent propane cc C.44 per cent methano-60 per eent propane Si ~ "' — --' D. 60 per cent methane-4 per eonl propane J 20 Figure 10. Viscos.ity of Propne, Methane and Mixtures

MOL. WT. 013 20 25 30 3.5. U RD"T """ - -1 - ^ - - - "r ^ PSEU DO REDUCE D)t | J|I XI:I 1 TEMPERATURE / 1,20:.':'" 120'*10 - --- T -t-:: -: --- ---------- 1-i —.:-,..-_ _l T_ _ T T- T m _ _ ~ ] J;~\ -_, |.O ~.^. —-----..-:=a -- -- -- -^ t — -- — ^ ^ ~|;'TT-,I~~~~ I I00 Figure 11. Viscosity of ParaffinHydrocarbons/(Correlation) -^ ---- EEE^" —^^ — --— 0, r',Z ~ I I I' ~ I,.! I I~~~~~~~~~~~~~~~~~'I PSEUDO~~~~~1 REDCE PRESSUR Figure 11. Visosity of Parafin Hydrocarbon (Correlation at High Reduced Temperatures~~~~~~~~~~~~~~~~~~;00 0, 026

4001 -- |-PSEUDO REDUCED P RESSURE T EMPERATURE Figure 12. Viscosity of Paraffin Hydrocarbons at Low Reduced Temperatures 23~~~00- -^ --— 27 -0 2 4 6 6 10 PSEUDO REDUCED PRESSURE Figure 12. Viscosity of Paraffin Hydrocarbons at Low Reduced Temperatures 27

and providing an interpolation procedure. Appendix G lists the viscosity data used by the computer. Pipeline Flow Calculations Upon discussing with the Advisory Committee the appropriate equation for making pipeline calculations, a copy of the report "Computation of Flow and Natural Gas Transmission Lines" by the Institute of Gas Technology with A. E. Uhl and Committee NB13 as the author (1964) was supplied to the project. It was agreed that this method of computing pipeline flow would be satisfactory from the standpoint of the sponsor companies. Therefore, an effort was made to see how this formulation of pipeline flow fitted into the usual Moody friction factor concept for flow of fluids in pipes. If possible, the flow formulas used in the report would be used but with an understanding of the friction factor which the procedure follows. It was found that the partially turbulent flow calculation procedure was that of using the Moody friction factors with a roughness corresponding to smooth pipe. Added factors for degrees of bending and pipeline flow efficiency are included. Otherwise, the procedure is exactly that which would be used in the normal Weymouth type equation which employs the Moody friction factor. In the fully turbulent case, a further simplification is made in the report which does not appear necessary in this project. Accordingly, the pipeline flow formula is presented in the manner which is believed to be compatible with the IGT report and the flow calculations with which the writer is already familiar. Flow Formula It is proposed to calculate flow in natural gas transmission lines by the following equation: b -77.5 Ftb Fpb Fgr Ftf Fpv Fd Ft Ff Ffe (1) 28

where Qb = gas flow rate - cu. ft./day at Pb and Tb P = pressure - psia P1 = inlet pressure P2 = outlet pressure L = total length of pipe between compressor stations excluding any equivalent length due to bends in pipe since such is included in Ff. Equivalent length due to valves, gates, etc. are to be included. L = Lt/NOS, miles L = total length of line, miles NOS number of stations T.lb Ftb = base temperature factor 520. A base temperature factor of 60F will be used. Ftb = 1.0 (2) 14 73 Fpb = base pressure factor 1 A base pressure of bP 14.73 will be used. F -1.0 (3) Fgr = gas gravity factor = 4) G = molecular weight/29.0 Ftf = flowing temperature factor = 5 (5) Tf = flowing temperature - ~R Fpv = supercompressibility factor = V (6) p (5 Fd = line diameter factor = D25 D = inside diameter of the pipe in inches (7) 1l 2 Ft = transmission factor = = (8 F 29 29

f = fanning friction factor F (9) fM = Moody friction factor Ff = drag factor = function (Bend Index). Graph (10) of Ff versus Bend Index is as shown in Figure 13 (reproduced from Figure IV-l, p. 56, IGT report, 1964). Ffe = flow efficiency factor. Normally use Ffe = 1.0 (11) unless there are data on cleanliness, etc. to reduce the value. For the above restrictions the equation reduces to 2- p2 5 1 2 b 775 gr Ftf Fpv Fd Ft Ff P (12) Calculation of Supercompressibility Factor In evaluating Fpv, a pressure and temperature are needed. The pressure to be used is the Paverage (Pavg) defined as follows: avg - 2 P + P2 (13) Calculation of Moody Friction Factor and Transmission Factor (Ft) The Moody friction factor has been plotted against Reynolds number with lines of constant wall roughness (Moody, 7-25), (Katz, Figure 7-3, P. 303)2 The Reynolds number for a gas flowing in pipe is given by the following equation: -4 Qbi/LGb) (14) where Re = Reynolds number, dimensionless Qb = gas flow - cu. ft./day at Pb and Tb lb = fluid viscosity - ft sec D = inside diameter of pipe - inches Pb = base pressure = psia Tb = base temperature - OR 50

For Pb = 14.73 psia and Tb = 520 R of this report Re = 1.3526 X 10- (15) D The friction factor will be found for a pipe roughness of 250 microinches. Colebrook's relationship, Handbook, p. 302, for evaluating the Moody friction factor in the form used by the AGA becomes F 4 log -+ 2.28 - 4 log + 9.34 D/EE (16) 41o?+ EE2 8 1 K ^ )Re Drag Factor (Ff) This factor is taken from Figure 13 corresponding to 200 degrees of bends per mile for plastic lined pipe and becomes 0.936. Work of Compression In obtaining the work of compression, one solves the basic flow equation which for horizontal flow and neglecting kinetic energy changes become2 (p.315, Equation (7-66)) 2 A = VdP (17) P1 where A = work of compression V =volume P = pressure During compression, the temperature rises and the relationship between volume and pressure is dependent upon the thermodynamic properties of the fluid, the heat transferred from the fluid during compression, and the flow inefficiencies which occur in the compressor. It has been customary to employ the ideal gas relationship for adiabatic and reversible compression in finding the relationship Where EE = pipe roughness, inches 31

HIGH VERY FYTREMELY EXTREMELY LOW VERY LOW LOW LOW AVG AVG AVG HIGH HIGH 141GH 0.9850 0.9800 _ _ 0.9750 0.9700 0.9500 \ 0.9400 0.9300 0.92000.9100'.... 0.9000 I I I 5 10 20 40 60 80 100 150 200 300 BEND INDEX, DEGREES/MILE Fig. IV-1.-DRAG FACTOR AS A FUNCTION OF PIPE TYPE AND BEND INDEX (For typical lines constructed of 40-foot pipe joints welded in the field, and involving a valve setting approximately every 10 miles) Fig. 13. Reproduced from Reference 1, Uhl et al. 32

between V and P, namely PVk = P1 = constant (18) where k = ratio of specific heats, Cp/Cv. When using this relationship between P and V and still retaining the units of ft. lbs./lb. for A, one obtains k - 1 k 53.241 Tf P[ k A k-l _ L = _ -G 1 G(19) G = gas gravity, molecular weight/29.0 Tf = inlet temperature, OR Subscript 1 refers to the outlet pressure of the compressor or maximum pressure in the pipeline. Subscript 2 refers to the inlet pressure to the compressor or minimum pressure in the pipeline. Retaining the ideal gas relationship but converting units of A to horsepower per million cubic feet of Gas (14.73 psia and 60~F) per day, one obtains k - 1 kT /P 1 A = 0.088 k 1 - 1 (20) The question arises as to the most suitable method of converting this formula based on ideal gases to one which will handle actual gases, knowing that the deviation from ideal gases can be of a considerable magnitude. Also, at what temperature should the value of k be evaluated? One way to evaluate the work is to invoke a parallel equation for work of compression based on en'i:]py increase during adiabatic reversible compression. Equation (7-79), p. 316 of Reference 2 with units of A given above shows the equation to be 33

A = 0.0432 AH (21) where AH is increase in enthalpy during pressure rise along a constant entropy line. Enthalpy - Entropy diagrams have been prepared for natural gases at various gas gravities, such as 0.6, 0.7, 0.8, 09, and 1.0, By use of such charts and selected conditions, one can obtain the work of compression. Three methods for correcting the deviation of the gas from ideal conditions have been used in modifying Equation (20)o None of these equations are exact; they are expected to find the same result as integrating the VdP term with the actual volume used at each P. This would require multiplying each ideal volume by the Z which corresponds not only to the pressure involved but to the temperature to which the gas has risen at each increment of pressure rise. The three versions are k - 1 A /\ 0854] /TfZ2 L - 14.73 1 EFF P1 YTI. A o.o8 ( l) EF (P 12 14765 (22) 14o73 where 16L-is a conversion of the constant to correspond to 14.73 as P Z2 = compressibility factor corresponding to inlet conditions. EFF = compressor efficiency, taken as 0.80 for centrifugal compressors. P, P1 = compression ratio. 2 Tf = inlet gas temperature, ~R. k = ratio of specific heat at constant pressure to that at constant volume. This equation was recommended.by the Natural Gas Pipeline Company of Americao 54

(k - 1) /kN _T P1 1 14.73 k A2 0.0853 (k-) EFF 1JP (23) 2 The equation is from the Handbook, p. 316. k - 1 44./64 i \ f 1 2 A (T (2k L -1 (24) 3 EFF 520 (k - 2 2 _ ) This equation was supplied by the Columbia Gas System Service Corporation. From this study, see Table 4, it was agreed to use Equation (22) for computing the work of compression. The equation uses the compressibility factor at the entrance to the compressors as a direct factor on the ideal gas quantity. Economics of Single Phase Pipeline Flow for Mixtures of Natural Gas and Liquid Hydrocarbons The purpose of this study is to devise a method of calculation for predicting the conditions at which natural gas and liquid hydrocarbons may be combined as a single phase system and transported economically in pipelines. It is known that the light hydrocarbons can be maintained in single phase with natural gases under specified temperatures and pressures. The ability to carry such light hydrocarbons over long distances along with natural gas may become economical if pressures higher than those normally used in pipelines are available. The use of higher strength steels would be advantageous in this connection. This survey proposes to set up a master economic program of pipeline flow in which the prime variables are investigated systematically to find the minimum cost of transportation. During the course of the study, three programs have been written for the economic calculations. At the time the first 35

4-o 05 P \O OcO Y- O J C- m mtZ KO00 0 L \ — KY O LLn L L Ln L\ LF LL U cQ 0 -q C*0 0 0 (n-:-o0 m O n n -4- O Ln o QD ); Pi o LO - - nQ0 _:- n m U T O Ln Ln n Ln Ln Ln Ln n *H 0 N C\ coO L0 Ocn O\CO O 0 Qc + cJ o.0 o C G\j C LCn < r —HHCQJ H H H H H ~ N r ~'"~ —~.r' U2 C O O O -P -P (a 0~ ~I O U )) N- -! O ~ L-! CH 0~ LCLC~L CJO r00 * O 4 0 H 1-( 0 N., - 00I o 0 0.4 C CD HH HH Om 4o C J o LO q oO c Va 4-~' N ~Q 0, o V 00 0 0 O\ O c0 4 [ VH FI *.- 0.... r Ca oq.. \ n co ~ 1 c C 1,~ 40 ri ~-' r"-i r" — r- -' r -I r O O N Nb U) 0 ~- O H O -^ -4 ^ -r-! 40 O 0n o -:Lco 9 C0 4 0 O c -....... co0 Lco Co LcO 0 00 c - E -H! r'- r- -- r-H H-H P r/2 H 0 n C OCO tr C C-r i -|r N 0 Cii 4& 0 LC\ 4HCO U H0 *r] - C- Q 4 00O H CY) L00G\ ciiA^~~~r- r- r- r- r4O O t- 0 N N L - 0- 4 V z O*~ - - * 0-o CYo *L L-O- 00 O0 LCL cii llm II C II II CI O o KO-i -! O CO,O o- O o CO 3 ~ ~ ~ ~ 3~ ~ ~ ~ 3' O O H > 0 11 0 L1 1 LCLC 0 H c- L' o L - C1 o CMoJ - ~ F,...O ~ *O * * O L* * o U H E', H H H ~r- ~HH ~ co~ CO C~ 0 90 D -P o n Ln In LAo\ Ln Ln L Ln UL U) HIN C~4 LQ U) cC<4 Lf u2 C~4 LC\ H 36

progress report was written, the calculations were directed toward finding the size of pipe and number of compression stations to give the minimum cost for a fixed flow rate, composition and strength of pipe. It included a Lagrangian method of undetermined multiplier to predict the compression ratio for the minimum cost before proceeding to calculate the minimum cost. The maximum pressure in the pipeline was fixed. The second method fixed the composition, pipe strength, diameter of the pipe, and maximum pressure in the pipeline as 1.65 times the minimum permissible pressure for the composition. The third method —which is the one used in reporting the results herein —fixes Composition Minimum pipeline pressure Strength of steel Pipe diameter For a series of flow rates, the cost of transporting gas is found for an increasing number of compression stations (decreasing compression ratio) until the cheapest cost is found for that flow rate. The flow rate is increased in increments, and the procedure is repeated until the cost increases over the previous minimum. Calculations are made for 16, 24- and 30 inch OD pipelines. The economic computer program has been devised to compute the cost of transporting a thousand cubic feet (Mcf) of natural gas 100 miles when using a pipeline 1000 miles long. The cost includes both amortization of the investment and operating expenses. The basic calculations made fix the following items: a. Composition b Strength of steel c. Pipe diameter d. Flow rate 57

e. Number of compressor stations f. Minimum pressure or inlet pressure to compressors (P2). For a given case, the pressure drop between stations is computed by Equation (12), and then the horsepower is computed by Equation (22). For this particular case, the cost of transportation can be foundo The pipeline investment is obtained by finding the tons of steel and laying cost. The pipe wall thickness is calculated by Equation (Al) using the maximum pressure calculated in connection with pipeline flow. From the wall thickness, diameter, and cost per ton of steel, the pipeline and communication system investment is computed (IINVL). 107 IINVL = (YW + N X OD + H) QB (25) Y = $/ton of steel W = tons of steel per mile (see Appendix A) N = cost of laying pipe, $/mile/in. OD = $1200 OD = outside diameter of pipe in inches H = cost of communication system, $/mile = $3000 QB = cubic feet of gas flowing per day IINVL = cents/100 miles/Mcf/day. The station investment (IINVS) is obtained from X110 A IINVS = Lx + A l Q 10L (26) IINVS = cents/100 miles/Mcf/day X1 = fixed station cost = $270,000 X = cost per horsepower = $165 A = horsepower per station per million cubic feet per day Lt NOS = number of stations for 1000 mile line, Lt = total length of pipeline, miles (used as 1000) L = length of line between stations, miles QB = flow rate in cubic feet per day. 38

