THE U N I V E R S IT Y OF MI C H I GAN COLLEGE OF ENGINEERING Department of Chemical and Metallurgical Engineering Progress Report NEW CONCEPTS ON UNDERGROUND STORAGE M. Rasin Tek Donald L. Katz James O. Wilkes Robert L. Reid Leonard K. Thomas ORA Project 05625 under contract with: THE AMERICAN GAS ASSOCIATION NEW YORK, NEW YORK administered through: OFFICE OF RESEARCH ADMINISTRATION ANN ARBOR November 1963

TABLE OF CONTENTS Page LIST OF TABLES v LIST OF FIGURES vii INTRODUCTION ix 1. IMPERMEATION OF UNDERGROUND FORMATIONS 1 Silicate Grouts 3 Chrome-Lignin Grouts 3 Polymer Grouts 5 Polymerization Mechanism 5 Herculox 5 Furfural Grouts 6 AM-9 Chemical Grouts 6 AM-9 Solution Properties 7 AM-9 Gel Properties 8 Core Tests With AM-9 8 Engineering Calculations on Injection of Grouts 8 References 20 2. UNDERGROUND STORAGE IN NON-POROUS SPACE 21 Salt Cavern Storage 23 Location of Dissolved Salt Caverns 23 Safety Considerations 24 Strength Data for Salt 24 Deliverability of Natural Gas From Salt Cavern Storage 25 Stress Considerations 27 Creation of Salt Cavern Reservoirs 27 Determination of the Size of Dissolved Salt Caverns 29 Recovery of LP Gas From Caverns 32 Mined Storage 33 Locations 33 Coal Mine Storage 34 Hard Rock Mined Storage 34 References 37 3. DETECTION AND REMEDY OF LEAKS FROM STORAGE RESERVOIRS 40 Overpressuring of Storage Reservoirs 40 Leakage Across Cap Rocks 42 Concept of Threshold Pressure 44 iii

TABLE OF CONTENTS (Concluded) Page Previous Theoretical Investigations 46 The Scope of Present and Future Theoretical Work 48 References 51 4. FRACTURING 53 Literature Survey and Design Calculation 53 Fracture Extent 53 Fracture Width 59 Pressure and Horsepower Requirements 69 Fracturing Fluids 70 Propping Agent 75 Design Procedure 77 Example Problem 78 Nomenclature 82 References 86 iv

LIST OF TABLES Table Page 1.1 Properties of Conventional Silicate Gels 4 1.2 A Typical AM-9 Formulation 7 1.3 Gel Properties 18 1.4 Factors Affecting AM-9 Gel Time 19 2.1 Costs of LPG Storage 36 4.1 Estimates of Young's Moduli of Formation Rocks 84 4.2 Injection Rates (Recommended) for Various Tubing Sizes 84 4.3 Fracturing-Treatment Cost Comparisons for Fluids of Various Fracturing-Fluid Coefficients Pumped at Different Injection Rates 85 v

LIST OF FIGURES Figure Page 1.1 Typical application of grouting to aquifer storage. 10 1.2 Radial grout penetration as a function of setting time and aquifer depth for a pressure of 0.9 psi/ft. 12 1.3 Application of fracturing and grouting to aquifer storage. 13 1.4 Linear grout penetration as a function of setting time and aquifer depth for a pressure of 0.9 psi/ft. 15 1.5 Optimum well spacing as a function of aquifer height for various depths. 17 2.1 Salt cavern storage variation of reservoir pressure with time for various degrees of water replacement. 28 2.2 Three methods of developing cavities. 30 2.3 A simplified view of a salt storage well. 31 2.4 Average cavern diameters as determined for equilibrium pressure calculations. 31 2.5 Geological formations suitable for construction of these underground storage caverns are found in many parts of the U. S. 35 3.1 Effect of depth on discovery pressures for various reservoirs. 41 3.2 Effect of overpressure on storage capacity of a reservoir. 43 353 Imbibition and drainage capillary pressure curves. 45 4.1 Nomogram for determination of C1. 56 4.2 Nomogram for determination of C11. 56 4.3 Fluid loss test results. 58 vii

LIST OF FIGURES (Continued) Figure Page 4.4 Nomogram for determination of C111. 58 4.5 Fracturing efficiency versus x. 58 4.6 Nomogram for determination of fracturing efficiency and fracture area. 60 4.7 Crack widths for restricted vertical fractures resulting from Newtonian fluids in laminar flow. 62 4.8 Crack widths for restricted vertical fractures resulting from Newtonian fluids turbulent flow. 62 4.9 Crack widths for restricted vertical fracture resulting from non-Newtonian fluids in laminar flow. 64 4.10 Approximate crack widths for horizontal fractures resulting from Newtonian fluids in laminar flow. 66 4.11 Viscosity of a slurry containing suspended solid material compared to the viscosity of the basic fluid. 68 4.12 Pressure loss due to flow of Dowell's Waterfrac 60 through various conduits. 71 4.13 Effect Of sand concentration on fluid head in psi/ft. 72 4.14 Effect of fluid loss control additive concentration on fluid loss for a specific crude. 74 4.15 Restricted and unrestricted vertical fractures. 63 viii

INTRODUCTION During the Spring of 1963, under the sponsorship of the American Gas Association, a research project was initiated at the University of Michigan to ".... formulate and explore new concepts on underground storage." The prolific growth experienced during the last decade on production, pipelining, storage and consumption of natural gas has justified recent deployment of significant research effort on various aspects of natural gas storage. The AGA Project NO 31 concluded during 1963 had as its main objective understanding of the ".... movement of water in contact with natural gas." Because practically all producing or underground storage reservoirs are subject to some degree of water drive, the extent and the nature of water movement is of utmost importance if accurate, reliable predictions are desired on the behavior of gas storage bubble. The AGA Monograph on "The Movement of Underground Water in Contact with Natural Gas" documents the final results on Project NO 31 where practical solutions to many gas storage problems were presented in minute detail. While the AGA Project NO. 31 basically implemented engineering research effort on macro-reservoir scale, a cognate research program sponsored by the Michigan Gas Association and still in progress at the University is directed toward the physics of microscopic phenomena where natural gas and water displace one another in a porous matrix. Both of these research programs provided definitive, quantitative answers to many problems while uncovering perhaps an equal number of problems yet to be solved. ix

The original underground storage projects were located in depleted gas or oil reservoirs, formations with well proved ability to retain hydrocarbons under pressure. In storing the gas in such natural reservoirs a very significant breakthrough was made when the practice of "overpressuring" became a practical reality. The injection of gas in these formations to pressures above the discovery resulted in large increases of the storage capacity of existing reservoirs. Ever increasing developments in production, processing and consumption of natural gas continues to result in expansion of marketing areas, particularly near highly populated industrial centers. Many such areas located in the Northeast and North Central United States and Eastern Canada have little proved natural gas reserves. These areas are normally supplied by long-distance pipelines, some as long as. 2000 miles from reserves located in Southwestern United States and Western Canada. Economic considerations in the operation of such pipelines require that their service load must be maintained as continuously near their design capacity as possible if low transportation cost is to be realized, In order to keep these pipelines full and in operation during the low domestic demand in summer the gas must be stored somewhere underground during the summer in areas where depleted gas or oil reservoirs are not generally available. During. the last decade this too became a reality in the development of "aquifer storage" where the pore volume for the storage was created through expulsion of water from its native formation by injection of gas into aquifers at pressures above the discovery pressure. A second breakthrough in gas storage was made when the movement of water in contact with natural gas was x

quantitatively related to the performance of the gas storage bubble. Through successful applications of digital computing techniques significant new contributions were made to our understanding of the behavior of gas storage reservoirs subject to water drive. Here too, along with new data, solutions, and contributions, a large number of new problems were uncovered. The physical processes leading to the development of the storage bubble during early stages of gas injection, mechanical and flow properties of caprocks related to leakage or breakage, nature of threshold pressure phenomena, instability and hysteresis of gas-water displacement phenomena are but a few of such typical problems uncovered during recent research work. While the expanding gas market does and will continue to foster the search for new gas reserves in areas of acute need, it was recognized that development of new ideas, new techniques and new concepts for gas storage must be explored if the industry is to meet the long range necessities indicated by the future expansion of the gas market. During the initiation of this research project it was further recognized that there are vast areas in the United States and Canada where sedimentary rocks do not exist. There were practically no underground storage reservoirs for natural gas in the forties, depleted gas or oil field storage since the fifties and aquifer storage during the last decade. At present, aquifer storage, if and when operated successfully, appears to be the most economical method for areas devoid of depleted oil or gas fields. It is well known, on the other hand, that the success of aquifer storage depends critically on the presence of suitable subsurface geology. Sufficient porosity, adequate permeability and satisfactory caprock and structural closure are the prime requirements xi

for such storage. Even in areas where sedimentary rocks abound the above factors do not always simultaneously co-exist, Sufficient porosity and permeability but lack of adequate closure, adequate structure but leaky caprock, semi-open, saddle type structure or no anticline at all are typical examples of such imperfect condi%tions. The storage of gas in such strata requires new- techniques, new concepts which have not been suggested or adequately explored to date. The basic objective of this research project is to formulate and explore "MNew Concepts on Underground Storage." It must be clear from the preceding review and introduction that a study of this type should be approached by a review of all existing methods of underground storage as related to geographic, geologic or geophysical conditions to which they are best suited. This report combines presentation of such a review along with new ideas and concepts suggested -and systematically analyzed during the first eight months of the research project. The evaluation of new techniques and concepts is of course not final but in progress at this writing. It might be appropriate at this point to list areas now under study and where potentially practical and economical new concepts and techniques are being developed. 1o Storage in semi-open or fully open structures where the movement of gas may be controlled through application of hydraulic control or soil impermeatior by injection of grouts. 2. Storage of gas in non-porous void continuum such as salt caverns, mine shafts, etco 3. Detection and remedy of leaks from aquiSfer storage. xii

4. Novel concepts in gas storage - surface sands, gravel pits, underwater storage. 5. Underground storage through soil impermeation by fracturing and grouting; design of artificial caps and storage bubble boundaries, xiii

1. IMPERMEATION OF UNDERGROUND FORMATIONS A large number of practical engineering problems encountered in subsurface construction, drilling, s:torage and mining require stabilization of soil using artificial techniques to impermeate the porous formation' along specifically controlled geometries. - Underground storage of natural gas whether in depleted oil or gas reservoirs or in aquifers depends critically upon the existence of an impervious cap.to prevent escape of natural gas to shallower or adjacent formations under the influence of buoyancy.. The possibility of gas leakage across the caprock or the prospect of using subsurface sands with high porosity and permeability but no suitable cap for underground storage- point to the interest in the possibility and desirability of application of special chemicals to permit soil stabilization along desired geometric -conflgurations. The process by which a special chemical solution is injected into the pores of a porous material to render it impervious to fluid flow across it is called "GROUTING". Research work on the composition, properties, and applications of grouts have been quite limited to shallow subsurface construction work and some laboratory studies by manufacturers of grouts. The information available in the literature on the application and success of grouting processes have been limited to a large extent on impermeation on an exposed surface. There has been very little, indeed if any information on the application of grouts to problems encountered in underground storage of natural gas. In order to explore and evaluate physical possibility and economic feasibility of subsurface grouting to remedy leaks from underground storage reservoirs, to provide storage pore volumes of sufficient size, shape, and characteristics, part of the research effort on the "New Concepts on Underground Storage" Project has been directed toward the study of problems associated with grouting. There are two kinds of grouting materials generally available in the industry today. These may be classified as suspension grouts and truesolution chemical grouts. The suspension grouts such as cement and 1

bent'onite have rather widespread application as, surface impermeating materials. These grouts, on the other hand, cannot be used in areas where it is desired to inject the grout beyond the surface pores of the formations. The lithology of typical porous formations where grouts must be used in such that the size of the pores are smaller than those of the particles in suspension in the grouts. In order to impermeate sandstone, limestone, dolomite or shale type of formations, one must go to applications of true solution grouts. A laboratory study of physical properties of various grouting agents, a systematic compilation of their significant characteristics and evaluation of their injectability into porous plugs and typical field formations, their flow properties, injection, setting, impermeation properties have been the primary objectives of the initial research work reported in the following chapte r. 2