The transportation charge due to investment is taken as 155 per year. Therefore the cost of transportation due to investment when flowing gas 365 days per year becomes CMMAM = L IINV I I (27) CMMAM = transportation charge or cost due to investment in cents/100 miles/Mcf transported. The operating charges are computed as follows by adding the fuel cost, compressor operating charge, the gas loss, the line maintenance, and the administration expense: CMMOP =;JiSPHR) 24 X 365 X CF + CLMS 10 A FOO L 365 f ~~ ~~3 6\~ ^~(28) + LG X GASCST X LT + A1 (0 LT QB x 3650 CMMOP = transportation cost for operations in cents/100 miles /Mcf FHPHR = Mcf per horsepower - hour = 8.7 X 10-3 A = horsepower per station per million cubic feet per day QB = flow rate of gas, cubic feet per day CF = fuel cost for compressors, $0.20/Mcf CLMS = maintenance charge of stations, $/hp/yr = $19 FOOP = fraction of time in operation = 1.0 1000 NOS = number of stations, used as GASCST = charge for gas lost, $/Mcf, used as $0o20 = CF LG = gas loss in passing through line, fraction, used as 00005 LT = total length of line = 1000 miles CLML = labor and maintenance cost for line, $/mile/yr, used as $850 AD = administration expenses, $/mile/yr/MMcf/day. The total cost of transportation then becomes the cost due to investment plus that due to operations. CY = CMMAM + CMMOP (29) CY = cents/100 miles/Mcf. * After all calculations had been made, it was found that the correct expression should have been AD/36.5. 39

TABLE 5 Economic and Other Factors Used in Study Length of line (Lt) 1000 miles Flowing temperature (T ) 60~F Pipe strength (S) 65,000 psi and 100,000 psi Pipe diameter OD) 16 inch, 24 inch and 30 inch (OD) Pipe roughness EE = 250 micro-inches Bend Index 200~ per mile Longitudinal joint factor for pipe (E) 1.0 Pipe design factor (F) 0.72 Compressor efficiency, EFF, 80% Pipe cost (Y) 65,000 psi strength, $265 per ton 100,000 psi strength, $384 per ton Cost of laying pipe (N) $1200 per inch OD per mile Communication system cost (H) $3000 per mile Compression station cost (X1 + X) $270,000 + $165 per horsepower Cost of fuel (CF) 20 cents/Mcf Fuel consumption (FHPHR) &8.7 x 10-3 Mcf per horsepower - hour Cost of labor and maintenance for pipeline (CLML) $850/mile/yr Cost of labor and maintenance for compressor stations (CLMS) $19/hp/yr Gas loss (LG) =0.0 5 fraction of flow at 20 cents/Mcf Administration expenses (AD) 1 cents/100 miles/Mcf 3650 Annual investment charge, 15% per year Line assumed to flow at 100% capacity 365 days/yr 40

Calculation of Transportation Costs With the computer program given in Appendix B, the costs of transporting the 10 mixtures given in Table 1 were computed as shown by example in Appendix C. For each mixture, the minimum single phase pressure was determined as listed in Table 1. To this pressure, 100 psi was added to find the minimum pipeline pressure. Calculations were made for this minimum pipeline pressure and for a pressure 400 psi higher. The variables used in addition to pressure when surveying the cost of transporting the various mixtures were Pipe strength Pipe diameter Number of stations in 1000 miles Flow rate. For each composition, strength of steel, minimum pressure, and pipe diameter, a series of calculations are made with increasing number of stations at each of a series of flow rates. As shown on Figure 14, for a fixed composition, strength of steel, pipe diameter, and minimum pipeline pressure, the cost is found at each of a series of flow rates for an increasing number of compression stations until the cost goes through a minimum value. Figure 14 is for the 80% natural gas-20% propane mixture. The starting minimum number or compressor stations is set by including it as data in the computer program, and the costs are calculated for it and the next larger number of stations in sequence until the cost rises. At this point, the flow is incremented, and the procedure is repeated as long as the minimum cost decreases for the new flow rate. The minimum cost at each flow rate of Figure 14 is plotted versus flow rate on Figure 15. All three pipe sizes are included on this one plot. As would be expected, the larger pipe sizes give lower costs of transportation. Figure 15 for the 80 natural 41

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gas-20% propane with 100,000 psi steel is included in the report. The remainder of these plots is included as Appendix E. The original calculations for the 65,000 psi steel cases were based on $228 per ton rather than the $265 agreed upon as the proper cost. Rather than redoing the entire calculations, a program was written to compute only the new cost based on the horsepower per million cubic feet, pipe thickness, number of stations, and flow rate already determined. These computations were made for the 65,000 psi cases using five different number of stations adjacent to the minimum point previously found. The 100,000 psi steel cases were run correctly as shown in the example print-out in Appendix B. The minimum cost for each case is listed on Table 6, 66 values for the 65,000 psi steel and 45 values for the 100,000 psi steel since only 7 compositions were run in the latter case. These costs for transporting various streams composed of natural gas and condensates are used to predict the cost of transporting the liquid portion of the gas stream. The strength of the steel is a variable in the computer program, but only the 65,000 psi steel at $265 per ton and the 100,000 psi steel at $384 per ton were investigatedo At these prices, the lines designed to use 100,000 psi steel gave cheaper transportation costs than the 65,000 psi steel. The flow rate is a key variable in determining the cost of transporting the mixtures. Figure 16 is a plot of cost of transportation versus flow rate, with an identification of the pipe diameter and minimum pipeline pressure all for the 100,000 psi steel. The relationship is much as one would expect, a decreasing cost with higher flow rate, The effect of pressure on the cost of transportation is indicated on.Figures 17 and 18; the flow rate is identified for each point, all for the 100,000 psi steel. It is difficult to separate flow rate and pressure, but it appears that the cost of transportation decreases with pressure up to about 2500-3000 44

c^ cn Q0 rN n c O'O — O C G^- - L H L Lr * e o0 oJ 4 o- 4 4 L( 0 i * * ** *.. *. * * * 0'oS -- O CU L o 0 0> H qn 4 0j 2 0000 00 00 00 0 000 00 00 0000! ~rn OODOO 00 OO 44 0 0 00 COGO O0 KO O O OO i. ue d O O O O O O ~D D -.d —d O O O O (I cO O O ~.O D 2~ O.H L —Hl Lr -- LH O" LO\> K O 0O C XC- COCkJ 04 O O0 CQ: o o. o oooo o oo oo o ooo o o oo o0o o o * u~ CQd r — r OJF rL- r' r~ O O' OJ rlCOJOJ OO OJL 0O% C OJrO: 0( v- 0000 00 00 00 0 0 00 00000 00 1cQ-pOC) 00000000000 00000000000 O H cd S t O C L\j COO > n L LnLn C n n n n Lr Heq LC & n P) x pq P= \H rHH HH H H HH HH HH HH r HH 0 rU o u LnLn =- Io K-eC CI CO LO >O Lf 3 O- HrO LOn h > — KO D (D o Q V2 _- oo CCO Ln n -- o O c, Cv CC O 0 0 c n O n- CO Cn = ~AH 0U * CnC- rq't C O O O t' — L CO t OcO -CO-O 0O CO O o D c -.................. mP-4 H *2H H H V2 Hl Cl-;: -0CO 0O0 0)k-) - H 0 m rO Ceq 01 KOKO L- HcO C *H O0 \O L> 4>- e K-KO,- 4 4(00 4t - 4- 1 H CO n 0 E rO!: (0C H* OOO O0 O C 0 O 0CO COCO COC O O 0 0O a) ^C0H4H rH rH ~ H H a,) mr O a ~R H (D] 0 4-4( rP S V OV \ _____-__ - *r 0 U2 0000 00 00 00 0 00000000000 rH 0 0 -P C0-C 00000000000 00000000000 V,-i20OC 00 O 0 0 0 0 OO 0 O 0O 00 O 0 O H 0 H 0 LnC) O --' LO O h O "O CO Oh'O COO O O —CO O rO Or- r-lri r- O lbO V k 4 P P \ rH H HHH lHH HH 0*H 0! I < -.H 0( C i 0 CO- C\j 0 LCCO -4 L- 1 t- 0 OCO KO q 2 *H'D OC OO >\Ir- C -O O 0 00>r H e.Oc COO 0 C COO C OO O *r- t *- 4.H CQ * oC L\K 4 LC-L- C Lf\n Ln Ln O 4L-A Ln n - K o- L-CO i-CO S:20 H1 P-HE2 c o,,. C\ ci cr 03 <.-I O! o0 0..H..................... v 20200 HHH HH H HSH H H ID * ~ —~ —~DCnx b —~ o-cO ot- oH o'- Lt- C - t- o o o oo Co - n 0 0 Is Z ~Ho oa c. c o m H 0 m *QG OO OO 00 OO O O44 0 0 O OG O O 0 COO eOO mO.0-4 H H 0 H~ i HH HHH 01 H H1 0o 1 1 ~oe 00 O0 0Q r00 0H1 0000 00 00 0 0> 0 0 00 00 00H 0 00 0>l GOO LCr eOq O 0L1P 00> eqo0 0O L O LLP\O O OL4LL " AH*,.' ~- 0- PK O o > m —-- -010 Leq. eq 1 eO e Lq 0Cq Cq = fthz CQ r - r"-''ro —, - r-i O o-,, o,- o —t- -. -,c - --- L( -0- la LO L~ ) Q. HO mO LuC OC i CiD O O O C O 4 O O nOO O CO UnOcO0 C. h co - - OL co G.! C o. Lc oo 0J O n o 2 j~.4...... * * *........... * o o-r o u Q 0 r-i P ( EA! 2 o - - -p O ^ ^ CD (D (D * r C))( m ff r 00\r (Y 00 Co C\0 tC 0 (D ( O o 0LC -C0 2C) n-7 4 U2. C G. ( a ^ r-l OQ O O ft:a o 3 4- P Hd 01 eqn Ln L %L H H C, 45

00) 0 [^- 00 -4- C rH 0h 0 C\J 0 [-H 4 OL r r-~H 0M 0M r0j 0 C\J 0 U) 000 00 00 0 0 00 00 00 - cd O r-OO OO-H K\b K 0 00 0 O O b O 00 1*r- C]U) rH rL CM i-l r1 rn ri CJ rI CH 01 CHrO 0K C0K -4Q4 D 0 D C- > 000 00 00 0 0 00 00 00 40 P 0- co 000 00 00 0 0 00 00 00 O(H r0-i CO 0 cM-14- _L-O -4K 4 — 4 b L -Kn Kb n LC E F p S irH r- H l rH r- r- r rH r r o! r- HL-O 4Kb 00 rH — 0 -0 0 0 KO 0 o) cO L —- - O OOb 0 K0 -4-H rH-CO ONCO = -.r- u j o'-. 01 K C — -K - - b -- K bO LKbn o 0 H-A F-A (D. ro P-i E-A ~ *H ) rH (\J 0 KbbCJ H4r-l COO 0 00 r-H1O 0 r0D ~ ~............... 4 ) 42 ) -p 4 ( 2 O O -I) c -- ~. ~ %o r; o / c:SOO 0 O c/ 000 00 0 0 0 0 00 00 00 *U) CT 0Kb0 0 0 Kbb 0 0 Kb b Kbb K cn U) 0 (2Hr-I H-ib - H n Kb-r 0LcoCr Q0 Kb'I'KbO DKO ro 0 r-I c) r-0I H C r- L r- r- OJ r- C C\JO CJOO Hrl 0 2 P-I -4 c0 q-A 0 -I ) 000 00 00 0 0 00 00 00 F ~ 0 0 -POC 000 0 00 0 0 0 0 00 00 Hl O HCot Kb bOOO 4 O OK O O OOH Hb ~- r H D d E,,g r co Oh -'- 0O 0 0 0H H r-H H- HHi:O: -P FM P' H r — i- l r-i r-h r-. *H0 0D ( c I PQ -H r-I cS X r-i- cHL- O CN O c\j c0 01 o -O - o -4 c\j Kb0 -iH.H r-1(O U) KOb O KOoLn (MN CK 0 -Ln 0K OCN 005 o H -, U) c \J C-1K rH-i Co oo oC -.b K - 4 Lb n nLbn ~ (D -r-O C,. 0............... U)J O Q= e-E-I(2:rE l, 0 *r -4 F-i ( U)C ( (D M D 4- r-' c HO-O-N K Cb O CJco N — ON OONr- ONO C O' N0 0 0.4-3 4>=c........... 0 c U OQO HrdH H- H 4- o o (D U) 0 _ _ 0 r — ~ d 00 00 0 0 0 0 00 00 00 o- o- o d 0001 O 0 *c 0 0c00 0 0 0 0 K 0 0 O0 00 KbO po ( ( d H "00 LH O UbH LLn nO 0 0 L LO n LO ~ E1 I *,r-i-dU HH0 - MH HH H 0 ('M rb _- 0 - M (M bO (o cn c0 N o Cn aO LaC\'CY C0\ c\ tC o N - o1-H;. C < o............... 0 ( ~rl I a~~, - 0i. ONOKO 01OK K Kb ON kONC -.0O -0' ^CQ^.H Ur-) rlr-I r-r- r-i r-H0 r —K r-HHH r-01-0 K~ 0(D 4 co 0 4C 0.. 011 Kb 01 01 0 13 0