Silicate Grouts The first chemical grouts were based on sodium silicate, but although sodium silicate is the basis of the silicate grouts, many formula variations have been patented. A survey in 1957 revealed patents on 27 non-soluble and 17 soluble silicate formulas. Examples and properties of the older silicate gels are listed in Table 1. 1. As can be seen from the tabulation, the compositions giving high strength gels had to be injected by the impractical and expensive two shot method. However, Diamond Alkali and Halliburton have recently introduced a one-shot silicate gel which has the strength of the two shot-gels. A limitation, however, of the silicates is the viscosity of the silicate solution, about 5-12 centipoises. Although silicate gels are still being investigated, they do not seem to have the low viscosity that this application requires. Chrome - Lignin Grouts The least expensive chemical grout is based on calcium ligno - sulfonate, a by product of the paper pulp industry. When catalyzed by sodium dichromate, a gel called chrome-lignin forms. An accelerator such as ferric chloride is sometimes used. The gel time can be controlled by varying the amount of catalyst and accelerator as well as the amount of water. Since water influences the setting properties, the material is highly sensitive to dilution with ground water, The viscosity of the chromelignin solution is 3-12 centipoises at room temperature; however, this viscosity increases from the moment of mixing until the gel forms, If dilution does not occur, these gels set with reasonable strength. Although this material has many desirable properties, its use may be limited in the gas storage formations because of its sensitivity to dilution. 1o 1* The numbers in upper script parentheses refer to literature citations given at the end of each chapter. 3

TABLE 1. 1 Properties of Conventional Silicate Gels Class Process Examples Strength of Gel Time of Set non-soluble one shot 1. Na2CO3 or Na2SO4 Low Sets immedisilicate or water glass to ately upon conmix with salt water tact with formin formations. ation water. 2. Ester of silicon which hydrolyzes non-soluble two shot Silicic acid- High Sets when gas containing substance reaches solfollowed by CO2 gas ution. soluble one shot 1. Sodium silicate + 1.Low 1. Sets slowly silicate sodium bicarbonate over a period of time. 2. Soluble silicate + 2. Low? 2. Gel time weak base controlled with pyridin, ammonium persulfate or ammonium acetate. soluble two shot NaSiO3 followed by High Sets when gas silicate CaC12 + COa(gas) reaches solut ion. Definitions: *' one shot process - Injection of a single solution that gels after a period of time. ** two shot process - Injection of a solution, followed by the injection of another solution which reacts with the first solution to form the gel.

Polymer Grouts Many polymer materials have also been used as chemical grouts. At least twenty different materials have been used ranging from a formula consisting of'furfural + urethane to one consisting of unsaturated fish oil + petroleum distillate + carbon tetrachloride + sulfur monochloride, In general, these materials fall into three classes:'(1) completely polymerized molten materials, (2) partially polymerized materials that complete their polymerization in the ground'formation, and (3) unpolymerized materials that polymerize in the ground formation. In regard to the present problem, class (1) and class (2) polymers probably are too viscous to flow through the porous media at reasonable rates. However, class (3) polymers seem to offer a satisfactory solution to the problem. Polymerization Mechanism Most of the class (3) polymerization reactions proceed by a free radical mechanism. An initiator, a catalyst, and an inhibitor are added to the monomer solution to induce and control the free radical polymerization. The initiator causes the catalyst to decompose into free radicals whereupon an induction period follows before polymerization starts. The inhibitor prolongs this induction period. The length of the induction period is controlled by the relative amounts of initiator, catalyst, and inhibitor present. When polymerization finally starts, the complete polymer is formed in a few seconds, Herculox Herculox is a hard setting resin grout available from Halliburton which can develop high compressive strengths. An extremely high strength is developed even though the initial viscosity of the solution is relatively low. This viscosity, however, may be too high for injection into porous media, In addition, the high strength of this gel is probably not needed for impermeation of sandstone but his grout may be excellent for the plugging of cracks and fractures, 5

Furfural Grouts The furfural gel was originally developed by Phillips Petroleum for sealing porous walls in oil wells. Laboratory tests indicate that this material may be useful in imperating sandstone or other typical formations in underground storage applications. The gel is prepared with furfural and thiour.ea with hydrochloric acid as a catalyst. Gel times of 4 to 6 hours have been obtained in the laboratory with about 3 hours required for complete formation of the gel. The viscosity has not yet been measured, but the solution appears very fluid although thickening occurs over a period of time. Since furfural is relatively inexpensive (obtained from corn cobs), this gel could be an inexpensive solution in problems where large injection volumes are required. AM - 9 Chemical Grouts Another grouting material on the market at present is American Cyanamid's AM-9 Chemical Grout. The AM-9 is supplied as a fine white powder and is a mixture of N, N'-methylene-bisacrylamide and acrylamide. The catalyst for the system is B-dimethylaminopropionitrile (DMAPN), the initiator is ammonium persulfate (AP), and the inhibitor is potassium ferricyanide (KFe). The AM-9, DMAPN, and KFe are dissolved in a water solution which is stable and can be stored for 24 hours if kept out of sunlight. The AP is dissolved in a separate solution and added to the AM-9 solution immediately before injection. 6

Table 1. 2 below gives a typical composition for AM-9 material. A typical AM-9 Formulation 1. AM-9 solution Weight (gm) per 100 gm of grout solut ion H2O 79. 000 AM- 9 10. 000 DMAPN.400 KFe 0. 025 2. AP solution H 0 10. 000 AP 0. 500 Gel time =2 hours at 600 F. AM-9 Solution Properties The outstanding characteristics of AM-9 are its low induction period viscosity (constant over the induction period at 1.6 cp) and its accurately controllable gel times. However, it does not appear that the gel times can be made longer than two hours if complete polymerization is to be insured. Another disadvantage is the gel time sensitivity to pH and temperature. Below a pH of 6. 5, the gel times become long and indefinite. Furthermore, temperature increase of ten degrees can cut the gel time in half. The factors affecting the gel time are summarized in Table 1.4. Because of AM-9's low viscosity, it is very effective in impermeating fine materials. However, considering the relationship between permeability and pumping pressure, it is uneconomical to stabilize very fine materials near the surface because of the difficulty of attaining high pressures. On the other hand, AM-9 was very effective in sealing fine sandstone in a deep shaft where 2000 psi pumping pressure was feasible, 7

AM-9 Gel Properties Another advantage of AM-9 is that it is impermeable to water, gases, and hydrocarbons in gelled state. In addition, it will displace water when it is in the liquid state. However, if the ground water is flowing rapidly the solution will be diluted on the periphery and will be displaced somewhat, If turbulent flow conditions are encountered, the dilution effect can be minimized by increasing the AM-9 concentration to 15-20% and by using special formulations to obtain short gel times. On the other hand, if the gel is injected into very dry materials, gravitational and capillary force will act to greatly disperse the solution, rendering it ineffective. While the AM-9 gel has good water retention properties, under dry conditions a small amount of water will escape causing shrinkage of the gel. Since soil does not shrink, the induced stresses may cause rupture of the gel-soil bonds. This may appear as a visible shrinkage crack. When exposed to humid conditions, the gel will expand and fill the voids but the rupture will not be healed. Strength and good impermeability will then be lost. This probably would not be a problem in deep formations as the water content of the formations remains high. Core Tests With AM-9 Preliminary tests with sandstone cores have indicated that AM-9 will satisfactorily impermeate the porous media. After AM-9 was injected into the cores and allowed to set, the cores were able to withstand substantial pressure. One core held to 150 psi while another held at 200 psi. It appears that this degree of impermeation will be satisfactory for the underground storage of natural gas. For a complete quantitative evaluation of gas withholding properties of grouts, studies in capillary inhibition, drainage and threshold pressures are now being planned for future work, Engineering Calculations on Injection of Grouts Before the grouting material can be injected into a porous formation, pressure requirements and well spacing must be determined to provide 8

adequate grout penetration. The following example problem illustrates a method of determining the radius of penetration as a function of the well bore pressure. It is desired to impermeate an aquifer 50 feet in thickness located at a depth of 2000 feet. The sandstone has a permeability of 250 millidarcys and a porosity of 0. 15. The grouting material is to be injected from a well 1/4 feet in radius to the porous matrix. Using a grout solution of 1. 6 cp viscosity, a gel time of 10 hours specified. Figure 1. 1 illustrates the field problem where such an impermeation might be desired. Formation parting pressure is usually taken as 1 psi/ft. of depth so this pressure is the maximum for grout injection without fracturing the formation. A 10% safety factor may be used making the well bore pressure 0. 9 ps:i/ft. of depth. A dimensionless flow rate is defined as: Qt (6. Z83)6chr2 (Pg - Pf) P g where: 3 2 2 21 q = total cumulative influx (ft3) = 6Th(r - r )~6trhr? = porosity = 0. 15 c = compressibility of grout solution, ( psi (assumed same as H20) = 7 x 10-6 psi-l h = formation thickness ft. r = radius of penetration (ft). Pw = pressure at the well pore (psi) = 1800 psig. pf = formation pressure (psi) = Pgg = 866 psig. gc rw = well bore radius (ft) = 1/4 2 2 61 hr __ r Qt =(6. 283)?chrpZ(w - Pf) (6. 283) Crp (pw - Pf) p P w A dimensionless time is defined as: (2. 634 x 10-4) kt (1. 3) o [ 5 cr 2 9

SAS A FIG. 1.1 TYPICAL APPLICATION OF OROUTING TO AQUIFER STORAGE. (I PERMEATION OF SPILL POINT)'~""'~ " ~ J ~*,... ---- rrrCI, ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ _ — AQOIF ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~..,

where: t = injection time (hours) = 10 hours k = permeability (md) = 250 md. = grout solution viscosity (cp) = 1. 6 cp. -4 (2. 634 x 10 )(250) 6t 5 6. 28 x 10 o (1. 6)(0. 15)(7 x 10-6)(0. 25)2 6. 8 x 10 Qt and to are related and the corresponding values are tabulated on pages 424 - 426 of reference 6. (For radial flow, infinite aquifer, constant 6 5 terminal pressure). For to = 6. 28 x 106,,t - 8. 19 x 10. Solving equation (2) for r, we obtain: r = \ (6. 283)(c)(rp2)(pw - pf) Qt (1 4) -6 2 j(6. 283)(7 x 10 )(0. 25) (1. 9)(2000) - 866 Qt 3. 1416 r -(8 17 x 10 Q (8. 17 x 10 )(8. 09 x 10 ) r = 25. 5 ft. Figure 1. 2 presents a plot of grout penetration radius as a function of total pumping time for various depths. Another typical application of grouting to aquifer storage is illustrated in Figure 1. 3. This application follows a fracturing treatment in a sandstone formation. Since the propped fracture will have a very large permeability, the pressure throughout the fracture can be assumed equal to the well bore pressure. Therefore, linear flow from the fracture becomes the primary consideration. Once the fracture has been created, well bore pressure must be maintained below the fracturing pressure to prevent possible undesirable fracture extension. Therefore, in the following example, 0.9 psi/foot was used for the well bore pressure. In this case using equation for linear flow7: We = 1. 13 1CA(Pw - pf) 0. 00633kt (1.5) 11

'l4/ISd 6.'0 iO 3unsS3Ud V HOl Hld3O 31mn'oV ONV 3V1l 9NI1135 N O N S N0IN V OIIV3N3d lrou9 tVIOVt Z'I'91. - (SUNOH) 3Wll 01 8 9 t z O 0 In 0 r) 01 o 0 0( 00 -I

....HORIZONTAL FRACTURE 1 ~2000' /GROUT 600' SANDSTONE' SANDSTONE,_H ---— ~ lII SANDSTONE --- _ _ VERTICAL FRACTURE AQUIFER E SANDSTONE GROUT FIG.I.3 APPLICATION OF FRACTURING AND GROUTING TO AQUIFER STORAGE ( NO CAPROCK ORIGINALLY ).

where: We = total cumulative influx (ft3) T'r 2h = porosity = 0, 15 C = compressibility of grout solution, psi = 7 x 10 psi 1 2 A = area = r = well bore pressure = (0. 9)(2000ft) = 180 psi. k = permeability = 250 md t = injection time (days) = 10/24 t -= viscosity = 1. 6 cp. r = radius of fracture = 600 ft. h = depth of penetration of grout, ft. pf = formation pressure (psig) = pg sh = 866 psig. gc 0. 00633kt Ih = 1. 13 6 CTr2)(p - pf ) 0. 0063kt h 1 (0.00633(25 0)0 - h = (1. 13)(0. 15)(7 x 10 6)(2000 - 866) 24 (7 x 10-6)(1, 6)(0. 15) h 0. 84 feet. Figure 1. 4 is a plot of grout penetration as a function of total pumping time for various aquifer depths. Once the required well bore pressure has been determined the power requirement for the pumps must be calculated. Although these power requirements have been determined, they are not presented here, Such power requirements would only be of interest in the final mechanical design for a field test and therefore are not considered within the scope of current investigation. A matter of economic importance in aquifer grouting is the optinum well spacing for lowest cost. Cost - grout cost + well cost. 14

L2Z 0.8 z w I — O 2 6 10 TIME (HOURS) FIG. 1.4 LINEAR GROUT PENENTRATION AS A FUNCTION OF SETTING TIME AND AQUIFER DEPTH FOR A PRESSURE OF 0.9 PSI/FT. 15

L number of wells needed. 2r 2 3 gTIr 2h ft of grout needed. Cost = - Ir 2h (7. 48)A + Bd- (1 7) 2r + r where: d = depth of formation, ft. h = height of aquifer, ft. = - porosity of aquifer r = radius of penetration, ft. L = length of grout wall, ft. A = cost per gal of gel solution B = cost per foot for wells (includes pumping) Finding the minimum of equation 7, we obtain: d(cost) L 6'h(7 48)A LBd dr = 2'2 r2 r (8) = Th (7. 48)A (8) Example: d = 1000ft. h = 30 ft. = 0. 20 A = $1.00/gal. B = $10.00/ft. (r 10)(1000) (0. 2)('T)(30)(7. 48)(1) r = 26.6 ft. spacing = Zr = 53. 2 ft. Figure 1. 5 presents a plot of optimum well spacing as a function of aquifer thickness for various depths. 16

160 120 d uJ 80 40 I I I I 0 30 50 70 AQUIFER THICKNESS (FT.) FIG. 1.5 OPTIMUM WELL SPACING AS A FUNCTION OF AQUIFER HEIGHT FOR VARIOUS DEPTHS.'7

Table 1. 3 below summarizes physical properties, cost and characteristics for various gels. Table 1.4 is a compelation of factors affecting gel time for the AM-9 grout. TABLE 1.5 3 GEL PROPERTIES AM- 9 CHROME- LIGNIN HERCULOX SILICATES 1. Initial 1. 3-1. 6cps 3-12 cps 10-13 cps 5-12 cps Viscosity ( 10%soln.) 2. Visc. - Fairly conTime Re- constant Increases some constant lationship with time 3. Compressive 70 psi 53 psi 1400 psi 140 psi Strength (30% soln. ) 4. Gel Time 0-2 hrs. 0-7 hours 0-5 hrs. 0-7 hrs, (700F) 0-10hrs 1000C 5. Stability'" permanent permanent pe rmanent loses some water 6. Cost 1.50/gal. 17-.40/ 1. 25/gal less than (tentative) gal. 040/ gal. 7. Toxcity Monomer is Do not use Vapors are Safe for contoxic, Gel does close to ground toxic. Do tact with not harm water supply not use in water supplies. ground water. unventilated places. 8. Corrosion corrosive least corrosive Most cor- least corData*'"' ros ive rosive 9. Sensi- Can be di- Very sensitive Not easy to No infortivity to water luted to a 3% to dilution dilute, but mation. dilution soln. it can be diluted. 10. Time from first bit of gel 0 hours 24 hours 24 hours 0 hours. to complete gel. "Sodium silicate gels made from lignon liquor treated w ith ammonium hydroxide give unstable gels, while those treated with lime yield stable gels. *,. None of the above grouts present serious corrosion problems. 18

TABLE 1.4 Factors affecting AM-9 Gel Time Factor Effect of Gel Time 1. Reduction of AM-9 concentration Slight increase 2. DMAPN, AP, and Too much or too little will proKF3 concentration duce weak gels or none at all. Lower limit is 0. 4% for DMAPN, 0. 25% for AP, and upper limit for KFe is 0. 035%.o 3. Temperature 10% rise cuts the time in half. 4. pH Best range is 7-11. DMAPN maintains pH at 8-9 except at high acid concentration. Below pH = 6. 5, gel times are long and indefinite. 5. Air If solution is saturated with air, the gel time is longer. 6. Metals Iron, copper, and copper alloys decrease gel time. Most use aluminum, stainless steel, plastic or rubber equipment. 7. Mix Water Impurity in mix water may affect time. Test should be carried out with water that will be used in the field. 8. Sunlight Sunlight will gel AM-9 solutions left uncovered. 9. Inhibitors Although most polymerization inhibitors can be used, these will result in weak gels. KFe does not hurt the strength. 10. Hydrogen sulfide Shortens gel time. 11. Salts Soluble salts (NaCl, CaC12, e tc), present in the formation decrease gel time although increasing strength. 12, Freezing Prevent by using any commercial antifreeze, 13, Insoluble material Fine insoluble particles such as clay or bentonite slow down the gelation to some extent 19

REFERENCES 1. 1. "Chemical Grouting, " ASCE Proc. v83 (Journal of the Soil Mechanics and Foundations Division) n SM 4, November 1957, Paper n 1426, 106 pages. 1. 2. Pamphlet "AM-9 Chemical Groat", American Cyanamid Company. 1. 3. Soluble Silicates, James G. Vail, Vol 2, Reinhold Publishing Co., 1952. 1. 4. "Field Experiences with Chemical Grouting", Milos Polivka, Leslie P. Witte, and John P. Gnaedinger. ASCE Proc. (Journal of the Soil Mechanics and Foundations Division) n SM 2, April 1957, paper n 1204. 1. 5. Various Publications of Halliburton Company (Grouting Service). 1. 6. Handbook of Natural Gas Engineering, Katz, et. al. McGraw Hill. 1. 7. Movement of Underground Water in Contact with Natural Gas, Katz et. al., Monograph American Gas Association, 1963. 20

2. UNDERGROUND STORAGE IN. NON- POROUS. SPACE The storage of first manufactured and later natural gas has evolved in the past along a pattern closely related to development and growth of production and consumption of natural gas. Through the years, this pattern followed the sequence from storage in surface tanks, to underground storage in depleted gas or oil reservoirs and finally to storage in aquifers. For reasons of capacity, economy and safety, the surface storage in tanks is now virtually completely out of the picture. On the other hand, wherever possible a depleted natural gas reservoir usually offers perhaps the most reliable means for underground storage of natural gas. Such a subsurface storage volume not only.has the distinct advantage of having been proved by nature throughout the geologic ages to retain the gas in-place but usually is of large capacity. Such subsurface formations also have the added feature of being well known, charted and adequately understood from the viewpoints of reservoir engineering by the time they are depleted and ready to revert to storage service. As experience and knowledge on properties of such a reservoir is added through reservoir engineering, as resistance to fracturing, threshold pressure, permeability, compressibility, etc. becomes better known and the extent and nature of water drive along with subsurface geometry is understood and verified, the practice of "overpressuring" such reservoirs within safe limits usually adds appreciably more storage capacity to the depleted gas producing field. The depleted oil reservoir affords approximately the same advantage as the depleted gas reservoir. Existence of reliable cap, suitable structural trap, reservoir properties determined from data collected throughout the producing life of the reservoir, e s timation of original and actually recovered reserves, thus of the pore space are among many typical characteristics quite helpful in initiation and maintenance of gas storage in such reservoirs. As opposed to these and some other advantages, however, the storage in depleted oil reservoirs poses some rather difficult engineering problems of unique nature. These problems usually stem from the presence of unrecovered residual crude oil in the pore space. The miscibility of 21

residual oil with injected gas, low relative permeability due to two phase flow, handling of the production of oil along with gas, difficulties in reconciling the inventory gas with production pressure behavior of total reserves are typical of problems which must be dealt with in storing the natural gas in depleted oil reservoirs. During the last decade the phenomenal growth of domestic consumption of natural gas precipitated the acute need for storage of natural gas in areas where there are no depleted oil or gas reservoirs present. The advent of aquifer storage where the pore volume necessary to store the gas is created by pressurizing aquifers above their discovery pressure through gas injection provided during the last decade very substantial storage reservoirs in such areas of need. 2. 40 The storage of natural gas in aquifers depends upon existence of suitable structure, closure, and, cap rock. These factors though perhaps more readily or more frequently available along with suitable porosity and permeability close to areas of high domestic gas consumption than producing or depleted gas or oil reservoirs are not always altogether present, Quite often an aquifer sand of high porosity and permeability will exist at some reasonable depth but will not have adequate structural closure. Quite often, on the other hand, such a structure will have adequate closure, but unfortunately no suitable cap rock. Other times, impervious cap rock, good porosity, high permeability will be present but only a semi-open structure will delimit the subsurface geology. There has been substantial amount of field data gathered recently indicating that caprocks overlying many storage reservoirs are subject to leakage of gas to shallower formations when the gas pressure exceeds a certain critical value. Such leaks are sometimes area distributed and related to drainage capillary pressure characteristics of the shale. At other times, it appears that the leak may be along a fracture line and primarily due to having the gas overpressure in excess of the threshold pressure of the shale. The possibility and desirability of storage in aquifer sands where one or more of the prime requirements is non existent, or storage in 22

depleted petroleum reservoirs above the original content of hydrocarbons, beyond levels indicated by location of spill points all point to needs of new concepts in underground storage where soil impermeation should play a significant role. 2. 39 There are many areas in the United States where sedimentary rocks are known to be practically nonexistant. Some of these areas are located near industrial complexes in highly dense populated areas where underground storage must depend on relatively or entirely new concepts and ideas. Subsurface storage of natural gas, in non-porous, void continuum such as salt caverns, mine shafts, have been suggested and empirically tried to limited extents in the past. Near surface porous storage in such areas as gravel pits, sand dunes, surface sands and the possibility of gas storage under lakes or oceans are among many new concepts which will be reviewed and discussed in the following. Salt Cavern Storage For many years, natural gas producers have needed a way to store their product near the consumer to provide a buffer during peak consumption periods. Storage in underground void spaces such as mines and salt cavities has been suggested as a means to provide such a reservoir for natural gas, Some technology is available in this field as liquified petroleum gases (propanebutane) have been stored in mines and cavities for over ten years. As early as 1952, the Natural Gasoline Association of America prepared standards for the operation and testing of underground storage wells. Location of Dissolved Salt Caverns Cavities may be formed in either salt beds or salt domes. Salt beds occur in the western part of Texas, Oklahoma, Kansas, and eastern New Mexico and in the Great Lakes region of Michigan, Ohio, Pennsylvania, and New York. Salt beds also occur in the Uintah Basin in Utah and Colorado outcropping at the surface in some areas and down to depths of 7000 ft. in others. In the Texas-Oklahoma-Kansas-New Mexico area, the salt beds range in depth from 1000 to 2000 feet and in thickness from 50 to 100 feet. In the Great Lakes region, the beds range in depth from 1500 to.7000 feet 23

and in thickness from 1-400 feet. Almost all of the beds contain thin layers of shale, anhydrite, etc. This causes some problems in the formation of cavities. Salt domes are for the most part located along the Gulf Coast of Texas, Louisiana, Mississippi, and Alabama. These domes vary in depth from near surface to depths that lie beyond the reach of present day drilling equipment. The dome usually consists of nearly pure rock salt. Salt domes 2. 33 are usually the best formations in which to provide underground storage. Safety Considerations The acid industry, as well as others, have brine wells exceeding 1, 000, 000 bbl. in cavern volume. A cave-in in a cavity containing brine usually does not involve serious damage to surface equipment. Collapse, fracture, or leakage of an LPG or natural gas storage cavity, however, may 2. 21 result in serious leaks, explosions or fires. It is, therefore, important to design the cavern within the limits of various safety considerations. Strength Data For Salt A specific safe limit to cavern size is, at the present time, virtually impossible to calculate. In homogeneity of rock compacted through complex geological processes confronts the designer with such variables as fracturing, slams, and faults. Some data for anhydrites and salt formations are available from core samples. A typical sample taken from salt formation at 2000 feet in West Texas, for instance is reported to yield the following data on 2 21 unconfined compressive strength. Salt - 2600-4000 psi Anhydrite - 4500-23, 000 psi 20 21 Ultimate compressive strength when confined, was found to be: Salt - 17, 000 psi @ 2000 atm and 1500C. Anhydrite - 82, 000 psi C(D2000 atm and 150~Co Triaxial tests on anhydrite under formation pressure conditions indicate ultimate shear strength in the range 12, 000 to 14, 200 psi while measured 2. 21 compressive strengths reached 28, 000 psi. The following fundamental properties of the aggregate salt from the Grand Saline salt mine were de term ined: 24