1.8 2.0 I I i I I I I I I I I I I I I I I I I I I I I I I I I 1 Parameter- psia min:100,000 psi Steel o 16" Pipe 1.8 Q::::I:I I:I:I:I:II:I I:I T IT IIIIIIII: 11_ x 24" Pipe * 30" Pipe 1.4 1.4 1. 1,i U ll I T t I l 1.4 0 I. -e[:c' 0;2 t 4 __________Flow Rate Milli1on Cu.ft/day 20 ____FiT I6 ~___ I Eft- oI nIFow ate o Cost11 _ I.8 I _ _ ___ _ _ I _J_ _ _ __ _ I I I I -I 1 1 I I I I I I I I I I I I I I I I I Ii,-t — I I-t- - lS h - — l,w _ _ _ _ _ _ T _ _ _ _ _ r r ij li^ - X;1 1 1 1 1 1 1 1 1 1 1 1'_ _l! 1r'..',l _I_____1 _I- _ __i___l l I I llJ~ J I I I I I I I I Il I I I I!1 1 Figure 16. Effect of Flow Rate on Cost

2.0 I LA I I I. I I I I 1:1 1 1 16" Pipe 100,000 psia steel Poaraeter: Flow Rate 1.8 I _ _ _ _ _ _ _ _ II I" I__ __ 1 1 _i _ _ _ _ _.,th l M i llion Cu.ft./day 1.6 1.4 0 450 0.I I I 1 I I 1 1 1 1 1 1 r LLlIrIT- II I T._ -----— _ _ ___ 0 i _E___E EE EEE E I I I________ II_____1 _ I 1 2111 L 1111111111_IEEIIE1EEE E 8 l l _ _ _ _ ll ^l l Ill II_._ I _ __ II I::::: _______IIIIII_______100,000 psi steel ~ 1 1.4 Parameter: Flow Rate ~~~~~~0 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~I Li100 CFigure 17. Ef::::::::ect o:: Pressure on Cu.ost o Transportation 1 +_-]48-I'0 IOIOO_ 2000 00::3OOOI I ___ __ I__ 1 _1 Fiue ". Effect+11 ofxim-u Pressure oCstTa-orao

I...... I I..I I _., -p I - - _- - - - -I _ _ -... _ _ _ - _ - _ _ _ - _ _ _ _' t l'2 _ _ _ _ _ _ _ _ _ _ O1LE C: E rq T 1 1 r ^ ^^ ~-t- 4 I 0i1 i-! I I1- 4,,- e — n 0 0) co r- o ~ L I I I i I I: I:I I 1 1 1:1 1 - - —::I::I I I I 1 Ie I X j \ I j > t > I I j~) "a " D.:I It l I I I I I I I l I I -T l T l U I I 1 11 1 h I I I 1111 I tl1 - 1 i I I I I I I I I I I I I ~ 1 1 1 1 I I I 1: -: --- 1 1 TI- TTTTIl-:::: IT-:- 0- <H W Tl I TI:lTITI -TI: 9111111 c- s. H EZ EI II E Z EEEE......... CCO - - - I 4 - -- I I I T I 0 1EEE EE I r rZO Ir E _ rEE Zl r s 1 r Io lI S - + — )AJ /SI!IW 001 / SIUa8 -so3 UO!ioDJOdSUDJj 49

psiao It should be noted that the maximum pipeline pressure is plotted on these figures. The maximum pressure was found by multiplying the minimum pressures in Table 6 by the compression ratio listed on Figure 15o A similar plot using minimum pressures for the 65,000 psi steel with the incorrect cost of steel as distributed in the progress report gave a similar impression. The effect of molecular weight on cost is given on Figures 19 and 20. Again, it is difficult to be sure the effect of flow rate is not obscuring the independent effect of molecular weight. Generally, increases in molecular weight are accompanied by a decrease in cost. That is, the addition of propane or butane gives a lower overall cost of transportation per unit of fluido The higher molecular weights represented by the Kurata mixtures give rising costs, but they could be influenced by the unusually high operating pressure needed to keep the mixtures in single phase. Effect of Temperature These calculations have all been made at 60~Fo The nature of the compressibility factors is such that there would be less effect on the density by adding higher molecular weight hydrocarbons at higher temperatures and greater effect on density at lower temperatures. Thus, the effect of increased pipeline capacity observed in winter when the temperatures are lower would be accentuated for gases carrying condensates. Cost of Hauling Liquids The objective is to find the cost of transporting the liquid constituent. To do this, it appears logical to set some cost for transporting the gas alone. Then it is necessary to set some total flow rate and divide the composition into the gas portion and the liquid portiono By knowing the transportation cost of the mixture and that of the gas alone, one can find the cost of transporting the liquido One method of proceeding is to use a standard cost for transporting gaso The value of lo. cents/Mcf/100 miles or 50

2.0 I-0 " " "srTO E 1n: I" " > 33a^ IF IF, I I I I ^1 I I I I I I I.. 16" Pipeline 65,000 psi Steel Parameter, Minimum Pressure 1.8 _ Flow Rate Million Cu. ft./day 1.6 ___ _ _ _ - ___ _ 3 _ E _ E EEEEEEEEEE E iE EE^? 450 I.I 0 1.2 U W rr 1.4.~ -;^^;;:z^:;^;;;;;;^^^^;;;^^;;;;: 24" Pipeline c _ ___ E [ _ r r |!f - X! | X 1 | 65,000 psi Steel o^:-::::::i::::i:::::::::::^::::::i::i::: Parameters' Min. Press. psia, o1.4''' lT;~I:;~~:-:: —Flow Rate Million Cu.ft./day. _ —-------- _ _ I I I L__ 11 T___L_____ T1 Ll ________r _rTIIIrr — T L T I I FL 10 2 - of Transportation (65,000 psi steel).l0 1-: e tth -I I,51. S I P M P.~~~~1 20 22 4 2I 28 I T50 r SLIL IIL ni>ieilLI. ^_ __ __ 7 1 r I TMorleculav pr WIgh11T1r777TT11117ITII177 1

2.0 r' 0 I I T - T _ J I I _I I I I I I......-___ 1 11-I - -r16" Pipeline JEEE'1 E IE _.....: —EE_-:_-EE- Ir TT I L_100,000 psi steel 1.8 9- z-~:-_:-1 1:: 4-~ —-- _ Parameters: Min. Press, psia, 1.4 C o 1.2=6: 22. T, f i; I I r _ _ n I I I I I _Mlcua I I I r I 1 i I l-n I I I ght I I'F I A Figurel- 20. - " I I _ o _M o u r I Io!C 0.I 16 48 20 22 24; 26 M of Transportation (l00,000 pi iste 52 ~-E, IEEEEEEEEE —EEEEEElEEEEEiE oeEEEEEEEEEEEEEEEE''EIEEi —'EEEFlowERateE MillE 0 "1 82 2 42 83 - Y 1 IL~ __Ji I, -,."~-, Molec.;!lar WightL U~ ~ ~ Fgr I 0 Efec of MoeIa Weigh on Cost~ iof Trnpraio (0,00 ps lil steel) J]! II;I I -r' C i I 1!r~ 3 I I', II II II'I _____5L_

11 cents/Mcf/100 miles is used as the best value at 500-600 million cu. ft./day and is the minimum value considered. At a flow rate of 900 million cu. ft./day, the cost of transporting gas is down to 0.95 cents/Mcf/100 miles. Table 7 gives two example calculations of the cost of hauling liquids. The propane cost of 13.4 cents per barrel per 1000 miles for Case I is considerably below that of Colonial Pipeline Company tariff for products shown in Table 8, but of course there is some cost of separating the liquids from the gas at terminal. Case II is for condensate where the mixture costs more to haul than does natural gas because a 16" line is used. Here, the condensate is still cheaper than product pipeline tariffs. In examining Tables 6A and 6B, one can find for 24" or 30" diameter pipelines several cases where the flow rates are the same for gas and for specific mixtures. Taking such pairs of conditions, the cost of hauling liquids is computed for several mixtures on Table 9. These calculations show very favorable rates for transporting liquids when extremely large quantities are involved. These results are ample justification for further pursuit of these concepts for hauling liquids, including investigation of separation costs. Conclusions 1. The addition of the light hydrocarbons propane, butane, and condensates to natural gas flowing in pipelines increases the total flow capacity of the line and reduces the cost of transportationo 2. The pressures required to keep these liquids in single phase are above present pipeline pressures, but not high enough to increase the cost of transporting the gas mixtures. 3. The cost of hauling liquids, dissolved in natural gas without consideration of separation costs, is some 35-50~ of the tariffs posted by the Colonial Pipeline Company for liquid products 53

4. A slight advantage was found for using 100,000 psi steel at $384 per ton over 65,000 psi steel at $265 per ton. 5. Operating pressures up to some 2500 psi in pipelines appear to decrease the cost of transporting single phase natural gas liquid mixtures. 6. This study should be a sufficient basis for further consideration of transporting liquid along with natural gas, whenever large quantities of liquid need to be transported over long distances. DLK 7-23-65

TABLE 7 Calculation of Cost of Transporting Liquids in Gas Pipeline for 1000 Miles Case I 20o Propane-80 Natural Gas 65,000 psi steel 24 inch pipe Minimum pressure 1960 psia Flow rate 900 million cu. ft./day (131,000 bbls/day propane) Cost of transportation = 0.938 cents/100 miles/Mcf Using a cost for natural gas of 0.95 cents/100 miles/Mcf (9-5 cents/1000 miles) and dividing stream into 0.7816 x 900,000 = 704,000 Mcf of gas and 131,000 bbls (0.2184 x 93~5'X'420) of propane. 10 Cost per day for 900 million at 0.938 x 100 = $84,500 10 Cost per day for 704,000 Mcf at 0.95 x 10 = 66,900 $17,600 In this case the propane is hauled 1000 miles for 17,600 x 100 17.3100xoo0 = 13.4 cents/bbl. 131,000 Case II Kurata S-4 Gas Condensate 100,000 psi steel Cost of hauling 1.26 cents/Mcf/100 miles Flow rate 450 million cu. ft./day 16 inch pipe Minimum pressure 2630 psia 84,300 bbls condensate/day 352 million cubic feet of natural gas Cost of hauling mixture 1000 miles 450,000 X 1.26 x 1- = $561700 Cost of hauling natural gas 352,000 X 1.1 X 1 = 38,700 100 $18.ooo $18,00018 100 The cost of hauling the condensate is 18,000 x 10 84,300 - 21.4 cents/bbls/1000 miles. 55

TABLE 8 Published Tariff for Product Transportation by Colonial Pipeline Company Entrance Exit from Estimated Cost Cents to Pipeline Miles cents /bbl Pipeline /bbl 1000 miles Beaumont Philadelphia (Pa.) 1380 31.75 23.0 (Texas) Lake Charles Philadelphia (Pa.) 1320 31.25 23.7 (Louisiana) Pasadena Philadelphia (Pa.) 1450 33-50 23.01 (Texas) Beaumont Chattanooga 860 24.65 28.7 (Texas) (Hamilton County) Beaumont Knoxville (Tenn.) 960 25.75 26.8 (Texas) Beaumont Nashville-Davidson 990 26.05 26.3 (Texas) (Davidson County) 56

r -4 Ira r-l HQ OH OD 0 0 00 cOc KG t- GD U2 0 S- H 0 4 t Ch4P0 r-H H H H > O O -* P > 0 CO -4 KG 4 G H r CO Q1 CO Od...... *H o r 4 4 L ri r H H 0o -\ H H H H 1 H H O O 0 00 n H LcL cco 0.. o.;. coco 0 o 0OH o(\ oJ J r \0J U O L O CY) C o CY) O C 4 — 0 -00 H QO..... C H L-0 CO K 4 r 0C2 *DO0 0 0 C C CO 0 4 H 4 O 0 ~ r O 1 (D 1 -P a KG 4 0 E o r-P O L00 c O -P V C P H O n ) v2 C C.H Gm bO CCI Cl KG r 2 KG 0 C LC G9 0 o 00 02 0 zx *H Cld vQ H.H Q Vd -~ ~ o ed O O O Uo o o o 1-1 r1 r Q: b O o U2(D<GINs 0 0~ 0 0 Co 0 0 0 0 c~ 0 o0. 0. H 0= > 4 CO r4 o Cl C *d r-I r H P KG HV o o CQ 00^ -n- -d- --- -- o z o C0 o0 CoJ CO M cn r 4 c0 0 rH 0c\ rH o c 0 a 0 )r-H r- r-H 2 0 0 0 0 0 00 00 00 0 0 *Cl U2 40 0O 0 K O 0K KG K cn O *H VAnH A(H Co G H H n Ln C KG KG rI gj co H C HC H CCM H H H H C C 0 *r-I cCS (CS 0 CCS CTS (D*r-i -i ~C OO CO O C0 0 M dH Oh ~ O cO O OU CU cO Q O0 0 0 00 0 O O I 0O.H CM- O1 r-U H CML C2 CU) o ~ ~ ~C IO O C O O 0 0 0 ~ I 0 0 U 57