The maximum compressive stress 2300 psi with the standard deviation 200 psi The 0. 5% yielding stress 2000 psi 6 Young's Modulus 0. 14x10 psi 6 with the standard deviation.03x10 psi Poisson's ratio with the compressive stress up to 300 psi 0. 25-0. 5 with the compressive stress over 300 psi 0o 5 Deliverability of Natural Gas from Salt Cavern Storage When natural gas is stored in a salt cavern, the stress condition induced in formations surrounding the dissolved cavity depends upon mechanical characteristics of these formations, weight of the overburden, shape of the cavity and the pressure of the gas inside the cavity. In the early phases of development of salt cavern storage because of uncertainty of stress calculations, it was felt that one would probably have to maintain full hydrostatic pressure at the salt cavern in order to prevent collapse due to the weight of the overburden. To make this possible, saturated brine would have to be pumped in and out during each production injection phase of the storage. In other words, a dissolved salt cavern 2000 feet deep would be maintained say at 860 psig all the. time. This cavern pressure can be maintained if every cu. ft. of gas pumped out is replaced by a cubic ft. of brine pumped in and vice versa. Accordingly, it becomes interesting from a storage engineering view point to determine the brine pumping requirement necessary to maintain cavern pressure at varying rates of gas deliverability. If the water pumped into the cavern only partially replaces the gas being produced, then the cavern pressure drops as a function of time accordingly. In the following example, a relationship will -be derived for predicting the decline of -cavern pressure versus time for various fractions of brine replacing the gas withdrawn. In order to fix the ideas, let us assume that: (1) Cavern has a volume of 109 ft3 and is located 2000 feet below the surface; (2) Withdrawal rate is 50 x 10 SCF/day; (3) Cavity temperature is constant at 100 F. 25

Qs = withdrawal rate = 50 x 106 SCF/day. Vc = cavity volume = 109 ft.3 T = cavity temperature = 1000F. TS Z s Ps = standard temperature, compressibility factor, and pressure, respectively. To, Zo, P = original temperature, compressibility factor, and pressure, 0 respectively P g/ ph - 865 psig t = time in days after withdrawal has started. T., Zi' P = temperature, compressibility factor, and pressure, respectively, at time t. VG$ nG = volume and moles of gas, respectively, at time t. no = initial number of moles of gas. f*e = fraction of gas withdrawn that is replaced by water (corrected to actual reservoir conditions). Q = water injection rate, ft3/day. QS = gas production rate STDcu. ft. per day. S P T i TZ Q - f*Q X 2.1 L s P T Z 0 s S Material balance: VG =VC QLt 2. 2 ZinGRTi but V = G P. 2. 3 P V Q P O C S S_ wh eet 2. 4 where nG Z RTi Z RT 2.4 Z.RTi PV Q'0C OsP V Q t __ oSC t 2. 5 C L P. ZRTi Z RTj L 0 S S PS 1 moles It should be noted that Z = 1 and Z RT5 = Substituting (1) in (5) and solving for Pi yields: 26

Z l o s s j ~ t Pi = P T(2.6) Q P T.Z. S SL L 1 - f*e...... t V P T.Z C 0 L S This equation must be solved by trial and error since Zi is a function of Pi and Ti. Z values are functions of pseudo-reduced temperature and 2. 39 pressure are available in the literature. 2 Equation (2. 6) is presented graphically in Figure 1 for various values of f*. Stress Considerations When the creation or extension of a salt cavern is considered, it is important to know the cavern volume that can be washed out without danger of cavern collapse. Induced stresses must also be considered when the cavern pressure is reduced below formation pressure. An approximate but reliable correlation giving the induced stresses as a function of geometry, rock' properties and reservoir variables is now being developed. More specifically, this correlation will give induced stresses from cavern dimensions, shape, pressure, depth, thickness of overlying consolidated. formations, and physical properties of the surrounding formations. With such a correlation, one could create maximum cavern volume without danger of collapse. in addition, one could calculate the minimum storage pressure which would be permissible for a given dissolved salt cavern. Once the operating maximum and allowable minimum cavern pressures are determined then the deliverability of gas from the cavern' and the necessary pumping requirement for maintenance of cavern pressure may be readily calculated. The results of the stress correlations developed for salt caverns along with comparisons and applications to direct field data will be included in the next progress report. Creation of Salt Cavern Reservoirs Washing - The process of washing out a cavern in rock salt is inexpensive (from 19 cents to $1. 80 per bbl) and simple:.a shaft is drilled into a subterranean salt stratum; and, by pumping water in suitable rates under appropriate pressure, the salt is dissolved and brought to the surface, 27

900 800 700 f':O. \S 600f: 0.5 500 f': 02 S f=: FRACTION OF GAS WITHDRAWN CORRECTED TO ORIGINAL RESERVIOR CONDITIONS THAT 400 L IS REPLACED BY WATER. f 0.O 300 0 100 200 300 400 500 TIME (DAYS) FIG. 2.1 SALT CAVERN -STORAGE VARIATION OF RESERVOIR PRESSURE WITH TIME FOR VARIOUS DEOREES OF WATER REPLACEMENT. ( V~sc 109 FT.., S'OX106 SCF/DAY ) 28

2. 7 leaving an opening of the desired size within the stratum. In theory, every 6.03 bbl of fresh water will dissolve one bbl of salt. In practice, about ll1% capacity is experienced with each unit volume of wash water. It has been observed that in about seven wash volume turnovers, the cavern 2. 5 size doubles, in 11 it triples. Salt cavities should be formed in an area free from shale ledges if possible. If present, these ledges may break off and kink or snap any brine or product tubes that might be located in the cavity. In some operations, the amount of insolubles may be excessive and tubing may have to be raised from the bottom of the cavity to prevent plugging. There are three methods of developing the salt cavity: (Figure 2. 2) 2 21 (a) bottom injection; (b) reverse circulation and (c) progression technique. Determination of the Size of Dissolved Salt Caverns After a cavern has been washed, accurate dimens ions of the caverns are usually desired. If the cavern shape is assumed to be without stringers of insoluble material and that it approximates a cylinder, then volume height 2. 15 data will fix the diameter. This volume height relationship can be obtained by measuring the difference in shut in annulus pressures of the liquified hydrocarbons at the surface after successive additions of known volumes to the cavern. The rise in pressure together w ith the calculated base pressure required on the annulus to balance the brine column from the bottom of the casing permits the calculation of an equivalent diameter at 2. 16 various test points. Refering to Figure 2. 3, it will be recognized that h 434d (2. 7) 0. 434(dB- d 1) or Lh = (2. 8) 0. 434(dB dp) Where h = depth to the LP gas brine contact, feet. P = casing pressure, psig. dB = specific gravity of brine. 29

UNDERGROUND STORAGE CAVITY UNDERGROUND STORAGE CAVITY CAVITY SHAPE BY CONVENTIONAL CIRCULATION BY REVERSE CIRCULATION CONVENTIONAL CIRCULATION FRESH WATER IN WATER IN BRINE OUT UNCONSOLIDATE UNCONSOLIDATE UNCON | NSO DATED FORMATIONSg I I g//X FORMATIONS I [ FORMATIONS SALT I PT.N. 4 SALT SHAPE D Al ~ ~.. N03 ~~~~~~~~~~~~~ -NO. 2.. T. * 0 0N -. (A) (B) (C) FIG. 2.2 THREE METHODS OF DEVELOPING CAVITIES: (A) CONENTIONAL BOTTOM INJECTION METHOD ( B) REVERSE CIRCULATION TECHNIQUE ( C) PROGRESSION TECHNIQUE WHERE BY WASH PIPE IS MOVED TO CONTROL CAVITY SHAPE.

P 9 5/8" 1939 7"- 2142' iod id LP-GAS 3- 2947 FIG. 2.3 A SIMPLIFIED VIEW FIG.2.4 AVERAGE CAVERN OF A SALT STORAGE WELL. DIAMETERS AS DETERMINED FOR EQUILIBRIUM PRESSURE CALCULATIONS. ~~ ~ ~ ~ ~ ~ ~~3

dp = specific gravity of LP gas. The average cavern radius for the part of the cavern can be calculated for any interval by, R = 3.40O( (2. 9) Where t/h = vertical height filled during interval, feet. AG = gallons LP gas injected for the interval. R = average cavern radius for the interval, feet. Figure 2, 4 shows a typical cross section that has been calculated for a 2. 16 Petal Dome storage cavern. Fracturing - When creating caverns in salt layers, fracturing may be employed to facilitate the cavern construction. Two or more wells may be sunk and connected by fracturing. The bed may then be washed out to provide a large storage area. Fracturing probably cannot be used in salt domes because the general homogeneity of physical properties of salt may not lenrd itself to controlled horizontal fracturing. Recovery of LP Gas From Caverns While this report is primarily concerned with storage of natural gas in caverns there are many aspects of L. P. G. storage know which may also be. applicable to natural gas storage. It is for th-i s. reason that literature in formation on recovery of L. P. gas is included in the following. When the reservoir is filled, some hydrocarbons will be lost in permanent storage. 2 15 This loss is relatively small and most of the gas can be recovered. Gas recovery can be accomplished by: (1) Brine displacement, (2) Pumping, (3) Vaporization, (4) Gas displacement. Brine displacement has one advantage and a serious disadvantage. If the brine used is saturated, the cavern size will not change. Surface storage or disposal of the brine usually constitutes a problem. In some instances simultaneous operation of brine wells near underground storage cavities provides the gas reservoir with ample brine for displacement. A second alternative is to have a large asphalt lined surface basin for temporary brine storage. Prefabricated asphalt lining 2. 5 can be installed for about 30 to 35 cents per square foot. The static 32

pressure difference between the brine and hydrocarbons is approximately 600#. It is necessary, therefore, to have a pump with about a 1000# dis2. 15 charge pressure to handle the pipeline floor rates. In LPG storage, product removal by pumping has several disadvantages although brine is eliminated in the storage process. The amount of product that can be handled by a centrifugal pump decreases rapidly with depth. In caverns up to 1000 feet deep, discharge rates are as high as 1500 GPM. If the depth is increased to 1500 feet, the rate drops off to about 20 GPM; 2. 5 and beyond 3000 feet the centrifugal'pump lo ses all practicality. In addition, the products being pumped are poor lubricants, creating high maintenance costs. ETlrthermore, pumping will allow the cavern pressure to drop to a point where cavern collapse may occur. Product removal can also be accomplished by vaporization lift. In this method, hydrocarbon vapors are withdrawn from a relatively small diameter tube that extends to the bottom of the storage chamber. These vapors are recompressed and injected into the vapor space above the liquid in the cavern. Bubbles caused by the vaporization of liquid hydrocarbons under reduced pressure within the tube create, in effect, a gas lift which will carry products out of the hole. Although this method is relatively expensive and is limited in depth of operation to 1400 feet, it eliminates the need for downhole pumping equipment and at least partially preserves the cavern pressure. Product removal by gas displacement forces the liquid out of the cavity by virtue of high injection pressures. It does not involve extra puimping equipment and is adaptable to any depth and rate. However, it requires a gas source capable of both giving and taking large quantities of gas at irregular rates. Mined Storage Locations At the present time, there.are at least 29 mined storage caverns completed or under construction in this country with a total capacity of nearly 2. 3 5 million barrels. Abandoned coal mines, salt mines, and ore mines are included in this category as well as mines especially constructed for 33

LPG storage. Geographic formations suitable for construction of underground caverns are indicated in Figure 2. 5. Coal Mine Storage A well constructed coal mine may constitute a ready-made storage reservoir. First, however, test drillings should be made to determine the permeability of the formations around the mine. Tests on a Denver 2. 13 mine showed that the strata above the coal seam were of sufficient strength and of low enough permeability to serve as a "cap rock" for the reservoir. The vertical distance between the surface outcrop and the miri.es operating level fixes the pressure at which the reservoir is to be operated. At the Denver mine, an upper limit of 300 psig for storage was selected while the operating pressure used for storage was 200 psig. Hard Rock Mined Storage Hard rock mining is often the only solution to a storage problem due to the conditions of the subsurface formation. This type of storage is exemplified by Sinclair Oil and Gas Co.'s 5, 000, 000 gallon hard rock 2,1 2 underground storage of LPG near Seminole, Oklahoma. Conventional mining methods and equipment were used to contruct the mine. The mine was tested for leakage with dehydrated air at 150 psig and 90 to 100 psig was used for storage. A hard: rock mine was also contructed at the Bayway refinery of 2. 7 Esso at New Jersey at a depth of 330 ft. Total capacity is about 675, 000 bbl. Large pillars of shale were left in place during the excavation to provide support. The support pillars are actually larger than the excavated area, making the reservoir a series of interconnected tunnels, The techniques presented for LPG storage possibly can be used in the storage of natural gas. The Gulf Coast, Mid West, and Great Lakes regions with salt formations offer the salt dome and salt bed storage, while the coal and ore mining areas might be considered for storage in abandoned mines. In the eastern states, many of the large centers of population are over solid rock formations. Hard rock mining may provide some possibilities for gas storage of the type first discussed, The table 20 1 compares costs of various types of LPG storage methods. 34

I ME CAVORABLES OR ~"~'~ NOT FAVORABLE FIG. 2.5 GEOLOGICAL FORMATIONS SUITABLE FOR CONSTRUCTION OF THESE UNDERGROUND STORAGE CAVERNS ARE FOUND IN MANY PARTS OF THE U.S. AND BROAD AREAS HAVE BEEN TENTATIVELY CLASSIFIED AS FAVORABLE OR UNFAVORABLE.

TABLE 2. 1. COSTS OF LPG STORAGE. 15 Type of Storage Cost per bbl., $ High pressure above ground storage (propane) 20. 00 - 30. 00 Mined Storage (propane-butane) 7. 00 - 15. 00 Low-Pressure-above ground sphereoid refrigerated (butane) 12. 00 - 20. 00 Salt cavern (propane-butane) 0. 75 - 3. 50 36

REFERENCES 2. 1 Jennings, G. P., Underground Storage Ideal for LPG, The Oil and Gas Journal, Vol.o 59, No, 18, May 1, 19610 2.2 Newman, B. F., Underground LPG Storage, The Petroleum Engineer, Volo 24, No. 13, December 1952. 2.3 Scisson, S, E., Planning for Mined Underground LPG Storage, The Oil and Gas Journal, Volo 58, Noo 18, May 2, 1960o 2.4 Kinney, Gene T., Underground Gas Storage Still Rising, The Oil and Gas Journal, April 231, 1956. 2.5 BrandtS C. T., 5 Ways to Recover Stored LPG, The Oil and Gas Journal, Volo 59, No, 15, April 10, 1961. 2.6 Famous Texas Salt Dome to Become LPG Cavern, The Oil and Gas Journal, Volo 57, No. 15, April 6, 1959, 2.7 Carving Out a Cavern Through a "Needles1 Eye, Engineering News Record, Vol. 1609 No0 4,'January 23, 19580 2, 8 Vance, Thaddeus B., Salt Cavern Gas Storage Boosts Profits, The Oil and Gas Journal, Vol 60, No. 42, October 15, 1962 2,9 Billue, G. H., and Roberts, T, E., How N.CoRoAo Operates its Underground LPG Storage''The Oil and Gas Journ9al, Volo 53, No, 19, September 13, 1954. 2, 10 Can Gas Be Stored Under Flat Caprock?, Petroleum Week, December 23, 1960o, 2. 11 Wheeler, Henry P., Jr,, and Eckard, William E,, Underground Storage of Natural Gas in Coal-Mining Areas, Information Circular 7654, United States Department of the Interior, December., 1952o 2, 12 Counts, E. Ho and Childress9 C, Lo Underground LPG Storage, The Oil and Gas Journal, Vol. 53, No, 17, August 30, 1954. 2, 13 Bleanley, W. B.o Old Coal Mine Converted -to Gas Storage, The Oil and Gas Journal, December 13,9 19610 2. 14 Daugherty, Patrick F., How Sun Created Underground Storage, The Oil and Gas Journal, Vol. 53, No. 43, February 28, 1955. 2.15 Henders.on, Go Ro., and Dougherty P. F., Underground Storage Created in Salt Beds at Sun's Sarnia Refinery, The Canadian Journal of Chemical Engineering, Volo 35, No. 2, August,. 1957. 2.16 Branyan, Stuart G., How Anchor Recovers 97% of LPG Stored Underground, World Oil, Volo 142, No. 2, February 1, 1956, 37

2.17 How LPG Was Stored in a Producing Brine Well, World Oil, Volo 139, No. 4, September 1954. 2.18 Wilson, W. Mo, Lion Oil Coo'S Experience with Underground Storage, The Oil and Gas Journal, Vol. 52, No. 43, March 1, 1954. 2.19 Wiederker, A MN., Barker Dome Gas Storage Project, The Petroleum Engineer, Vol. 24, No. 13, December, 1952. 2.20 Richards, A, Wo, San Diego Goes Underground to Increase Storage Facilities, Gas, Volo 32, No. 5, May 1956. 2.21 Johns, D. F., Formation Strength in Salt Cavern Storage, The Petroleum Engineer, Vol. 29, No. 9, August.: 1957. 2.22 Landes, Kenneth K., LPG, Fuel Oil for Natural Gas Storage Possibilities in Western New York, 1005 Berkshire Rd, Ann Arbor, Michigan, April 19, 1955. 2. 23 Erickson, A. R., and Svoboda, R. F., Redfield Gas Storage Structure, AAPG Annual Meeting Program, 1956. 2.24 Chisholm, J. P,, and Patterson, G. D,, Sonar Caliper Simplifies LPG Storage Surveys, The Petroleum Engineer, Vol. 30, No. 1, January, 1958, 2.25 Landes, Kenneth K., International Salt Company-Ludlowville Brine Field, 1005 Berkshire Rd., Ann Arbor, Michigan, December 3, 1962. 2.26 Todd, Raymond W., Progress in Gas Storage, Gas, Vol. 38, No. 5J, May. 1962o 2.o 27 Galpin, Sidney So, and Montgomery, Palmer Ho, Unique Tools and Methods Used in Gas Well Workovers, The Petroleum Engineer, Vol. 28, Noo 10, September 1956, 2.28 NoG.AA. Prepares Standards for Underground LP-Gas Storage, The Petroleum Engineer, Volo 24, No. 13, December 1952, 2.29 Huff, Rable L., Here's How Texas Gas Recovers More LPG, The Petroleum Refiner, Vol. 35, No, 5, May 1956. 2.30 Dougherty, Pat, and Fenix, Gilbert J., How Sun Oil Co. Mines and Operates LPG Storage Caverns, The Oil and Gas Journal, Vol. 59, No. 21, May 22, 1961, 2.31 Gentry, H. Lo., Natural Gas Successfully Stored in Salt Cavern, The Oil and Gas Journal, Vol. 60, No. 42, October 15, 1962, 2,32 Givens, Homer Co, Depleted Sands Make Dual Reservoir for LPG Product, The Oil and Gas Journal, Volo 56, Noo 73, September 24, 19560 38

2,33 Doughty, K. V., and Cole, Charles M., Jr., Status and Progress of Underground Storage, The Petroleum Engineer, September 1954. 2. 34 Chapin, Earl V,, LPG in Volume Can Be Stored Underground, The Petroleum Engineer, Vol. 26, No. 4, April 1954. 2,35 Goebel, E. Do, and Jewett, J. M.o Possibilities for Underground Storage of Natural Gas Near the Kansas River Valley, University of Kansas Publications, State Geological Survey of Kansas, Oil and Gas Investigations No. 27, 1962. 2.36 Serata, Shosei, and Gloyna, Earnest, Design Principles for Underground Salt Cavities, Trans. ASCE, Part III, Paper No. 3146, 1961. 2037 Sippel, Robert Fo. and Hodges, H. Darwin, LPG Storage Well Logging, The Petroleum Engineer, April 1958. 2, 8 Grow, George C. Jr., and Zack, Julia, Bibliography on Underground Storage, American Gas Association, July 1, 1959. 2.39 Katz, D. L,. et al,, Handbook of Natural Gas Engineering, McGraw Hill Book Co., Inc., New York, 1959. 2.40 Katz, D. L. et al,, Movement of Water in Contact with Natural Gas, Monography, American Gas Association, 1963.0 39

3. DETECTION AND REMEDY -OF LEAKS FROM STORAGE RESERVOIRS When natural gas is stored in underground formations, whether such storage is in depleted gas or oil reservoirs, or in aquifers, the presence of a suitable cap rock is of paramount importance for the required retention of gas. Obviously, a depleted reservoir must have a cap proved throughout the geologic ages as impervious to the migration of hydrocarbons across it, However, if it is desired to "overpressure" the reservoir, an excessive overpressure may cause the cap rock to leak. In aquifer storage, the gas bubble is practically always at a pressure above the original aquifer pressure. Because aquifer storage projects are continuously operated under "overpressure" conditions, the leak from aquifers across the cap is likely to occur if and when the reservoir pressure reaches some critical value. Overpressuring of Storage Reservoirs A large number of oil and gas reservoirs are in contact with blanket3, 12 water sands or aquifers which outcrop somewhere to the surface of the earth. Such reservoirs are usually discovered at a pressure resulting from the hydraulic gradient related to the elevation of the outcrop location. Even when there is no direct communication with surface waters, many such reservoirs have pressures that conform to this gradient. This fact is considered by many as the supporting evidence to theories of underwater sedimentation and compaction usually advanced to explain the origin and occurirence petroleum deposits. Any moderate variations in depth-pressure distributions are from those predicted by the normal hydrostatic effect are sometimes explained by a varying salt composition of subsurface waters along with existing geothermal gradients in the crust of the earth. Figure 3. 1 shows discovery pressures vs. depth for various petroleum reservoirs. In examining Figure 3. 1, one must observe the significance of the limiting gradients; the upper-limit of 1. 0 psi/ft is considered to be due to the weight of the overburden, and the lower limit of 0.433 psi/ft is the hydraulic gradient for pure water. Beyond these two limits, abnormal discovery pressures are occasionally found on boththe:high 40

2000 4000 \6 6000 c @13 8000 012 c 164 4 8 ~c-10,00C,- 2 @9 15 10.7 ~~~~~~~~~3212,0 14,000 16,000 6. _ 18.000L bper /00 ft 43.3 453 17 20,000 i 0 2000 4000 6000 8000 10,000 12,000 14,000 Pressure, psia Fig. 3.1 Effect of depth on discovery pressures for various reservoirs. 41

and the low sides. Sometimes the abnormally high pressures are due to compaction of shales surrounding the strata bearing the hydrocarbons. Abnormal pressures usually indicate that the particular reservoir fluids are not in communication with outer formations. Because the number of moles that can be put in storage for a given reservoir volume is roughly proportional to the pressure in the reservoir and because the higher the storage reservoir pressure the larger will be the reservoir volume due to displacement of water from the underburden, "overpressuring" is a desired practice as long as it does not cause the cap rock to leak or break. The effect of over-pressuring on the storage capacity of a reservoir is illustrated in Figure 3. 2. The original gas water interface AB corresponds to the discovery pressure of the gas field. This interface is pushed down and more gas enters into storage if the gas reservoir is held at a pressure higher than the original discovery pressure. If the interface AB on the other hand, is pushed beyond the level CD, the gas may leak out across the "spill-point" indicated in the vicinity of point D. If the extent of over-pressuring is too high, the gas may leak vertically across the cap rock or even mechanically fracture the cap rock. Leakage Across Cap rocks Caprocks are continuous permeability barriers usually of shale and occasionally of sand stone and dolomites of very low porosity and permeability. It is believed and has been demonstrated on several occasions that the caprock is made impervious to fluid leakage across it by the pressure of water in its pores. Upon discovery of any reservoir, the cap rock is usually fully saturated with water and under no differential pressure gradient, except that due to the ordinary hydrostatic effect. When gas pressure is applied to the underside of the cap rock at a sufficiently high overpressure, the gas works its way to displace the water from some permeable channel and establishes communications with more porous and more permeable formations above. When this happens, a gradual drying of more channels occurs and leakage accordingly increases. Under these circumstances, the leak first appears to be a point sink but later becomes area distributed. If mechanical failure 42