BIBLIOGRAPHY 1. Uhl, A. E., "Computation of Flow in Natural Gas Transmission Lines", Pipeline Research Committee, American Gas Association (1964)o 2. Katz, D. L. et al, Handbook of Natural Gas Engineering, McGrawHill (1959). 3. Katz, Do Lo and Fred Kurata, "Retrograde Condensation", Ind. Engo Chem,, 32, p. 817 (1940). 4. Kurata, Fred, "Critical Properties of Volatile Hydrocarbon Mixtures", Ph.D. Thesis (April 1941). 5. Bloomer, 0. To, Gami, D. C. and Jo D. Parent, "Physical Chemical Properties of Methane-Ethane Mixtures", Inst. Gas Technolo Research Bull., 22 (1953). 60 Reamer, H. Ho, Sage, B. H. and W. N. Lacey, "Volumetric and Phase Behavior of the Methane-Propane System", Ind. Eng. Chem., 42, p. 534 (1950). 7. Sage, B. Ho, Budenholzer, R. A. and W. No Lacey, "Phase Equilibria in Hydrocarbon Systems - Methane-n-Butane System in Gaseous and Liquid Regions"', Ind Eng. Chem,, 32, pgs. 1085 and 1262 (1940). 8. Olds, R. Ho, Sage, B. H. and W. N. Lacey, "Methane-Isobutane System", Ind Eng. Chem., 34, p 1008 (1942). 9, Sage, B. H., Reamer, H. H., Olds, R. H. and W. No Lacey, "Volumetric and Phase Behavior of Methane-n-Pentane System", Ind. Eng. Chem., 34., p. 1108 (1942) 10. Carter, R. T., Sage, B. H. and W. N. Lacey, "Phase Behavior in the Methane-Propane-Pentane System", Trans. A.Io MoE, 142, p. 170 (1941). 11. Dourson, R. H., Sage, B. H. and W. N. Lacey, "Phase Behavior in the Methane-Propane-Pentane System", Trans. A.IoMoEo, 151, p. 206 (1943). 12. Price, A. Ro, "Low Temperature Vapor-Liquid Equilibrium in Light Hydrocarbon Mixtures: Methane-Ethane-Propane System", PhoDo Thesis, The Rice Institute, Houston, Texas (1957). 13. Nysewander, Co N., Sage, H. B. and W. N. Lacey, "The Propanen-Butane System in the Critical Region", Ind. Eng. Chem., 32, po 118 (1940)o 58

14. Reamer, H. H., Sage, B. H. and W. N. Lacey, "Methane-n-ButaneDecane System", Ind. Eng. Chem., 39, p. 77 (1947). 15. Reamer, H. H., Fiskin, J. M. and B. H. Sage, "Phase Behavior in the Methane-n-Butane-Decane System at 160 F", Ind. Eng. Chem., 41, p. 2871 (1949). 16. Reamer, H. H., Sage, B. H. and W. N. Lacey, "Volumetric and Phase Behavior of the Methane-n-Butane-Decane System", Ind. Eng. Chem., 39, p. 77 (1947); 43, p. 1436 (1941); 44, p. 1671 (19527 17. Sarem, A. M., "Z Factor Equation Developed for Use in Digital Computers", Oil and Gas Journal, p. 118 (September 18, 1961). 18. Bicher, L. B. and D. L. Katz, "Viscosity of the Methane-Propane System", Ind. Eng. Chem., 35, p. 754 (1943). 19. Carr, N. L., Kobayaski, R. and D. B. Burrows, "Viscosity of Hydrocarbon Gases Under Pressure", Trans. A.I.M.E., 201, p. 264 (1954). 20. Carr, N. L., Parent, J. D. and R. E. Peck, "Viscosity of Hydrocarbon Gases Under Pressure" Chem. Engr. Progress Sym. Series 51, 16, p. 91 (1955). 21. Carr. N. L., "Viscosity of Natural Gas Component Mixtures", Inst. Gas Technol. Research Bull., 23 (1953). 22. Smith A. S. and G. G. Brown, "Viscosity of Ethane and Propane", Ind. Eng. Chem., 35, p. 705 (1943). 23. Dolane, J. P., Ellington, R. T. and H. L. Lee, "Viscosity of Methane-Butane Mixtures", Jr. Chem. and Eng. Data (December 1964). 24. Hubbard, R. M. and G. G. Brown, "Viscosity of n-Pentane", Ind. Eng. Chem., 35, p. 1276 (1943). 25. "American Standard Code of Pressure Piping, Gas Transmission, and Distribution Piping Systems", ASA B31.8 (1963), The American Society of Mechanical Engineers (1963). 26. Huntington, R. L., "High Pressure Pipeline Research, Project No. 49", Clark Bros. Co., Ohan, New York (1943). 27. Bell, H. S., Petroleum Transportation Handbook, McGraw-Hill (1963). 59

APPENDIX A FORMULA FOR:COST OF PIPE

The thickness of the pipe can be calculated by the following formula (Eqn. 841.1, ASME code B31.8, 1963)25 (P1)(OD) THK (A-l) (2S)(F)(E) The cost of pipe is given by YW y x 5280 x C(OD2 - (OD-2THK))2 x62.4 x 7.86(A2) 4x144 2000 = 70o8 (oD2 - (OD +4THK2-2(oD)(2THK))(Y) YW = 28.2 THK(OD-THK)(Y) (A-3) Y = Cost of pipe material, $/ton OD = Outside diameter of pipe, in. ID = Inside diameter of pipe, in. P1 = Maximum pressure in pipe, psig Ps = Density of steel 490, lb/ft3 S = Minimum specified yield strength of steel, psi F = Construction type design factor as given in Table 841.11, ASME code B35.8, 1963 (Ref. 25) (taken as 0.72) E = Longitudinal joint factor as given in Table 831.12, ASME code (taken as 1,0) T = Temperature derating factor for project (taken as 1.0) YW = Cost of pipe, $/mile 65

APPENDIX B COMPUTER PROGRAM AND NOMENCLATURE

The computer program written in MAD solves in sequence the flow equation for pressure drop in the pipeline, the horsepower requirement for compression of the gas, and economical equations for obtaining the cost of transportation of the gas. Table B-1 is a print-out of the program as used in the pipeline flow calculations reported herein. It is the third program developed. The program was written to make it as general as possible and not all of the possible cases have been used in the example problem. The hand calculation follows in Appendix C. The nomenclature follows the program. It is believed that a reading of the program along with the nomenclature will provide an understanding of the calculations. Some explanations are given where they are thought to be necessary. The program reads all the data. It stores the information about the composition and initializes all the counters for diameter of the pipe, the strength of steel, minimimum specified flow rate, maximum pressure in the pipeline and the initial number of stations. The diameter of the pipe and the strength of steel are fixed parameters. A provision is made to allow for different initial and final flow rates, and number of stations. The initial flow rate corresponding to the diameter selected is read in as data. The switch (COMPSW) is turned "on" or "off" by making its values 1 or 0. By having it off the program computes the composition of the gas based on addition of propane and butane in barrels/day. If the switch is "on" the program expects the compositions of gas specified as part of the data. The next step is to compute the pseudo critical properties of the mixture and the molecular weight. The program allows for N2, C02, and methane to heptanes in thne mixture. The gas gravity is computed by dividing the molecular weight of the mixture by 29, the molecular weight of the air. From gas gravity the gas gravity factor is computed. The next step is to have the machine know what the minimum pressure in the pipeline is going to be. If this pressure is already known then the value of MMAWT should be set higher than the. molecular weight of the mixtureo As we do not expect any mixture to exceed:-a molecular weight of 40, this number can be safely used. The program also has provisions for computing the minimum pressure as a function of the molecular weight at 40~ or 60~F, In order for the computer to calculate the minimum pressure the value of MMWT should be set less than the expected molecular weight. In case nothing is read in the data for MMWT, it will be taken as zero making it safe automatically. This feature was put in the program when a correlation of minimum pressure with molecular weight was being developed. Whenever the interpolation is required as in the calculation of viscosity, compressibility factor and ratio of specific heats, the program makes use of subroutine TAB. A comment "unsuccessful interpolation" is printed whenever some error in interpolation occurs, The TAB subroutine follows the program. 67

The maximum pressure in the pipeline is computed by adding 100 psia to the minimum pressure (for safety when handling condensate)and multiplying by the assumed compression ratio. The initial value for the starting number of stations is furnished as input data. The length between the compressor stations is computed~ The thickness of the pipe, the inside diameter of the pipe and the line diameter factor are computedo Since both the maximum and the minimum pressure in the pipeline are known the average pressure is computed. From this value the reduced pressure is calc.ul.ated the reduced temperature is computed from the temperature of the line supplied as part of the data. Based on the reduced temperature and pressure the compressibility factor of the single phase fluid is computed by Sarem's17 method. A separate subroutine (ZFAC) has been prepared for this purpose, Appendix F, The compressibility factor calculation by Saremns method is good only when reduced temperature is greater than 1lo. The program has the facility to compute compressibility factors for reduced temperatures less than 1<.1 provided the experimental data is available. In the case of the methane-propane system the data has been obtained from Sage and Lacey The data are stored as a two-dimensional array. Multiple interpolation with the help of subroutine TAB has been used to obtain Z values at any reduced temperature and pressureo At any stage if there is any difficulty in obtaining interpolation a comment is printed out indicating that effect. At the same time based on molecular weight and the reduced temperature and pressure the viscosity of the mixture is comp'uted by the method of Bicher and Katzo8 The points on the curves of the viscosity correlation are supplied as part of the data in this program and interpolation techniques are used (see Appendix G) In order to compute the transmission factor (Ft) the value for the Moody friction factor must be known. The Moody friction factor chart is well satisfied by Colebrook's relationship2 as given by EqO (16) both in the fully turbulent region and. in the transition zoneo If the value for FTB is set as I, it indicates fully turbulent region, and if the value is zero it is taken as the transition regiono In most of our calculations we are in the transition region. Therefore, the value of FTB has been set as zero. The Moody friction factor requires a trial. and error calculation and therefore it has beer. prepared as an external function and named FNGFRIo This external function computes the value of transmission factor (= 2//FM) directly. Since the gas gravity factor, temperature flowing factors supercompressibility factor5 transmission factor, drag factor (read from Figo 13 and, fed as part of the data), flow efficiency factor (known by experience) and line diameter factor are known the program is ready to calculate the pressure drop. The compression ratio is computed using the minim'~m pressure, P2, and the pressure drop~ If the d.ifference between the assumed and calcu.lated values of the compression ratio is greater than 1%, the calculated compression ratio is 68

taken as the assumed value and the calculation repeated until there is agreement within 1%. Based on this compression ratio, the new maximum pressure in the pipeline, new thickness of the pipe and new internal diameter of the pipe are calculated. A new flow rate is also computed. This will be automatically within 1% of the flow rate for which the entire calculations are based. Once the compression ratio is fixed the horsepower required is computed with the help of Eq. (22). A new value of compressibility factor based on inlet conditions at the compressor is computed and used in the formula. At this stage the program is ready to compute all the costs required. The operating cost,ammortization cost, initial line and station investment are computed based on the flow rate existing in the line at that particular section of the line. The fuel consumed at each station is subtracted from the flow rate existing in the line.* When the calculations are completed for the minimum flow rate and number of stations, the number of stations is incremented by one and the calculations repeated until the transportation cost increases for that flow rate. The minimum cost is stored separately for each flow rate. The flow rate is increased in appropriate increments (set in data)until the minimum cost corresponding to each flow rate starts rising. The absolute minimum cost corresponding to a certain diameter of the line and flow rate is stored separately and is printed out at the end when all the calculations pertaining to that line have been completed. For each flow rate the program makes a plot of transportation cost (sum of operating cost and ammortization cost) as a function of number of stations. Upon completion of the calculations for each diameter of the line it also makes a plot of the minimum cost of transportation as a function of flow rate. These plots are very handy for a quick survey of the answers obtained. It may be pointed out that any information fed to the computer in one set of data remains unaltered even when that set of data has been processed and a new set is getting processed unless and until those values get changed in the program or are changed by the new set of data. As an example if the composition of propane is 0.05% for one mixture and is zero for the other mixture, then it will be necessary to make the value of the composition of the propane as O, otherwise it will be counted as 0.05. *The initial line and station investment and the transportation cost are based on the average value of gas flowing which amounts to saying that the cost of the fuel should include a transportation cost to the station at which it is used. 69

Explanation of the Input Data The computer program was written to be very flexible in processing data for various types of conditions. This flexibility is controlled by various control variables which are defined in the nomenclature to make the understanding and use of the program simpler. A brief description of the input variables are given below with a detailed account of how to use the control variables. Reference may be made to Table B-3 for an example print-out of the input data. KCP, MWT1 These represent the points taken from a graph of K(Cp/Cv) as a function of molecular weight.. For any value of molecular weight of the mixture the subroutine TAB finds the corresponding value of K. PP, VFM VFMV 1 COMl, MP These are used to calculate the specific volume and then the compressibility factor at any pressure between 200 and 5000 psia and any temperature between 40 to 100~F for methane-propane system and having reduced temperature less than 1.1. PP represents the array for the pressure, VFM the specific volumes at 40~F starting at 0.2 mole fraction methane to 0.9 mole fraction methane. Similarly VFM1 represents the specific volumes at 100~F. COM1 specifies the mole fraction methane. MP represents the number of pressures used which in turn become the number of columns in the two-dimensional array of VFM and VFMI. V, Vl, PRD, NP, MT, KS These are used to calculate the viscosity at any reduced temperature, pressure and molecular weight for the mixtures under study. V represents the points taken from curves starting at reduced temperature of 3 to the ones at 0.65. VI represents the array for reduced temperatures. PRD gives the array for reduced pressures, and NP for the number of reduced pressures. MT and KS represent the graph of KI (correction factor for viscosity) as a function of molecular weight. TN2, TC02,...o TNC6H4, PN2, PC02,..., PNC6H4, MN2, MC02,... MNC6H4 These are data for the critical temperatures and pressures and the molecular weights for N2, C02, CH4, C6H14, iC.Hlo, and iC5H12. 70