GROUND LEVEL WELL SHALLOWER WATER BEARING SAND ~*S.H.SH GAS. CAP ROCK > WAE -..- - - -.WATER,, Y.',,,._. = - - - -= = _/ \ SHALE ~ SPILL POINT LEVEL FIG. 3.2 EFFECT OF OVER PRESSURE ON STORAGE CAPACITY OF A RESERVOIR ~~A ~~~SILPIN EE FIG......-e EF -~ --- ---- PRSUEO T-/ECPCT O EEV......... _.. ----

of the rock occurs because of stresses involved in the porous matrix due to the gas pressure from below, the leak may first appear to be a line sink along the fracture curve but again soon becomes area distributed. It must be recognized at this point that very little is known at present concerning initiation, extent and nature of leaks across caprocks but studies are underway to separate and study leak characteristics of cap rocks, both theoretically and in the laboratory. Concept of Threshold Pressure When a cap rock sample fully saturated with water is subject to gas pressure on one side, the leak does not occur so long as the pressure of the gas remains below some critical value. When it reaches this critical value, the water gets pushed out from the first permeable channel and leakage begins to take place. The pressure at which this phenomenon occurs is called the threshold pressure. A bone dry core sample when partially submerged in water as indicated in Figure 3. 3 will soak up the water by capillary inhbibition. As the water rises through the pores, the saturation will adjust itself so that there is a distribution of saturation with height, resulting in the capillary pressure saturation curve indicated. If, on the other hand, a core fully saturated with water is left to drain by gravity and pressure on one side the capillary drainage curve AB will result. In drainage, all the water will not drain out as indicated by asymptotic approach to the irreducible water saturation Si. If the core is let to soak up water by imbibition, again a different curve BC is observed. This phenomena is called capillary hysteresis. On the drainage curve, the minimum pressure PA necessary to reduce the saturation infinitesimally is called "the threshold pressure". It must be noted that in order to have a quantitative basis for determining the safe limit on overpressuring and to assess the conditions which may lead to leakage one must have a clear understanding of capillary imrrbibition and drainage phenomena. Special equipment to measure these imbibition and drainage curves on core samples by measuring the vapor pressure of water above the core samples in a bell jar is now being constructed. 44

DRAINING STARTING ~ enI S W=MBIBITION FOLLOING' OSW C 1.0 W ATT _ WATER SATURATION SSV FIG. I 3.3I MBIBITION FOLLOWING wn NDRAINAGE S~.4 Ir 0 STARTING BONE I THRESHOLD WATER SATURATION SW FIG. 3.3 IMBIBITION AND DRAINAGE CAPILLARY PRESSURE CURVES STARTING BONE:5

Previous Theoretical Investigations Previous work has largly been devoted to leakage effect when only a single phase (water, in particular) has been involved. For example, 3.5-3.11 Hantush and Jacob have made extensive studies of the leakage of incompressible or slightly compressible fluids to and from horizontal storage reservoirs bounded above and/or below by less permeable layers. Although their interest was primarily in the addition of water to Artesian sand layers from the bounding strata, their solutions hold equally well for depletion or leakage. Essentially, Hantush and Jacob studied various special cases of the differential equation (here stated in cylindrical co-ordinates) governing water motion in the aquifer: 2 a 2 I 8 1 H a2 c aI IV -I - + 1 _ (3. 1) 2 r r 2 2 2 k at (3.1) ar az r ae where H = flow potential (= p + pgz) r = radial distance z = vertical distance E - angle in horizontal plane t = time = porosity. = viscosity c - compressibility k = permeability Frequently, in their analyses, the term a p/az was neglected. The flow or leak in the less permeable bounding layers was assumed to be in a vertical direction and at a rate proportional to (~ - "*)/A, where 4* is a constant opposing potential and A is a constant depending on the permeability and thickness of these layers (or cap rock). This leakage rate appears, of course, as a boundary condition to equation (3. 1) in the aquifer. By using Green's function and the method of images, Hantush and Jacob extended their results to a variety of geometries, which included infinite and finite 46

radial regions, infinite strips and quadrants, etc, under'various types of boundary conditions. 3, 15 Theis..made an early investigation of the transient pressure in a non-leaking infinite plarne radial region with a constant injection rate at the centre. The corresponding case with a leaking cap rock of semiinfinite vertical extent was one of the series analysed by Hartush whose results for the aquifer pressure are represented by Witherspoon, Mueller and Donovan as a plot of PD versus tD. with P as a parameter, where 21 kHa p PD = dimensionless pressure increase, TkHp D q [ t dimensionless tLme, r D i Fcr re 1 k'~'c' 4H kqc Lp = increase of aquifer pressure above discovery pressure H = aquifer thickness q - volumetric injection rate The superscript primes denote cap rock properties, and all quanitities are assumed to be in consistent units. Note that the Theis solution corresponds to the case p = 0o 3. 17 Witherspoon et al assert that, under practical conditions (in particular for a cap rock of low permeability), the value of 3 is so small as to cause no significant deviation in the aquifer pressure from that predicted for the no-leak case. They demonstrate, however, that pressure observations in the leaky cap rock itself afford a more sensitive method for determining the effectiveness of the cap rock as a barrier, Witherspoon et al. used an unspecified finite difference method which allowed for radial and vertical flow in both the aquifer and in the semi-infinite cap rock, Their results were presented as plots of a ratio Bpg'/p versus H, with 0t as a parameter, where Ap' = pressure changed in cap rock Up pressure change in aquifer without leak H = dimensionless height above the bottom of the aquifer, z/H 47

o< = tDr k'/k (note this is not a dimensionless parameter) The Scope of Present and Future Theoretical Work It will be observed from the above comments that previous studies on leaking caprocks have primarily considered the case of a single fluid (water) with the leak uniformly distributed over an area. Also, the concept of a "threshold pressure difference", below which there is no leak, does not appear to have been used widely. Probably the most important questions that may be answered by a theoretical investigation are (1) How does a leak occur? (2) How can a leak be detected? (3) What is the performance of a reservoir whose cap rock properties have already been evaluated-? These problems will now be discussed in turn. Firstly, it has already been mentioned that a leak may be produced by either (a) displacement of cap rock water by gas, or (b) mechanical failure of the; cap rock due to excessive over-pressurizing. In the case of water displacement, it is unlikely that the gas/water interface advances in a pistonlike manner. A slightly uneven distribution of permeability or porosity in the caprock will serve to initiate "fingering" or "channelling" of the gas. This phenomenon is likely to become accentuated because of the diminishing length of water column ahead of the "finger", although this effect may be partially offset by an increasing pressure gradient in the water as the local interface accelerates. It is possible that fingering may be minimized, and hence eventual leaking delayed, by a gradual rather than a sudden overpressurizing. In the case of a sufficiently thick cap rock, the reservoir might possibly be operated over yearly cycles in such a manner that the gas/liquid interface always oscillates within the cap rock. Secondly, the question of leak detection has partly been answered by Witherspoon et al. for the case of a cap rock of homogeneous texture. An obvious extension is to be the situation involving a non-homogeneous caprock. In such a case, the leaks may be localized and can be treated by assuming they behave approximately either as isolated point sinks or 48

(especially when caused by a fracture) as line sinks. The first step would be to postulate a particular type of leak and its location relative to an injection well and a set of observation wells. Note that the problem is now two-dimensional in horizontal extent alone. For a given injection schedule of either water or gas, the transient pressures in the observation wells may be predicted. By repeating for different leak models, a "case-bookt" of performances can be devloped against which actual field behaviors might be checked and hence diagnosed. There is probably little hope (or even desirability) of being able to distinguish between (e. g. ) a uniformly distributed leak and a number of point leaks themselves uniformly distributed. The third question, that of predicting reservoir performance when the cap rock properties are known, is similar to the second, except that both water and gas are now definitely involved. The key to answering the above three questions clearly lies in being able to predict the simultaneous motion of gas and water in porous media, vix in the aquifer and/or cap rock. It is true that certain problems may be treated in a simplified manner. For example, a study is currently being made of the performance of a leaking reservoir with given cap rock properties and a given injection/withdrawal schedule. The following assumptions are made: (a) Uniform pressure throughout the gas bubble. (b) Water movement can be predicted by the method of Van Ever3. 16 3 13 dingen and Hurst, also presented by Katz et al. (c) Leak occurs only above a certain threshold pressure. (d) Leak rate across cap rock is that predicted for steady state-"one dimensional flow. More generally, however, the starting point will be the differential equations governing unsteady two-phase flow in a. porous medium, An approximate treatment is to think of the gas and water forming two separate regions between which there is a distinct interface. In this case, equations of:the type (3.1) will have to be solved in each region, together with a procedure for predicting the velocity of the moving interface. In practice, the interface will probably be indefinite, due to an 49

incomplete displacement of w-a!te-r as the gas advances. It is convenient to deal in terms of a water saturation S, which may vary from zero (all gas) to unity (all water). The governing simultaneous partial differential equations, which result from unsteady material balances and the application of d'Arcy's law, are given by Douglas, Peaceman and 3. 3 Rachford as'CJ7k Vr \7g -QS'i ag - w k g "at at.k. a(3. 2) 7k'Ew 1 5w - k k erg,.rw = relative permeabilities for gas and water, ILg, p w = gas and water viscosities 15g = gas potential, pg + pggh w water potential, Pw + pw gh = porosity t = time In equations (3. 2), S' denotes the derivative of the water saturation with respect to capillary pressure, and arised from an accumulation term as/at. This is permissible, since, by definition of capillary pressure, Pc = Pg + Pw i. e. (3.3) at dpc at S at pwg - p w) Note that S' may depend on whether gas is displacing water, or vice versa, due to the hysteresis effect mentioned earlier. It is obvious that any attempts to solve equations (3. 2) by analytical means are likely to fail- unless considerable simplifying assumptions are made. Rather, finite difference approximations to their solution are clearly indicated, and the implicit alternating direction method used by 3.3 3.1, 3.2,3,14 Douglas, Peaceman- and Rachford, and also discussed earlier, is an obvious choice. It is also anticipated that the Dufort and Frankel method may be of utility. 50

REFERENCES 2 2 2 2 (1) Douglas, J9, Jr., "On the Numerical Integration of a u/ax + a u/ay au/8t by Implicit Methods", J. Soc. Indust. Appl, Math,, 3, 42-64 (1955). (2) Douglas, J., Jr., and Rachford, H. H., Jr,, "On the Numerical Solutionr of Heat Conduction Problems in Two and Three Space Variables, Trans. Amer. Math. Soc,, 82, 421-439 (1956). (3) Douglas, J,, Jr., Peaceman, D. W. and Rachford, H. H,., Jr, "A Method for Calculating Multi-Dimensional Immiscible Displacement, " Pet, Trans, of AIME, 216, 297 - 308 (1959). (4) Dufort, E. C., and Frankel, S. P., "Stability Conditions in the Numerical Treatment of Parabolic Differential Equations, " Malth Tables Aids Comput.,;7, 135 - 152 (1953). (5) Hantush, M. S., and Jacob., C. E., "Plane Potential Flow of Groundwater with Linear Leakage," Trans. Am. Geophys. Union, 35, 917936 (1954). (6) Hantush, M. S., and Jacob., C. E., "Non-Steady Radial Flow in an Infinite Leaky Aquifer", Trans, Amo Geophys. Union, 36, 95 - 100 (1955), (7) Hantush, M. S., and Jacob., C, E., "Non-Steady Green's Function for an Infinite Strip of Leaky Aquifer", Trans, Am. Geophys. Union, 36, 101 - 11 (1955). (8) Hantush, M. S. and Jacob, C. E,, "Steady Three-Dimensional Flow to a Well in a Two-Layered Aquifer, Trans, Am, Geop~.ys. Union, 36, 286 - 292 (1955). (9) Hantush, M. S., "Analysis of Data from Pumping Tests in Leaky Aquifers", Trans. Am. Geophys. Union, 37, 702 - 714 (1958). (10) Hantush, M. S,, "Non-steady Flow to Flowing Wells in Leaky Aquifers"' Jour. Geophys. Res., 64, 1043 - 1052 (1959). (11) Hantush, M. S., "Modification of the Theory of Leaky Aquifers", Jour. Geophys0 Res,, 65, 3713- 3725 (1960). (12) Katz, D, L., et al., "Handbook of Natural Gas Engineeeing. " 51

McGraw-Hill, New York (1959). (13) Katz, D. L., et al., at the University of Michigan, "Movement of Underground Water in Contact with Natural Gas", American Gas Association (1963). (14) Peaceman, D. W., and Rachford, H. H., Jr., "The Numerical Solution of Parabolic and Elliptic Partial Differential Equations", J. Soc. Indust. Appl. Math., 3, 28 - 41 (1955). (15) Theis, C. V., "''The Relation between the Lowering of the Piezometric Surface and the Rate and Duration of Discharge of a Well Using GroundWater Storage", Trans. Am. Geophys. Union, 16, 519 (1955). (16) Van Everdingen, A. F., and Hurst, W., "The Application of the Laplace Transformation to Flow Problems in Reservoirs", Trans. AIME, 186, 305 - 324 (1949). (17) Witherspoon, P. A., Mueller, T. D., and Donovan, R. W., "Evaluation of Underground Gas-Storage Conditions in Aquifers Through Investigations of Ground Water Hydrology, J. Pet. Tech., 14, 555 - 561 (1962). 52

4. FRACTURING Literature Survey and Design''Calculation When soil impermeation through application of grouting into porous materials such as sandstone is considered for creation of storage reservoirs the need to induce fractures to provide continuum for grouting materials becomes important, This is why it was pointed out in Chapter 1 that hydraulic fracturing can be of definite assistance in design and development of storage reservoirs. Once an underground formation has been fractured, grout can be injected into the fracture to provide an impervious layer. Grouted horizontal fractures may serve as caprock while grouted vertical fractures will act as walls to provide impervious boundaries around or amidst the permeable sandstone. Hydraulic fracturing was first introduced to the petroleum industry in 1949 as a method of increasing oil well productivity. Since 19499 many methods and theories concerning fracturing have been proposed. Information dealing with fracturing occurs frequently in the literature, but it appears that no one has summarized the material to the extent that practical and realistic fracture calculations can be made, In order to provide a basis for the design of fractures in the creation of gas storage reservoirs, this paper presents methods of creating fractures, equations to calculate fracture extent, a discussion of fluids and propping agents to be used, along with a complete procedure for design. Fracture Extent The basic. equation for fracture design was presented by Howard 1, 2 and Fast in 1957, 53

Q.W (eX 2 A = 2(ex erfc(x) + x - 1) (4.1) where x = 2C t dimensionless time A = total area of one face of the fracture, ft2 Qi = constant injection rate during treatment, ft3/min, or (bbl/min) (5.614) t = total pumping-;time, min. W = constant fracture clearance or width, ft. C = a constant which is a measure of flow resistance of the fluid leaking off into the formation during fracturing treatment, ft/(min.)0~5 erfc(x) = complementary error function of x. The fracturing fluid coefficient, C, in equation (4.1) is the rate of fluid loss from the fracture to the formation. There are three mechanisms which control rate of fluid flow into a -~2formation. These are'2 1. Fracturing fluid viscosity and reservoir permeability. 2, Viscosity and compressibility of reservoir-fluid. 3. Wall building effects. Coefficients for mechanisms 1, 2, and 3 are calculated and the lowest value is taken as controlling. The coefficient for mechanism 3 is considered only when water loss additives are added in order to control fluid loss into the formation. Fracturing fluid viscosity and formation permeability coefficient, CI, is calculated as follows:2 54

Ci =0.0469 AK P ft (4.2) where K = permeability of formation to fracturing fluid, darcys = porosity of formation, fractional quantity A P = difference in pressure between the fluid at the formation face and the fluid in the formation, psi F = viscosity of fracturing fluid, CP. Equation (4.2) can be solved by the nomogram in Figure 4 1. Reservoir fluid viscosity and compressibility effect, CIIV can be expressed by:' K 9( C C 0.0374 A P t where CF = compressibility of reservoir fluid, 1/psi LLR = viscosity of reservoir fluid, CP. Equation (4.3) can be solved by the nomogram in Figure 4.0. Note: Figure 4.2 has incorporated in it a compressibility of 1 x 10-5 psi-1 an approximate value for crude oils. If the actual compressibility of the reservoir fluid is significantly different from this, the CII value obtained from the nomogram should be multiplied by \rCF(true value) 1 x 10-5 Wall building effect, CIII, is calculated as follows 92 CiiI = 00164 (4.4) 55

k a NOMOGRAM FOR 0 1000 0 LO CALCULATING C (FRAC FLUID VISCOSITY 100. _ / 20 3 - 0 10 4 0 3j oo P 0 b _1 - oo -- I -- 316 oo-.o o1000 0 u) w U-0.1 I =- - w Q- -I.0 o.: -oj- k,:& MARK o Q ( d AP- O:MARK b a- b: READ Ci -0.1 FIG. 4.1. NOMOGRAM FOR DETERMINATION OF CI k, a C_ b 0 0II NOMOGRAM FOR ~~~~000~_ 5000 CALCULATING Cii (RESERVOIR FLUID -I00. z V.'o00 ~ - VISCOSITY) -I00 x I 20 U U)10 0 ol -1 1000 d -. 0o-'1.0 W.1 m KEY: k-//: MARK 0 AP- 0: MARK b ~~0.1,)~~~~~50 oa-b:' READ Cii FIG. 4.2. NOMOSRAM FOR DETERMINATION OF Ci! 56

where m = slope of experimental fluid loss line when cm3 fluid loss is plotted versus V\t(time), cc/\Tmino 2 a = area of filter medium, cm The fluid loss test is carried out in a filter press which consists of a pressure cell with one end containing filter paper or a thin core wafer. A standard pressure difference, e.g., 1000 psi, is applied across the cell and the volume of filtrate collected is recorded as a function of time. A sample fluid loss test is shown in Figure 4.3. The test must be corrected to the actual reservoir pressure difference, /\ P. Figure 4o4 is used to make this correction of CIIV based upon the relationship that fluid loss through a filter is proportional to the pressure difference. These fluid loss tests almost always give a positive intercept at time equals zero, as indicated in Figure 4o.3 A method for including this spurt loss in calculating fracture area will be presented below. The solution to equation (4.1) can be simplified and put in nomographic form in the following manner. By rearrangement, it is possible to express equation (4,1) in the form. A =ME (4.5) where A = total area of one face of the fracture, ft2 V = volume of fracturing fluid pumped, ft3 W = width of fracture, ft E = efficiency, the volume of fracture created expressed as a fraction of the volume of fluid pumpedq E is a function only of xo 57

C EXPERIMENTA L NOMOGRAM FOR AP F) CALCULATING Cii o III 500 x (FLUID LOSS ADDITIVES) 14 w,a 0 FIG. 4.3 -FLUIDL05STESRESULTSREDz l O\ I:sV',z,. 0.i.. ~w ~ 1.0 C) -1.0 1000X La. 5 ILI rr 5:< I KEY: T ME N w -N FIG.4.3 FLUID LOSS TEST RESULTS RE C FIG.4.4 NOMOGRAM FOR DETERMINATION OF C11 100 FRACTURING EFFICIENCY CHANGE WITH C, VQtAND W w Z ~ X c CT'rv/Q 10 X 50 100 X2 EFP., I/ X2 [IXeifcC(X) +2X ] FIG.4.5 FRACTURING EFFICIENCY VERSUS X 58

A plot of efficiency versus x is presented in Figure 4,5. Efficiency as a fraction is calculated from the equation: E = 2 ex erfc(x) + 2x 1 (4.6) Figure 4,6 presents a nomographic solution for efficiency and then allows solution of equation (4.5) for fracture areao Fracture Width'inhe preceding equations for fracture area depend upon the knowledge of the fracture width, Perkins and Kern have developed a method for the determination of fracture widths, One case considered by Perkins and Kern was that of a vertical fracture created from Newtonian fluids in laminar flowo The condition for laminar flow exists when the Reynolds number is less than (7.81 x 103)(0o32) = 2500, where NRE = 8,70 x 103 (Q)(SpGr) (47) It must be noted that in Eqo (4,o7) the numerical constant 8~70 x 103 has the dimensions of density (i.e. mass/cubic length). NRE = Reynolds number Q = total injection rate, bbl/min. SpGr = specific gravity of fracturing fluid H = height of fracture, fto f = viscosity of fracturing fluid, cpo When the condition for laminar flow is satisfied, equation (4.8) applies, W = 0,58 ()()( / (8) where W = maximum crack width at the well bore, in, 59

NOMOGRAM FOR FRACTURE AND FRACTURING EFFICIENY C a WI E-EFF A W2 V2/W2 V2 VI b Q C.) 4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~C.I -W104 O-I ~~~~~~~~0.! I~ ~ L U A. Ii 0 W 0 i~~~~~ 05- 1 -10011e z 11 o do 0 9 10 2 c' 2 - x co I eo- cw A S co 15 50- -- c - "A —— di4IL- I&, CY\ IL t ~~o AI 1w = co II- -b M E o 0 C-W'MARKO 50 4~o 0 w o IL IJ ~~~~~~~t t~I Q-V,: MARK b IL,. -'b. MARK E.c OTRANSFER TO EFF. 0.1 V-W2 MARK V2/W 0 V./W2..EFF- READ A FIG.4.6 NOMOGRAM FOR DETERMINATION OF FRACTURING EFFICIENY AND FRACTURE AREA.

Q = total pump rate, bbl/min. PI = effective fracturing fluid viscosity, cp. L = length of a vertical fracture measured from the well bore, fto Ey = Young's modulus of formation rock, psi. (values presented in Table 4.1) This equation is presented graphically in Figure 4.7. In the case of a homogeneous formation, the crack would take the shape of a disc making L = 1/2 H. This is illustrated in Figure 4.15. However, if a very tight layer is within the potential fracture radius, the fracture will be restricted yielding different values for H and Lo If (Q)(SpGr)/(H)(4i) is greater than 0,32, then the fluid will be in turbulent flow within the fracture. For this case, the width is given by equation (4.9),4 W = 06 0(Q)2(SpGr) ( L) (4~9) This equation is presented graphically in Figure 4.8, If non-Newtonian fluids such as gelled oils or emulsions are used, then it is necessary to determine the fluid's flow properties before estimating crack width. From Fann meter (measures shear stress as a function of shear rate) data, two constants, k0' and n', are determined and these constants used in place of viscosity. Once k' and n' have been determined, crack widths can be estimated from Figure 4,9, If a fracture is oriented horizontally, crack width may result from two types of rock movement~ If the fracture is deep 61

LEGEND: r/ J UNCONSOLIDATED TO LIGHTLY CONSOLIDATED SANDSTONE IrAI MEDIUM SANDSTONE USE THIS CHART IF: HARD SANDSTONE (PM) (Sp. r) I /I LIMESTONE AND DOLOMITE < 0.32 (HFT.) (,&/CP.) Zi 1.0 EX. PROB. Os TOTAL PUM P RATE, SPM IL 0 01 ~ EP Z I~~~~~~~~~ I t ~~ 12 20 w 40.01 60 10 103 IO IO Q TOTAL PUMP RATE, 8PM P s FRACTURING FLUID VISCOSITY, CENTIPOISE L* LENGTH OF VERTICAL fRACTURE MEASURED FROM THE WELL BORE, FT. SR GR.z SPECIFIC GRAVITY OF FRACTURING FLUID H= CRACK HEIGHT, FT.,FIG. 4.-CRACK WIDTHS FOR RESTRICTED VERTICAL FRACTURES RESULTING FROM NEWTONIAN FLUIDS IN LAMINAR FLOW, LEGEND: USE THIS CHART IF:!7J UNCONSOLIDATED TO LIGHTLY CONSOLIDATED SANDSTONE (QBeM) (Sp Gr) 331 MEDIUM SANDSTONE HARD SANDSTONE > 0.32 - ___LIMESTONE AND DOLOMITE (H FT.) (/./CR) EX. PROS. "4 Ze 0.1 - *8 20W I 1 r II,0 I Os (QOlM )2 (Sp. Gr.) (LFT) ( H FT.) QG TOTAL PUMP RATE, 8PM /,/z FRACTURING FLUID VISCOSITY, CENTIPOISE L z LENGTH OF VERTICAL FRACTURE MEASURED FROM THE WELL BORE,FT. SR GR.a SPECIFIC GRAVITY OF FRACTURING FLUID H a CRACK HEIGHT, FT. TURBULENT FLOW. 62

WELL BORE UNRESTRICTED VERTICAL FRACTURE ~/ow-L. RESTRICTED VERTICAL FRACTURE W ISMAXIMUM WIDTH OF FRACTURE AT WELL RESTRICTED VERTICAL FRACTURE FI G.4.15 RESTRICTED AND UNRESTRICTED VERTICAL FRACTURES. 63