SRi, R2, SR.. SR6, Y These represent the strength of steels and their corresponding costs in $/ton. In case only one strength of steel is to be processed set SR2 to SR6 as zero. BUTI, DBUT BUTF AND PROPI, DPROP, PROPF If information is desired for the additionof butane and/or propane to the gas in barrels/day the variables above may be used. These variables represent the quantity of butane or propane added in barrels/day. The initial and final values will be set as zero in case there is no addition as barrels/ day. DBUT and DPROP are the incremental additions of butane and propane used in the iteration if a series of calculations are desired. Additions are normally added by specifying the desired values of the gas composition. NOSF This represents the maximum value for the number of stations, Depending on what is considered a minimum length between compressor stations, the value of NOSF should be set. CRI AND DCR These represent the initial value for the compression ratio. If the maximum allowable compression ratio (CRMAX) has been set as 1o65 CRI may be set as 1.2. DCR allows for changes in CRI during the processing of the data, but normally it should be set as zero. COMPSW If we have mixture of known composition and no additional propane or butane (PROPI, BUTI) is added then this should be set as 1. Otherwise it may be set as zero. QBI, DQB, QBF These represent the initial, incremental, and final flow rates for the flow rate iteration loop. Judgment should be used in setting up these values. QBF may be set higher than normally expected as the program is going to stop increasing the flow rate once the cost starts increasing. 71

MMWT Normally we should set its value greater than the expected molecular weight. In case we have data for the minimum pressure as a function of molecular weight at 40~ or 60~F then MMWT may be set as zero. ODl1, OD12, OD13 These represent the outside diameters of the pipe chosen for investigation, In case we went to process only one diameter, OD11 should be set equal to the desired diameter and OD12 and OD13 should be set as zero. CRMAX This represents the maximum allowable compression ratio. NN This represents the minimum number of stations which will be processed irrespective of whether the minimum cost has occurred or not. This is usually set at 5. FFF Minimum number of flow rates which will be processed. If only one flow rate is to be processed set FF equal to 1. Normally FF should be set as 3 since if the second flow rate gives a higher cost than the first, the program will set the flow rate one step less than the first flow rate and process that condition, It will repeat the process until it finds a suitable flow rate, This helps set the initial flow rate when poor judgment is used in selecting it. FF This is a drag factor. Its value is read from the graph of drag factor as a function of bend index. NST1, NST2, DQB2, DQB4, QBMX, QBMX2 In certain mixtures it will be wasteful to process the costs starting from the same number of stations for all the flow rates. To avoid thisq the program has the facility to change the initial value for the number of sta72

tions and the flow rate increment. NST1 and DQB2 represent the initial number of stations and the incremental flow rate to be used when the flow rate becomes equal to QBMX. Similarly NST2 and DQB4 represent the initial number of stations and the incremental flow rate when the flow rate becomes equal to QBMX2. QBMX2 should be set higher than QBMX. In case no change is needed then their values should be set higher than the expected final flow rates (QBFl, QBF12, QBF13) Three external functions available from the Computer Library of The University of Michigan Computing Center were used in the program. They were TAB9 SETPLT, and ZERO. A brief description of how to use the external functions is included, 73

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TABLE B-1 (Continued) TAB 1/20/62 SINGLE TABLE INTERPOLATION PURPOSE GIVEN THE VALUE OF AN INDEPENDENT ARGUMENT X, PERFORM A KTH ORDER INTERPOLATION ON A TABLE OF (X(I)Yt )) VALUES FOR THE CORRESPONDING DEPENDENT ARGUMENT Y. CALLING SEQUENCES MAD Y a TAB.(XXTtYT,MlM2,K,N,SW) FORTRAN Y a TABIX,XT,YT,MlM2,K,N,SW) UMAP CALL TAB PAR X PAR XT PAR YT PAR Ml PAR M2 PAR K PAR N PAR SW NORMAL RETURN - Y IN THE ACCUMULATOR ARGUMENTS X INDEPENDENT FLOATING POINT ARGUMENT X FOR WHICH THE CORRESPONDING VALUE Y IS DESIRED. XT NAME OF THE FIRST ENTRY IN THE TABLE OF FLOATING POINT INDEPENDENT VARIABLES, X()}. YT NAME OF THE FIRST ENTRY IN THE TABLE OF FLOATING POINT DEPENDENT VARIABLESt Y(I). Ml INTEGRAL NUMBER OF STORAGE LOCATION STEPS BETWEEN EACH ENTRY OF THE INDEPENDENT VARIABLE TABLE. NORMALLY Ml a I WHEN THE VARIABLES ARE STORED IN SEQUENTIAL LOCATIONS. M2 INTEGRAL NUMBER OF LOCATIONS BETWEEN EACH ENTRY OF THE DEPENDENT VARIABLE TABLE. NORMALLY M2 a 1. K INTEGRAL ORDER OF INTERPOLATION DESIREDt K.LE. 5. N INTEGRAL NUMBER OF ENTRIES IN THE INDEPENDENT VARIABLE TABLE INUMBER OF PAIRS (X(I),Y(I))). SW FLOATING POINT COMPUTATION SWITCH SW a 1.0 NORMAL RETURN, INTERPOLATION SUCCESSFUL. SW = 2.0 AC OR MQ OVERFLOW OR UNDERFLOW OR DIVIDE CHECK - - ERROR RETURN. Y FLOATING POINT DEPENDENT VARIABLE, THE INTERPOLATED VALUE FOR THE INDEPENDENT VARIABLE X. CODING INFORMATION STORAGE REQUIRED TAB 307 ERASABLB 22 81

TABLE B-1 (Continued) SETPLT 1/20/62 USTPLT SET UP FOR PLOT SUBROUTINE (IT MAKES PLOT PAINLESS) PURPOSE -- THIS SUBROUTINE IS DESIGNED TO BE USED WITH THE PLOT SUBROUTINE (WHICH IS ON LIBRARY TAPE). THE PLOT SUBROUTINE PRODUCES GRAPHS OF THE QUANTITIES GIVEN IT BY THE USER. (FOR A DETAILED EXPLANATIONtSEE THE PLOT WRITEUP) IT IS A POWERFUL AND VERSATILE TOOL, BUT IS, AS A RESULT, RATHER COMPLICATED AND CLUMSY TO USE. IT REQUIRES THAT THE USER MAKE 4 ENTRIES TO THE SUBROUTINE WITH A TOTAL OF 16 ARGUMENTS, AND IN ORDER TO DETERMINE THE VALUES FOR THESE ARGUMENTS (SUCH AS THE NUMBER OF HORIZONTAL LINES, NUMBER OF SPACES BETWEEN HORIZONTAL LINES, ETC.) THE USER MUST DO CONSIDERABLE PRECALCULAT ION THE USER MUST ALSO KNOW THE RANGE OF'ANSWERS IN ADVANCE SO HE CAN SET THE MAXIMUM AND MINIMUM VALUES FOR THE ABSCISSA AND FOR THE ORDINATE. THIS IS ALL WORK THAT CAN BE DONE BY THE COMPUTER, AND SETPLT IS A SUBROUTINE THAT DOES IT. FEATURES -- SETPLT INSPECTS THE DATA TO BE PLOTTED, CALCULATES THE ARGUMENTS, AND THEN EXECUTES PLOT SUCH THAT - - 1. ALL POINTS TO BE PLOTTED LIE IN THE RANGE OF THE GRAPH. 2. GRIDWORK IS SQUARE. 3. NUMERIC LABELS ON ABSCISSA AND ORDINATE GRID LINES ARE "'NICE" VALUES. 4. GRAPH IS APPROXIMATELY SQUARE. 5. IF THE POINTS TO BE PLOTTED HAVE ABSCISSA AND/OR ORDINATE VALUES WHOSE MAGNITUDE IS GREATER THAN 10.P.7, THE NUMERIC LABELS TO THE GRID LINES ARE MODIFIED BY A SCALE FACTOR, AND A HEADING IS PRINTED OUT INFORMING THE USER OF THE 9IZE OF THE SCALE FACTOR. 6. IF THE SIZE OF THE GRAPH IS INDETERMINATE IN EITHER THE Y(VERTICAL) AND/OR THE XtHORIZONTAL) DIRECTION (IE. A HORIZONTAL OR VERTICAL LINE, OR A POINT), AN APPROPRIATE COMMENT IS PRINTED OUT AND THE MAXIMUM AND MINIMUM VALUES OF THE APPROPRIATE AXES ARE ADJUSTED SO THAT THE VALUES MAY BE GRAPHED. RESTRICTIONS — ALL POINTS (XY) WHICH ARE TO BE PLOTTED MUST BE OBTAINED AND STORED IN TABLES BERORE EXECUTING SETPLT. CALLING SEQUENCES -- THERE ARE TWO CALLING SEQUENCES AVAILABLE, A REGULAR AND AN ALTERNATE ONE. REGULAR CALLING SEQUENCE - USER EXECUTES ONLY SETPLT (OR USTPLT). USER DOES NOT EXECUTE PLOT. MAD- EXECUPE SETPLT.(L XLOCYLOCNUMBCDNCHARtLABEL) FORTRAN- CALL SETPLT(LXLOCYLOCNUMtBCDNCHARtNHABCD*..) UMAP- CALL USTPLT PAR L PAR LABEL OR ANY EQUIVALENT UMAP SUBROUTINE CALL 82

TABLE B-1 (Continued) ALTERNATE CALLING SEQUENCE -- THIS IS FOR USERS WHO WANT TO USE''OMIT'1 TO CHANGE THE GRAPH BEFORE IT IS PRINTED, WHO WANT TO PRINT MORE THAN ONE COPY OF THE GRAPH, WHO WANT TO USE DIFFERENT PLOTTING CHARACTERS FOR DIFFERENT PARTS OF THE DATA, OR, IN GENERAL,. WHO WANT TO TAKE ADVANTAGE OF SOME OF THE SPECIAL FEATURES OF PLOT ( FOR DETAILS ON THESE SPECIAL FEATURES, SEE THE PLOT WRITEUP) WHEP USING THIS ALTERNATE CALLING SEQUENCE, USER EXECUTES SETPL,. AND THEN MUST EXECUTE PLOT3 AND PLOT4 IOR FPLOT4) HIMSELF. MAD- EXECUTE SETPLT.(L,XLOC,YLOCNUM) FORTRAN- CALL 9ETPLT(L,XLOCtYLOCNUM) UMAP- (FOR THIS ALTERNATE CALLING SEQUENCE EITHER THE NAME SETPLT OR USTPLT MAY BE USED) CALL USTPLT, LXLOCYLOC,NUM OR EQUIVALENT SUBROUTINE CALL ARGUMENTS L *,NONZERO IF MAX GRAPH LENGTH IS TO BE ONE PAGE -ZERO OTHERWISE. IIN THIS CASE, LENGTH.LE. 2 PAGES) XLOC =LOCATION OF FIRST VALUE OF X OR POINTS (X,Y) TO BE PLOTTED ( N TABLE OF X VALUES) YLOC =LOCATION OF FIRST VALUE OF Y OF POINTS (XY) TO BE PLOTTED (IN TABLE OF Y VALUES) (THESE TWO TABLES MUST BE STORED BACKWARDS IN STORAGE, AS MAD AND FORTRAN DO. THE VALUES OF X AND Y STORED IN THESE MUST BE FLOATING' POINT VALUES) NUM aNUMBER OF POI.NTS TO BE PLOTTED (EITHER MAD,UMAPOR FORTRAN INTEGER) BCD aLEFT-ADJUSTED BCD(HOLLERITH) PLOTTING CHARACTER. NCHAR aNUMBER OF BCD CHARACTERS (INCLUDING BLANKS) IN THE LABEL ARRAY. LABEL -NAME OF ARRAYW CONTAINING THE STRING OF BCD CHARACTERS TO BE PRINTED AT LEFT EDGE OF OUTPUT PAGE (LABEL FOR ORDINATE). MUST BE STORED BACKWARD WHEN USING MAD (USING VECTOR VALUES STATEMENT), OR FORWARD WHEN USING UMAP (USING BCD OR BCI BLOCK). MUST BE STORED 6 CHARACTERS TO THE WORD (C6). NHABCO... FOR FORTRAN USERS, THE STRING OF CHARACTERS FOR THE ORDINATE LABEL APPEARS DIRECTLY IN THE CALLING SEQUENCE. THE N PRECEEDING THE H (SPECIFYING THE HOLLERITH STRING) SHOULD BE THE SAME AS THE VALUE OF NCHAR. EXAMPLES — SEE NEXT PAGE CODING INFORMAT IONSTORAGE USED SUBROUTINES USED 6ESTPLT 701.PRINT ERASABLE 1750.IF L-NONZERO PLOTI 4064.I F LZERO PLOT2 (FIRtST 25 LOCATIONS PLOT3 OF BRASABLE ARE PLOT4 NOT USED) FPLOT4 ELOG STORAGE REQUIRED.01301 SETPLT 701 ERASABLE 4064 85

TABLE B-1 (Continued) SAMPLE PROBLEM THIS PROBLEM IS THE FIRST EXAMPLE PROBLEM AT THE END OF THE PLOT WRITEUP, REWRITTEN TO USE S.ETPLT. IT IS SUGGESTED THAT THE READER COMPARE THEM. BOTH MAD AND FORTRAN VERSIONS ARE GIVEN. SCOMPILE MAO, PUNCH OBJECT PLMADOOO R R PROGRAM TO ILLUSTRATE PLOTTING MULTIPLE POINTS WITH MAD R DIMENSION X(100)p YI100) INTEGER N FIRST READ FORMAT ENTR, N READ FORMAT DATA, Xl)..o.XIN) READ FORMAT DATA, YI1)...YIN) PRINT FORMAT TITLE EXECUTE SETPLT.(lt,Xl),Y(1l)N, $*$32,ORDI PRINT FORMAT ABS TRANSFER TO FLRST R R FORMAT STATEMENTS R VECTOR VALUES ENTR * S110*S VECTOR VALUES DATA tS7F1Oo4$. VECTOR VALUES TITLE SIHISS4,15SHPLOT OF X VS Y /1H *$ VECTOR VALUES ABS a $1HOS559l4HTHE ABSCISSA X *$ VECTOR VALUES ORD mS THE ORDINATE Y $ END OF PROGRAM SOATA SCOMPILE FORTRAN, PRINT OBJECT,. PUNCH OBJECT PLFTROOO C C PROGRAM TO ILLUSTRATE PLOTTING MULTIPLE POINTS WITH FORTRAN DIZMENSION XI 100),Y(il00) 1 READ INPUT TAPE 7,100, N READ INPUT TAPE 7,101(X(I), I1ltN) READ INPUT TAPE 7,LOl(Y(I), Il1~.NI WRITE OUTPUT TAPE 69102 CALL SETPLTI1,XI t1)Y(l)tNtH*,33232H THE ORDINATE X Y ) WRITE OUTPUT TAPE 6,r103 GO TO 1 C C FORMAT STATEMENTS C 100 FORMAT 1110) 101 FORMAT (7F10.9) 102 FORMAT (1H1,5411H ),15HPLOT OF X VS Y /IH ) 103 FORMAT IHOS5(IH ),l4HTHe ABSCISSA X ) $ DATA 84

MOD NR 16 TABLE B-l (Concluded) 10-21-64 I l of 6 UEMS WRtITEUPS ZERO - SPRAY SEPTEBER 196b STORE CONSTANT PURPOSE ZERO STORES ZERO SPRAY STORES ARBITRARY CONSTANT. CALLING SEQUENCES MAD EXECUTE ZERO (L1IL2,..- LN) UMAP CALL ZERO LI L2 LN ARGUMENTS THE LI ARE STANDARD ARGUMENT LIST ELEMENTS OF THE FORM MAD Ao*.O OR A UMAP BLK A,D OR PAR A SPRAY IS CALLED EXACTLY AS ZERO EXCEPT THAT THE FIRST ARGUMENT IS A SINGLE CONSTANT (IN MAD) OR THE LOCATION OF A SINGLE CONSTANT (IN UMAP) WHICH IS TO BE STORED INSTEAD OF ZERO. PROGRAMMI NG NFORMAT ION LOCATIONS REQUIRED ZERO = SPRAY 34 ERASABLE 0 85

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TABLE B-3 (Continued) 24.75, 11.71, 7.11, 4.87, 3.54, 2.49, 1.868, 1.632, 1.459 1.353, 1.27, 1.214, 1.173, 1.109, 1.062, 1.C27, C. S974 VFM1(1)= 24.86, 7.26, 3.5, 1.465, 1.442, 1.414, 1.389, 1.366, 1.353, 1.338, 1.325, 1.313, 1.303, 1.283, 1.26o, 1.25, 1.236, 25.8, 9.2, 4.59, 2.5, 1.482, 1.431, 1.399, 1.364, 1.345, 1.326, 1.31, 1.292, 1.279, 1.255, 1.234, 1.217, 1.202, 26.61, 9.75, 5.6, 3.54, 2.42, 1.533, 1.456, 1.4C1, 1.363, 1.333, 1.337, 1.286, 1.266, 1.235, 1.213, 1.191, 1.173, 27.29, 12.11, 6.45, 4.32, 3.09, 2.21, 1.615, 1.497, 1.424, 1.373, 1.3333, 1.3, 1.273, 1.23, 1.197, 1.17, 1.147, 27.88, 12.81, 7.71, 5., 3.67, 2.63, 1.946, 1.704, 1.55, 1.453, 1.388, 1.34, 1.301, 1.241, 1.198, 1.162, 1.134, 28.38, 13.33, 8.29, 5.78, 4.28, 3.06, 2.445, 2.C33, 1.767, 1.594, 1.494, 1.415, 1.356, 1.268, 1.208, 1.161, 1.125, 28.8, 13.75, 8.73, 6.24, 4.75, 3.6, 2.861, 2.366, 2.039, 1.811, 1.652, 1.531, 1.441, 1.317, 1.234, 1.172, 1.127 COM1(1)= 0.2,.3,.4,.5,.6,.7,.8,.9 V(1)= 36.9, 38.,39.1,40.,41.1,42.1,43.2,44.1,45.4,46.1, 32.4,34.1,36.,38.1,40.,42.3,44.8,46.4,48.2,50., 29.,31.,33.9,37.,40.8,4,4.2,48.,'51.,54.1,57., 98

TABLE B-3 (Continued) 26.,29.2,34.,38.3,43.2,47.8,51.8,55.2,59.,62.3, 24.2,29.,34.1,40.2,46.2,52.,57.,62.,66.3,73.8, 23.,30.,39.8,48.8,57.2,64.8,72.,79.,85.9,92., 23., 34.,48.1,60.6, 71. 3, 80., 87.8,95.1, 12.1,1 8.3, 26.,42.2,63.,77.8,89.,98.4,108.,116.,124.1,13C.3 52.,78.,95.,101.6, 116.,124.,132.,14C.,148.,152., 90., 102., 113., 123., 132., 142., 151., 159., 163., 171., 115., 126., 139., 149., 156., 163., 172., 180., 186., 192., 135., 147., 158., 168., 178., 186., 195., 202., 210., 215., 160., 170., 181., 192., 202., 212., 222., 231., 240., 248., 186., 200., 210., 219., 228., 238., 247., 256., 265., 273., 222., 233., 246., 256., 265., 273., 282., 290., 3GC., 3C5., 265., 278., 290., 300., 310, 320., 330., 340., 35C., 360. fMW(1)= 22.74,28.1, 33.38 VPl(1)= 1400., 1340., 1050. MF= 3, TG= 16 VI(1)= 3., 2.5, 2., 1.7, 1.5, 1.3, 1.2, 1.1, 1..95,.90,.85,.75,.7,.65 MT(1)=15., 18., 21., 24., 27., 30., 33., 35. KS(l)= 1.3, 1.205,1.14, 1.08, 1.04, 1.C08, 1.004, 1. 99

TABLE B-3 (Continued) PRD(l)= 1., 2., 3., 4., 5., 6., 7., H., 9., 1J. NP=10 TN2= 226.9, TC02= 277.9, TCH4 = 343.3, TC2H6 = 549.8, TC3H8 = 6bo. TIC4HO = 734.7, TNC4H( = 765.3, TIC5H2 = 829.t, TNC5H2= 845.6 TNC6H4 = 914.1 PN2= 492., PC02= 730., PCH4 = 673.1, PC2H6 = 708.3, PC3H8 = 617.4 PIC4HO = 529.1, PNC4HO = 55.7, PIC5H2 = 483., PNC5H2= 489.5 PNC6H4 = 439.7 MN2= 28.02, MC02= 32., MCH4 = 16.04, MC2H6 = 3C.07, MC3H8 = 44.09 MIC4HO = 58.12, MNC4HO = 58.12, MIC5H2 = 72.15, MNC5H2= 72.15 MNC6H4 = 84.16 SRI= 65.E3,SR2=1.E5, SR3= 0., SR4= 0., SR5= G., SR6= C. Y(1)= 228., 254., 265., 384., 467., 535. Y (1)= 254., 384., 0., 0., 0., 0. FF=.936, FFE= 1., F=.72, E= i.0, EFF= 0.8 X= 165., N=12C(C., H= 300C., ALPHA=.15, CF= C.2, CLVL= 656. CLMS=19., LG= 0.005, B= 0.15, FHPHR= 8.7E-3, FCLP=1. PRPRHO= 0.51, IBUTRH= 0.563, NBUTRH= 0.583, BUTI= C., DBLT= 1.E4 BUTF= 0., EE= 250.E-6 GASCOST= 0.20, XI=2.7E5, AD= 1. 100

TABLE B-3 (Continued) LT= 1CCO. NOSI= 6, DNGS= 1, NOSF= 25 CRI= 1.4, CCR=.1 TF= 520., COMPSW=1 PROPI= O., DPRCP=2L4, PROPF= C. QBI=3.0E8, DQB=0.5E8, QB3F= 6.E8 CBI= 1.5E8, QB12= 4.0E8,QB13= 5.CE8 NOSI= 7, NOS12= 6, NOS13= 6 QBF12= 1.6E9, QBF13= 1.7 E9 PMIN= 600., PMWT= 30. 0011= 16., OD12= 24., CD13= 3'. CRMAX= 1.65, NN= 5, CRI= 1.2 SR1= 65.E3, SR2= 1.E5, Y(2)= 384. TNC7H6=972.36, PNC7H6= 397.71, MNC7H6= 1CC.2 MMWT= 30. NOSF= 35 NCS12= 10, NOS13= 14 FF=.936, FFF= 3 101

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APPENDIX C EXAMPLE HAND CALCULATION

ILLUSTRATIVE EXAMPLE PROBLEM BY HAND CALCULATION Problem Compute the minimum cost of the pipeline system and cost of transporting 600 million cu ft per day of a mixture of 80% natural gas and 20% propane (molal basis) over a distance of 1000 miles at 60~F through 24-in. OD pipe having a strength of 100,000 psi. Select the minimum pressure as 100 psi above the dew point at 60~F. This is the first of a series of calculations to be done on the computer at increasing flow rates to find the minimim cost of some optimum flow rate. The number of compressor stations is a variable in this calculation and will include one more and one less station than the optimum. Solution MINIMUM PRESSURE The minimum pressure for 80% natural gas and 20% propane in the range 40~ to 100F is l460 psia and therefore the minimum pressure in the pipeline is set at 1560 psia. This information is given in the program as data, HORSEPOWER AND MAXIMUM LINE PRESSURE By use of the flow equation (Eq. 12) the pressure drop in the line is computed to obtain the maximum pressure in the line. From the inlet and outlet pressures the horsepower will be computed. The steps solving the flow equation are given. 1. Calculation of Gas Gravity Factor (FGR) The molecular weight of the gas from Table 1 is 17o4. Molecular Weight = 0.8 x 17.4 + 0.2 x 44.09 = 22.73 (22.728*) (C-1) *The values in parentheses are those on the computer print-out for this example. 109

Gas gravity, G = 22- = 0.784 (0.7837) (C-2) 29.0 FGR - 0. 0.874 (C-3) Temperature flowing factor (FTF) FTF = T (C-4) 520 2. Trial and Error Calculations for Compression Ratio From computer results we know that optimum value for number of stations is 22. So we shall make computations for 21 stations. NOS = 21 (including the one at the entrance). Let assumed compression ratio be = 1.16 (C-5) Maximum pressure in pipeline Pi = 1.16 x 1560 = 1810 psia (C-6) 3. Length Between Compressor Stations L = 1000 = 47.6 (47.62) miles (C-7) 21 4. Thickness and ID of the Pipe TK= P xOD - 1810x24 THK = 0.301 in (C-8) 2xFxExS 2x0.72x1x100,000 D(ID) = 24-2 x 0.301 = 23.398 in. (C-9) FD = Line diameter factor = D25 = 23.3982'5 = 2620 in.2'5 (C-10) 110

5. Average Pressure PAVG - (Pl + P2 - P 53 Pl+P2/ (1810 + 1560 - 810x1560/ (2532) = 1690 psia (Cll) 6. Calculation of Compressibility Factor (Z) and FPV This is calculated by Sarem's method using Lagrange polynomials which fit best the compressibility factor chart. A subroutine ZFAC has been prepared which calculates Z based on TR and PR, the reduced temperature and pressure, respectively. Pseudo Critical Properties TC = 0.8 x 364.7 + 0.2 x 666 = 424~R (422) (C-12) PC = 0.8 x 673.6 + 0.2 x 617.4 = 662.4 psia (662.3) (C-13) TR 520 = 1.2 (1.232) (C-14) 42PR =- 11 2.73 (C-15) 662.4 z = 0.58 (C =t6) FPV = = = 1.315 (C-16a) 7. Calculation of Viscosity (Bicher and Katz Method) TR = 1.253 Eqs. (C-14), (C-15) above PR = 2.75j 111

Molecular weight (MWT) = 22.73 Fig. 11, KI = 1.1 (C-17) and VISKM = 5.18 or VISKM = 51.8 x 1.1 x \/22.73 KIx /MWT = 272 micropoises MU = VISKM = 272 x 6.72 x 108 = 1.825 x 10-5 lb/ft sec (C-18) 8. Calculation of Transmission Factor (FT) FT = - (C-19) \,/F where FM = Moody friction factor RE = E = 1.3526 x 10-5 BxG (C-20) DxMU from Eqs. (C-2), (C-9), and (C-18) 1.3526 x 600 x 106 x 0.784 23.4xl.825 =1.49 x 107 (C-21) 2 D/EE 4 log D + 2.28 - 4 log (1 + 9.34 D/E JFM EE RE /FM Let 2 = 21.45 /FM 112

Is 25.4x21.45\ 21.5 4 log 23.4 20x106 21.45 O 4 log 24 + 2.28 - 4 log (1 + 9.34 250x10 1.49x107x2 = 4 x 4.974 + 2.28 - 4 log (1 + 6.3 x 101) = 22.17 - 0.82 = 21.35. = 21.40 (C-22) \.FM 9. Drag Factor (FF) It was agreed to use a bend index of 2000/mile, plastic lined pipe (Fig. 13) FF = 0.936 (C-23) 10. Checking for Assumed Compression Ratio Let K6 = 77.5 x FGR x FTF x FPV x FT x FF x FFE x FD From Eqs. (C-3), (C-4), (C-10), (C-16a), (C-22), (C-23) K6 = 77.5 x 0.874 x 1 x 1.34 x 21.4 x 0.956 x 1 x 2620 K6 = 4.76 x 106 P1 = IP22 + (K6)2 =15602 + (600 x 106)2 x 476 (4.76 106)2 = 1790 (1790) psia CR P1 _1790 = 1.147 P2 1- 160 1153

Second Trial for Compression Ratio Therefore let us assume CR as 1.147. Repeating steps 2-10 we have P1 = 1.147 x 1560 = 1790 psia PlxOD 1790x24 THK = = = 0.298 in. (0.298) 2xFxExS 2x0.72x1x100,000 D = 24 - 2 x 0.298 = 23.40 in. (23.403) FD = 23.403205 = 26.25 in.2'5 Average pressure = PAVG = 2 (1790 + 1560 - 1790x1560) 5 1790+1560/ = 1677 psia (1678) TR = 1.25 (1.232) PR = 1677 2.53 (2.533) 662.4 z = o.565 1 FPV = = - 1.33 0.565 VISKM = 59. or VISKM = 59. x x V22-75 KI vMWT = 206 micropoises MU = 206 x 6.72 x 108 = 1.39 x 10-5 lb/ft sec RE = Dv = 1.5526 x 10-5 pJ. DxMU o 0.784 = 1.5526 x 10-5 x 600 x 106 x 29105 = 1.96 x 107 114

= 4 log D + 2.28 - 4 log (1 + 9.34 D/E iFM EE RE I/FM/ Let 21.45 /FM 23.4x21.45 _ _23~4 2 0 = 4 log 234 + 2.28 - 4 log (1 + 9.34 250x16) JFM 250x106 1.96x107x2 0.48 4 x 4.97 + 2.28 - 4 x 0.17 = 21.49 Verification from Moody Friction Factor Chart E/D 250x106 -6 EE/D = 25.4 = 10.7 x 106 = 0.0000107 23..4 FM = 0.0086 2 2 21 21.6 /FM 9.22x10K6 = 77,5 x FGR x FTF x FPV x FT x FF x FFE x FD = 77.5 x 0.874 x 1 x 1.33 x 21.46 x 0.936 x 1 x 2625 = 4.77 x 106 P1 = P22. +.QBL /15602 + (600 x 106)2 x 47.6 (4.77x106)2 1790 psia CR = P = 1790 = 1.147 which checks P2 L 60 - 115

Calculation of Horsepower of Compressor Using Equation (22) to obtain the horsepower per station K-1 A 0.0854 x K x TF x Z*(CR K - 1) 14.73 (K-1) x EFF 14.65 *Z is based on inlet conditions. PR = 6624 2.353 TR = 1.232 z = 0.575 (0.591) Molecular weight = 22.73 Using chart in NGSMA, p. 27 (1957) to find K K = Cp = 1.22 (1.22) Cv 1.22-1 1 0.0854 x 1.22 x 520 x 0.575 x 1.147 1. -22 1) 1473 Horsepower A = 1..2 x ___ 0,22 x 0.8 14.65 = 4.48 (4.588) hp/MMcf/day Cost of Pipeline and Compression Stations From Eqn. (A-3) the cost of the pipeline in dollars per mile (YW) is computed YW = 28.2 x (D + THK) x THK x Y = 28.2 x (23,4 + 0.298) x 0.298 x 384 =7.65 x 104 (7.656 x 104) $/mile The Initial Investment in Pipeline (IINVL) IINVL = (YW + N x OD + H) x —QB 116

=(765 x l04 + 1200 x 24 + 3000) x 6~x 600x106 = 1805 (1827*) cents/100 miles/Mcf/day Note: *This value takes into account the adjustment in quantity of gas flowing through the pipeline due to fuel consumption at each station. This is the reason for the discrepancy in the two values. This also occurs in the costs stated below. Initial Investment for Stations (IINVS) The initial investment for stations in given by Eq. (26) XlxlO A IINVS (X + Xlx10 ) xA x NOS x 10 AxQB LT 10(X)(A)(NOS) (Xl)(107) (NOS) LT (QB)(LT) (0) (l65)(4.48)(2l) 270,000 x 107 x 21 1000 6 600 x 10 x 1000 = 155.2 + 94.4 = 249.6 (254.3) cents/100 miles/Mcf/day Operating Cost (CMMOP) The operating cost is given by Eq. (28) A x NOS x FOOP CMlIOP = ((365 x 24 x FHPHR x CF + CLMS) x 6 x LT 565 x LT + LG x GASCST x 3 + CIML x 10 6 10 + AD LT QB x 365 3650 j 4.48 x 21 x 1 = ((65 x 24 x 8.7 x 10-3 x 0.20 + 19) 448x 21 x.7' 5x 10 365 x 1000 + 0.005 x 0.20 x --- + 0 106 x 10 + 36 1000 600 x 10 x x 36 /650 = (355.2 x 2.58 x 10o4 + 0.001 + 3.88 x 10-3) x 10 + -- 117

1 *x = (0.00882 + 0.001 + 0.00388) x 10 + 650 3650 = 0.1395 (0.139965) cents/100 miles/Mcf. Amortization Cost The amortization cost is based on paying 15% of investment per year, Eq. (27). CMMAM = (((YW + N x OD + H) x B x 1 A x + ALPHA x (X + Xl x B x NOS)()FP1) x lO A x B / LT 1(365) = ((7.65 x 104 + 1200 x 24 + 3000) (0.15) x 106 600 x 10 + 0.15 (165 + 270,000 x 106 48 x 21 1x10 + 0.15 (165 + 6 o x 4.48 x 600 x o 6 1000 3) 565 = (27.1 + 3.75) x 10 365 =0.845 (0.8555*) cents/100 miles/Mcf *See note at the end of the Initial Investment on Pipeline. Fuel Consumption at the Compressor Stations (LSG) This is needed to obtain the pipe line delivery. LSG = (24 x FHPHR x A x QB x 10-3) x NOS + LG x QB = 24 x 8.7 x 10-3 x 4.48 x 600 x 10+6 x 10-3 x 21 + 0.005 x 600 x 106 = (11.75 + 5) x 106 = 14.75 x 106 it3/day *As indicated earlier, this should be AD/36.5. For this example the cost of transporting gas, CY, would be raised about 53 by the correction. 118

Quantity of gas, at the exit = (600 - 14.75) x 106 = 585.25 x 106 (585.33 x106) ft3/day CY = CMMAM + CMMOP = 0.845 + 0.1395 = 0.9845 (0.9955) cents/100 miles/Mcf IIINV = IINVIL + IINVS = 1805 + 250 = 2075 cents/100 miles/Mcf In reviewing the method of finding amortization and operating cost, the full 600 million cu ft of gas are used even though only 585.25 million are sold. The computer program finds costs by using the actual flow in each segment, and therefore is based on an average pipeline delivery somewhere between 600 and 585 million cu ft, Total Investment (TINV) = IINV x QB x 10-7 x LT = 2075 x 600 x 106 x 10-7 x 1000 = 1.245 x 108 (1.250 x108) dollars/day Total Operating Cost (TOPCST) CY x QB x 10-7 x LT = 0.9845 x 600 x 10+6 x 10-7 x 1000 = 59,070 (59,730) dollars/day 119

APPENDIX D PHASE DIAGRAMS DETERMINED BY KURATA FOR MIXTURES NOT STUDIED IN THIS REPORT These diagrams, reproduced from the Ph.D. thesis of Fred Kurata at The University of Michigan in 1941, under the direction of Professor Donald L. Katz, represent the experimentally determined phase diagrams. The compositions of the mixtures are listed on the diagrams.

2800 2600 2400 2200 II60C 1000,7/ / / / y /' 1800 1600 30 I o I / / LF.a1400sm i e < oo/, / /2 oool/ COMPOSITION COMP MOL% \0%^ N2 0.535 cl 72.40 600 Ct 5.430 C3 3.000 C4 3.100 C, 7. f00 Cg 4. 555 C7+ 3. 880 10 30 50 70 90 110 130 150 170 190 210 TEMPERATURE DEG. F Fig. D-l. Phase diagram for mixture S-5.

2800 2400 2200 -o0 lllI__ 2000 1800 2C w.. 0 100 -J 1000 COMPOSITION COMP MOLo% N2 0.383 CO0 0.454 600 ------ Ci 83.000-o C2 3 760 C3 1 439 C4 0.890 C, 4. 364 C6 3. 060 400 ________ — - - - - - -- - C7 2. 630 200 - 0 20 40 60 80 100 120 140 160 180 200 TEMPERATURE DEG. F. Fig. D-2. Phase diagram for mixture T-1. 124

2700 2700 2500 -/ 2300 --- ~ —----- 2100 < / 1500 w1300 D u) COMPG SITION COMP. MOL - I 1.409 300 --— __ ~C4 1-.025 C~ 5.010 C. 3.540 CF 3. 025 100 20 40 60 80 J 20 ICOMPO 0 TION ~~~~~TE~COMPERATURE DEG. F./, Fig. D-35. Phase diagram for mixture T-3. 125

2800 260 200 ____________________________ / / /I /' s x/ /::. F D Phs / / L 1100 1 00 // / / aoo ~ //. //~ y ^1400 ----— N —-- ------ — 2^o ------------ --- -^ --- 0.362 C02 0.29 -5% C i% 78.4G C, 3.55 C I.359 400._.~~~~~~~ C4 I.296 4 00 ------------------------------------------------- - C 5 6.3 - C, 4.474 C74 3.82 I 0 3 0 5 0 70 90 I10 130 150 170 190 210 TEMPERATURE DEG. F Fig. D-4. Phase diagram for mixture T-4. 126

300 2800 ---- - 0/0 2600 Jr 2400 --- 2200 800 _ COMP MOLZ 600 ------ --- ~1400 _______ _______ - C7 740 16200 ----------------------- - 0 -— 20 40 6-0 80 00 120 140 60 160 2C TEMPERATURCOMP DEG. FMOL Fig D-C Phase diagram for mixture T- 2.940 127,~oo ~ ~ AI-n ~ sn 1

2000 1800 1600 ~' f/ / I 0/ / A /0/O 1400 1200 I'n CL~~~~~~~O ^^~~~~~~~~COM I iC CO. 800. - --- COMPOS4 2i2N N2 0.326 co0 0.387 C, 70.65 C2 3.23 400 _ __ _ __ —---— 2 200 --- 0 20 40 60 80 100 120 140 160 180 20( TEMPERATURE DEG. F. Fig. D-6. Phase diagram for mixture B-l. 128

2000 [Soo 1800 ---- raven4600 400 -~> ~^ 0_~ 00162 01 U) ^ /,oo a- 800 _____ I I z COMPOS TION \/,,,I /I ~ ICOMP MOLL. % 800 N2 0.300 C02 0.350 Ci 65.24 C2 2.98 G.. I,.13 400 C4______ 3000 200 0 20 40 60 80 100 I120 140 160 18O 20 TEMPEORATURE DEG. F Fig. D-7. Phase diagram for mixture B-2. 129

2000 1800 160 0 2 0 4 2t /1 ~/ ^ -1T /D 1200 ---- 6 000_,1__ COM POS IT ION' OM P. M OL o 600 N_ 0.283 0 20 40 6010 12CO 0.3 36 TEMPERATUEC 6E,3 F/ig D Pa 2. 80 1\50Q/ C.3 - C.~~~~~~4 34. 2: 400 200 0 20 40 60 80 100oo 120 140 160 180 20 TEMPERATURE DEC. F Fig. D-8. Phase diagram for mixture B-3. 130

1800 1600 1400 0______ — )3' 1200 __, -' o, r,ooo-., 000 COMPOSIT ON COMP. MOL % 600 0 200 40 60 8N0 100 120 140 2 0.2 0 66 \,~ /' C02 O.J! 7 /~ C 58.25 C2 2'.66 C3 I.007 400 ------— 1 ------ - C4 37.50 0 20 40 60 80 100 120 140 160 180 20 TEMPERATURE DEG. F. Fig. D-9. Phase diagram for mixture B-4. L15

APPENDIX E CHARTS GIVING RESULTS OF ECONOMIC CALCULATIONS

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APPENDIX F EXAMPLES OF SAREM'S METHOD FOR COMPUTING COMPRESSIBILITY FACTOR

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Z-factor equation developed for use in digital computers Only 36 coefficients need be stored to permit a digital... computer to generate Z factors. Capacity of small computers is not taxed, and mean deviation is as low as 0.004 NATURAL-GAS and reservoir-en- 2.95. Polynomials up to fifth degineering calculations involving the gree were used.. M SAREM compressibility factor Z can best be The general equation is: handled in a computer program if... research engineer in the production the Z factors can be generated in- A P(y research department of Sinclair Reternally by a digital computer. n Pm(x) P(y) search, Inc. He joined Sinclair in 1954 and since that time has done research An accurate method of getting Z An accurate method of getting Z Where: in the field of fluid flow in porous factors from a computer by use of 2pr - 15 media and phase behavior of hydroa 20-by-20 input table was recently x -- carbons and associated fluids. He holds developed by Gray and Sims.1 But 14.8 BS and MS degrees from University of for small and medium-sized com- Tulsa where he has also done postputers the memory storage needed 2Tr - 4 graduate work in mathematics. for this table lookup method seri- Y ously limits the scope of related pro- 1.9 Mean deviation between Z facgrams. What is needed is a method Pm, P are Legendre polynomials tors calculated by the method shown that will supply the Z factors with- of degree m and n respectively. here and those appearing in the out using much storage capacity in original chart was found to be aca small computer. ff Z(x,y) Pm(X) P (y) dydx ceptable. On the boundaries of the The solution. To solve this prob- A xm = chart, where Tr = 1.05 and 2.95, lem, an equation requiring storage fxfyPm2(x) Pn2(y) dydx and Pr = 0.1 and 14.9, 53 points of only 36 coefficients was fitted to showed a mean deviation of 0.013. a chart in which Z was expressed Expressions for the Legendre For 300 points scattered uniformly as a function of pr and Tr. Two sets polynomials of degree 0-5 are given throughout the chart, mean deviaof Legendre polynomials were used in Table 1. Calculated coefficients, tion was found to be 0.004. and the coefficients were found by obtained by numerical integration R the method of least squares. from the Z factor chart, are listed eere Accuracy of such an approxima- in Table 2. 1. Gray, E. H., and Simms, H. L., "Z Accuracy o suc an aprxia i TbeFactor Determination in Digital Computers": tion depends on the degree of the The Oil and Gas Journal, July 20, 1959, polynomials and the magnitude of TABLE 1 -LEGENDRE POLYNOMIALS p. 80. the intervals chosen for fitting, OF DEGREE 0-5 2. Poettman, F. H., and Carpenter, P. G., "The Multiphase Flow of Gas, Oil, and among other things. For conven- 7071068 Water Through Vertical Flow Strings with ience and desired accuracy, the com- P(x) 0.7071068 Application to the Design of Gas-Lift InpressibilityP(x) = 1.224745x stallations": API Drilling & Production Pracpressibility chart was tabulated at P2(x) = 0.7905695 (3x2 - 1) tices, (1952), p. 257. intervals of 0.1 on pr and Tr for P() = 0.9354145 (5x3 - 3x) 3. Brown, G. G., Katz, D. L., Oberfell, values of Pr between 0.1 and 14.9, P(x) 0.265165 (5x 3x + G. G., Alden, R. G., "Natural Gasoline and values of r between 0.1 and 14.9, P4(x) 0.265165 (35x4 - 30x2 + 3) the Volatile Hydrocarbons": Section One and values of Tr between 1.05 and P5(x) = 0.293151 (63x5 - 70x3 + 15x) Sponsored by NGAA, Tulsa, (1948), p. 38. TABLE 2-VALUES OF THE COEFFICIENTS, Amn m=0 m=1 m=2 m=3 m=4 m=5 n=0....... 2.1433504 0.083176184 -0.021467042 -0.00087140318 0.0042846283 - 0.0016595343 n=....... 0.33123524 -0.13403614 0.066880961 -0.027174261 0.0088512291 - 0.0021520929 n=2....... 0.10572871 -0.050393654 0.0050924798 0.010551336 -0.0073181933 0.0026959963 n=3....... -0.052184040 0.044312146 -0.019329465 0.0058972516 0.0015366676 -0.0028326809 n=4....... 0.019703980 -0.026383354 0.019262143 -0.01153539 0.0042910089 -0.00081302526 n=5....... -0.0053095900 0.0089178330 -0.010894821 0.009559389 -0.0060114017 0.0031175170 THE OIL AND GAS JOURNAL * SEPTEMBER 18, 1961 176

APPENDIX G VISCOSITY DATA USED TO REPRESENT CORRELATION

The points on the curves of Figs. 11 and 12 are listed in matrix form for interpolation by TAB to obtain viscosity at any reduced temperature, pressure, and molecular weight. V(1)= 36.9, 38.,39.1,40.e41.1,42.143.2944.1,45.4,46.19 32.4,34.1,36. 381,40.,42.344.8946.4~48.2,50*, 29..31.,33.9t37,940.8,44.2,48.,51. 54.1957.~ 26. 29.2,34.,38.3,43.2947.8,51.855.2,59. 62.3, 24.2,29.,34.1.40.2,46.252. 57. 62.66.3,70.8, 23. 30.,39.8.48.857.2,64.8.72. 79. 85.9992.. 23. 34*.48.1,60.6,71.3,80.,87.8,95.1,102.1.108.3, 26.,42.2,63.,77.8,89.t98.4t108..116. 124.1130.3 52.,78.,95.9101.6116. 124.,132. 140. 148. 152. 90., 102., 113.. 123.* 132., 142., 151.. 159., 163., 171.. 115., 126., 139., 149., 156*, 163., 172., 180., 186., 192., 135., 147., 158., 168., 178., 186., 195. 202.9 210.t 215., 160., 170., 181., 192., 202.. 212., 222., 231.. 240.. 248., 186., 200.. 210.. 219.. 228., 238., 247.t 256., 265., 273., 222.. 233., 246.. 256., 265., 273., 282., 290., 300., 305.. 265., 278.. 290., 300., 310, 320.. 330., 340., 350.. 360. V1(1)= 3., 2.5. 2., 1.7, 1.5, 1.3, 1.2, 1.1, 1., *95,.909 *85,.75,.7,.65 MT(1)=15., 18.9 21., 24.* 27., 30.* 33*. 35. KS(1)= 1.3. 1.205,1.14, 1.08, 1.04, 1.008, 1.004, 1. PRD(1)= 1.. 2.. 3., 4., 5., 6., 7., 8., 9., 10. NP=10 179

APPENDIX H DATA FOR COMPRESSIBILITY FACTOR OF METHANE-PROPANE SYSTEM IN MATRIX FORM

cO 0 co i 40 (00 in e 1 u4 \ ~ O *n et o, * p-I * ( 0 o Cl~ 0 oo - lr-q N Co N n V C in r- 0 O 4'J r-0 I O (O (f( (1- LA L r c-I eN N'-' u r- - 0Orc ~ ~ r-* 4 r-* uo. r —* uV I - (vl 0- -- t I 0,u- C *, — r — 0 e,-n, — It VI ei e - 1 0 **0 0(0 e, co r-~ N * oh,, - 4 Nn N r-4 MI r- n O Ln i * n r-I {' Or 1 N- r-i * *CO M N *04 U' 4 0 4t LA N-O N o r-4 r-4.4 — I ~ u- *.'1o' n * * * ~ ~ 0 ~ 0'i ~,- IN.-I - 0 00O u- *i O N- N O0' ~ 1 - - N OL'oou-i ~,-4 CD 0 NO uI) — N - 4' (l 0,0o —10 u- ot LA 4 ('"3 4 r- U O 0 (M i Ori C* 0 ~ N (O0 O 0 4 N c )- o t " O- 0 Or ~ -4 I. ~ 0- ~ - u-I 0d eO 04 0 0 c *-NNO rOO (30 e~ O - O C - Ln O e, *-r a% ~ q,-4 O r-4 e~ - o- 4 — o4 ~ ~ U' ~ 0< uU' O u N ON - e- O — N (9 - ~ 00 00 00*- 0r-I 0 N 0,-4 N *N -IOr-I 0 OO.-4 *OLA O-ON ON ~ -4 L C'- o r-I N N * -I e N 0 O4 *4 u -4 r-4 I nrI ~ LAN- N OCO -i i 0 O L o ~ A OLA %,ur-I.,,-4 40r-I-i ~ r-. Olr — oO' — e'-,- 4 4 t NO N * * N (1 ICo 0* co C O ~ O -N - -. r- ~r-I4 r-4 0 * 0 -Il —I Or-Ir-( * ou-I 0 * ^h O c'cm o 4(c *u-I 0 9 *%0%O NO O r-C c u-4 Or-(I ~ - C00 *r- O 0 - OO — I" r-, N r-4 00 - 0 0~0 U'% 0u u-r — 0 4 * fln 0 *ONr-Ir-iur-r —- 0 * u*-l *0 -4 co00 r sN O 00 u-oI 0C%.0 0 -q N * 0(M 0*- r-4Ijc 0 0 O-,- I O't-O-I eu- ~O % 0 O' r — 0t - r-~l -4 -I~ C 0 ~0 r- 00 0 c O -- u C OL - -N0 - r-i r- u-4 -C ~ -O r-i ~ O * O * O q> ~ -I-j n c,n O -, O ~ *o ~ O e N 0 (O -G0 * 0r-iN qO LA-N - - ON NC *Oc n O r-I *cm 04 - ~ 0e i %NO 0 - O n 00 0 ~ 0r-' O0 N Nl 1(C\j *Oi 0 Or-I 0N 0 Cn - ~ -lu —I - Od N O\ O' r' — u — 0 ~0 0 0 M C( r \r ~ L * - ~ r-I rl CO e r- lA I r- 0 O.o ru v 0 - u 0 r-4 1 - 0 N ~ L -I ~ 0 1N N O -r 40 r- 0 Or — (NJ- iN 0 0 r-4 0 O- e 0 CO 0 ON- O N CCn OOCO 4 oku-l( o 4cn co oo 000 *NC1 u -IN~ ON O V j V r-I 0 * in Mn 0 * * O Ch NOt-r 00 u-4 < 4UC4" u —I Nu< J C~ "* -4 C4 oi n *r-m *Lnuv-1 00 )O ON C r-4 0 O N- Or *O I O *- co- Or-I or-4 0 -, c O ~ r-4 ~ - r-4 * 0 0 e, Mr- Ir-I Or-I- r 0 O-r-' 0 009-4 0- 0,-i 0 0, 0 0 c,-I'C 0 r-l Nw r-f(r-I4 4r-C lAu- r-im U u-rIL r- iLr A *n 0 0 OC OD ~r — r O - 0 N - -,O' 0 0 0 N- (I N 0 M Oq 1c o 0sk Ok OD 00,-1 tLA N O4) 0 0 0k -0 r- C o r-i, *0o f-4 nOLcAfn (( n Nf M (cmr-O4 N U' C, ( a"r- "r- O' LA 0LAtiNc Ir'Ou-4 N Ou —I\j~~r-lIr-I o, m ON- Ncv W cnio 0 0 r- e r- I *0 * r -1 ~ o ~ N 0,0 ~ * N~ ~ *N~ o oN- ~ O) 4 Nw-u-4I U r- ~ r- ~ *Or- O 4r-N - * r-in * *r~Or- ~ - aO ~ *-4 r-I --- 0 N r-i r-I 00 *r-iLn u- r-i 00 O0 N' Cr-4 N0r-4i N( N O-4 * r-i ~ ONC (3 OU I,'- 0 * * ~0 4 - uLr O NAI O 04N O 0 *0(cr- * 0 O * rO- 0 * NN * *N l-N(N C(O1 0 0 0 N u-I O r-4 u-I r- 0 ~ - r- r — r- e-r-4 II r-G ~ O('.-r4 -H r- r- u-i (Cn r- If LA) r-e U, 1 ",r — 0 r-4 r-( -,'~ 0' 0 ) 000' 000 0. O.1 O0 ul, — a r-s,,0 0 0 4 ^-~ 0 CO O NNP- 4 0 0 N N0iLA M - O M r-CO (% co co oN ^r -LA NOc OD - tN4 ie I %ON4 0-0n r-Cn OD r-(%oN 0 1 Mco( M 04 oo'n rQ.N 000r-4 0 0r-044r-4r-ir-4 *crj *o j *e n r-'C *N- oN- o *O o C0 O0 0~fN - NInr-lr-r-rNJr-I4 r-iCSr-4Ncr-4>r-4 Ncr-4N -I\ u-r-Iq N9r-Cr-ij r-IU,-4 Ns Nq 185

APPENDIX I SUBROUTINE FNGFRI FOR CALCULATION OF MOODY FRICTION FACTOR BY COLEBROOK RELATIONSHIP

EXPLANATION OF THE EXTERNAL FUNCTION FNGFRI This external function solves by trial and error for the Moody friction factor using Colebrook relationship. It is good for both fully turbulent flow and for the flow in the transition zone. Explanation of its usage is as follows: FNGFRI (FTB, D, EE, QB, G, MV, FT) FTB = Set FTB = 1 for fully turbulent flow = 0 for transition zone D = Inside diameter of the pipe, in. EE = Pipe roughness, in. QB = Gas flow rate, ft3/day G = Gas gravity (mol wt/29.0) MV = Viscosity of the mixture, lb/ft/sec FT = 2/FM FM = Moody friction factor $COMPILE MAD, EXECUTE, DUMP,PRINT OBJECT FNGFR RSUBROUTINE FOR FANNING FRICTION FACTOR(1/SQRT(F)) RFOR FULLY TURBULANT SET FTB = 1.O, OTHERWISE SET IT ANYTHING RFT= 1/ SgRT(F) = 2/SQRT(FM) RREF. KATZ HANDBOOK EQUATION 7-239 PAGE 302 R EXTERNAL FUNCTION (FTB, D, EE, QB, G. MU, FT) E'O FNGFRI INTEGER FTB FT= 4.* LOG10O(D/EE)+2.28 FT2 = FT W'R FTB *E. 1 i T'O FB RE= 1.3526E-5* QB*G/(MU*D) LOOP FT1= FT2-4. *LOG10.(1+ 4.67*D* FT/(EE*RE ) W'R *ABS. (FT1-FT)/FT *L..001 T'O FB O'E FT= FT1 T'O LOOP E'L FB F'N E'N 187

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