- THIS EQUATION DEFINES kt AND n/ 10 Q:TOTAL PUMP RATE, BPM L = DISTANCE FROM EXTENDING EDGE OF CRACK, FT. -c |H - CRACK HEIGHT, FT, - 6 E E YOUNG'S MODULUS FOR THE FORMATION ROCK, PSI. e I -7 co CY *M''I0 FIG. 4.9 CRACK WIDTHS FOR ReSTRICTED VERTICAL FRACTURE RESULTING FROM NONNEWTONIAN FUWIDS IN LAM INAR FLOW. 64

within the earth, cracks result principally from compression of rock in the vicinity of the fracture, However, if the fracture is very shallow, crack width may also result from flexing and 4 lifting of the overburden. It has been shown that compression of surrounding rock is the principal mechanism leading to crack width if the depth is greater than about three-fourths of the fracture radius. Therefore, this is the mechanism that controls during most fracture treatments. For this condition the width is given approximately by equation (llo.10). ~Q(bbl/min) pf(cp) Cy(ft~ 1/4 W(in.) = 0.22 ~Q(bb/miL p ) (f /(4.10) where CY = radius of fracture, ft. Figure 4.10 presents this equation graphically. Laminar flow of the fluid at every point in a horizontal fracture is probably encountered only rarely in field operations. Hence, turbulent flow must also be considered before a generally applicable equation can be derived. However, the turbulent zone usually will not extend far from the well bore; therefore, Figure 4 4o10 is approximately correct in most cases. The crack widths estimated from Figures 4.7 4.8, 4.9, and 4.10 apply when pure fluids are being pumped along a fracture, These estimated widths are also valid when there is a sparse distribution of propping agent suspended in the fluid, However, if a large amount of sand is injected as a propping agent, then its presence in the fracture will influence pressure drop and thereby 4 crack width, The following equation will give the average slurry 65

LEGEND: EIZI UNCONSOLIDATED TO LIGHTLY CONSOLIDATED SANDSTONE MEDIUM SANDSTONE HARD SANDSTONE! AI 1 LIMESTONE AND DOLOMITE 1.0o 2E 0.1 4O~~~~~~~~~~~~~~~~~~~ ~4 0 I44~~~~~~o (QBPM3 (PCR) (Cr FT.) Q TOTAL PUMP RATE, 8PM 1 -FRACTURING FLUID VISCOSITY, CENTIPOISES Cr FRACTURE RADIUS, FT. FIG. 4.10 APPROXIMATE CRACK WIDTHS FOR HORIZONTAL FRACTURES RESULTING FROM NEWTONIAN FLUIDS IN LAMINAR FLOW.

concentration taking into account fluid leak-off. V CS = (4.11) where CS = slurry concentration vol/vol VS = volume of sand injected into fracture, ft3 A = fracture area, ft2 W = fracture width, fto The average slurry viscosity can then be estimated from Figure 4.11. The crack width is then estimated from Figures 4,7, 4L,8, 4,9, or 4.10 using the average slurry viscosity and density rather than the viscosity and density of the pure fracturing fluid. In the actual case, slurry properties vary from point to point in the fracture. Hence, the width calculated as just shown must be interpreted only as an approximate width. If it is desired to include the spurt loss, VSp, in the calculation of fracture area, it may be done by including this value as an increased fracture clearance 12 whereo V W = W + Sp15o2 (4,12) where W = fracture width, ft V = spurt loss in cm3 Sp a - filter area, cm A group of Russian engineers5 have advanced theories concerning the initiation and development of fractures, However, there appears to be a controversy as to the validity of their 67

40 0 o 0 -L 20 IL _a 0 0.1 0.2 0.3 0.4 0.5 0.6 VOLUME FRACTION OF SOLID MATERIAL IN THE SLURRY FIG. 4.11 VISCOSITY OF A SLURRY CONTAINING SUSPENDED SOLID MATERIAL COMPARED TO THE VISCOSITY OF THE BASIC FLUID..J >t'o~~~~~~~ 20 o 30~~~~ c 1 MATERIAL COM~PARED TO THE~ VISCOSITY OF THE BASIC FLUID.

approach, and for this reason these equations have been omitted from the discussion0 Pressure and Horsepower Requirements Other important factors in the design of a fracturing job are the pressure and horsepower requirements. Surface pressure requirements to create and extend a fracture may be divided into 6 two basic categories; breakdown and treating pressure. The breakdown pressure is dependent on several variables such as formation face contamination (filter cake, cement, etco), existence or absence of formation fractures, bedding planes, rock strength and type, etc. and generally cannot be predicted accurately, However, since injection rates are not significantly important during breakdown other than insuring that the formation has ruptured, horsepower requirements are normally computed using predicted treating pressures and injection rates. Treating pressure or pump pressure (Ps) requirement is equal to the sum of the hydraulic pressure (Pr) required to maintain fracture parting plus fluid friction losses (Pf) minus the hydrostatic fluid head (Ph)9 or 5s P r f Ph (4L13) The pressure required to maintain fracture parting and extension (Pr) may be estimated as 1 psi/foot of depth to approximately 5,000 feet and 07 psi/foot of depth for deeper formations. A minimum pressure requirement of 0.'6 psi/foot of depth may be estimated for all depths. Pressure losses due to friction (Pf) in the conductor-pipe and through the perforations (if any) are dependent on fluid viscosity, injection rate, sand codncentration and- size of conductor pipe' and may be estimated from charts 69

available from fluid supplies such as those appearing in Figure 4.12. Many fluid friction charts do not account for the sand content of the fluid and an approximate correction for sand can be made by increasing friction losses of sand-laden fluids by 8.02%/lb of sand 6 per gallon. Static fluid head may then be obtained from Figure 4.13. Ps can then be calculated from equation (4.13). The choice of a good injection rate is also important for a successful fracture treatment. Recommended injection rates for various sized tubing are given in Table 4.2. After the injection pressure and the injection rate have been determined, equation (4.14) can be used to give the hydraulic horsepower requirement. HHP = 0.0245 PsVi (4.14) where P= injection surface pressure in psi. Vi = injection rate in bbl/min. Fr actur ing Fluids Another important factor in the design of fracture treatments is the selection of a good fracturing fluid. Some basic requirements for a fluid are as follows:6 1. Must be able to physically open and extend a fracture. 2. Must be capable of carrying a "propping" agent which can be left in the formation to prevent "healing" of the fracture. 3. Should be easily back-flushed from the formation. 4. Should be compatible with native formation fluids. 5. Should create a minimum of permeability damage within the formation. 6. Should have low friction-loss properties and be easily pumped. Fracturing fluids may be divided into three basic categories, 70

I" REGULAR TUBING ANNULUS ANNULUS 4400 | 12 EUE TUBING 400 CASING 2"TUBING 2 ~B 1 /0G0 3"EUE TUBING 2'I J TUBING 16 0 0 o o -300 %10 X 300 2 EUE TUBING 0. 20 0 - 20NULUS PwUM RATE (C@ )CASING 2P TUBING 1I00 100 j CCASING 0 4 8 12 0 10 20 30 40 PUMP RATE (BBL/MIN.) PUMP RATE (BBL/MIN.) FIG.4.12 PRESSURE LOSS DUE TO FLOW OF DOWELL'S WATERFRAC 60 THROUGH VARIOUS CONDUITS.

1.04 EFFECT OF SAND CONCENTRATION ON FLUID HEAD IN PSI/FT. LO0 1015 20 - lei (D _ 4 =92 -2'7' LL.9 2 ( 25 w~ ~ P Q ~ 0..88a 30- I 0.9 83 4 0 40-.3 50.400.450.500 HYDROSTATIC FLUID HEAD. (PSI/FT.) FIG. 4.13 72

water, oil, and acid. Although water is the cheapest of the fracturing fluids, its use usually is restricted to treatments where emulsions or swelling clay minerals are not considered to be a problem. Even if swelling is not a problem, use of unmodified water should be restricted to treatments in which high injection rates are obtainable 6 One method to modify water is to add fluid loss control additives to inhibit fluid loss from the fractures formed and thereby increase the efficiency of the hydraulic fluid as a "Vprying" agent in opening and extending a fracture. Water may also be gelled to increase sand suspension ability without increasing effective viscosity. Gels usually exhibit high apparent viscosities when measured in a laboratory; however, their effective viscosity decreases rapidly with increased flow rates. Special chemicals such as surfactants, bentonite and clay swelling inhibitors, emulsion breakers, precipitate solvents, etc,, are sometimes added to gelled and ungelled water and are used if laboratory tests justify the additional expense. Oil is the most common fluid used in fracturing operations because of its compatibility with most reservoir fluids and good sand-carrying ability, Both refined oil and lease crudes are used and are modified in the same manner as water. Figure 14 illustrates the effect of water loss additives on lease crude fluid loss. Gelled or ungelled acid is a common fracturing fluid in some areas for hydraulically fracturing carbonate reservoirs or carbonate bearing sandstones. One technique involves the addition 73

150 EFFECT OF FLUID LOSS CONTROL ADDITIVE CONCENTRATION ON FLUID LOSS FOR A SPECIFC CRUDE o\. 100... 50 RECOMMENDED CONCENTRATION 0.05.10.15 FLUID LOSS CONTROL ADDITIVE CONCENTRATION (LB./GAL.) FIG. 4.14

of dry crystals of sulfanic acid to the fracturing fluid. Because of the additional expense involved, acid treatment is not normally used if other fluids can be satisfactorily applied. In fracturing to create a gas storage reservoir, it may be more expedient to use chemical grout as the fracturing fluid, Then, after the fracture has been opened and propped, the grout would set to provide an impervious boundary, The addition of water loss additives to a viscous chemical grout would probably be sufficient to give the added properties necessary to make the solution a fracturing fluid as well as a grouting material, Propping Agent The evaluation and selection of the fracture propping agent is also an important part of fracture treatment design, 10,12 The main propping agent is sand although aluminum pellets 12 8'11 and crushed walnut shells are used occasionally and have proved satisfactory. Most of the papers presented on propping agent selection, however, have been concerned with the propping agent concentration for maximum fracture flow capacity in oil well stimulationo13 However, in. the creation of an underground storage reservoir, this evaluation probably would be less important, For the purpose of this investigation, the amount of sand needed can be taken as 4.4 lb sand/gal. of fracture volume createdo3 In deep wells with high overburden pressure and/or soft formations, it may be desirable to use more sand, The maximum amount that can be added is that which will fill the entire volume of fracture created, The amount of sand necessary to "sand pack' the fracture is obtained by multiplying the recommended value by 2,7.3 When and if a fracture field test is made, a method exists for determining the injection schedule for a fracture treatment9 (i.e., 75

the time and amount of fluid and propping agent injection). The conventional well bore preparation for fracturing has been to use a perforated pipe, thus creating many small fractures on application of pressure. The method, however, probably would not provide satisfactory control of the location of the fracture in creating fractures for soil impermeation through grouting. Several new techniques, however, allow selective fracturing. One 14 method involves the use of high velocity projectiles to start the fracture, thus providing a weak point for the hydraulic pressure to initiate the fracture. Another method involves the use 15 of an evacuated cylinder that implodes under the hydraulic pressure and thus causes a sudden burst of very high pressure as the fluid in the pipe accelerates to fill the volume previously occupied by the cylinder. Still another method consists of notching the well 16 bore to allow single-point entry. Another method involves the 17 injection of small rubber balls into the well. As pressure is applied, the balls are pushed into the perforations thus preventing a fracture in that section of the well. 18 Some data have been published in the literature to aid in the calculation of the cost for a fracturing job. Table 4.3 gives the cost of oil fracturing fluid with water loss additives (CIII values are also listed for the oils). One dollar per hydraulic horsepower can be assumed for pumping cost.l8 76

Design Procedure 1. Select propping agent, fracturing fluid, tubing size, pumping time. 2. Run a fluid loss test and use the results to plot filtrate volume versus /time. 3. Use the recommended injection rate, Vi, from Table 4.2. 4. Knowing the depth, calculate Pr (1 psi/ft at depths less than 5,000 ft). 5. Obtain friction loss, Pf, from a graph such as Figure 4.12 (also can be calculated via Reynolds Number and friction factor). 6. Obtain static fluid head, Ph' from Figure 4.13. 7. Calculate Ps from equation 4.13. 8. Calculate horsepower requirement by equation 4.14. 9. Calculate AP. (AP = P - P where P =h = formation r g G g pressure). 10. Calculate CI by Figure 4.1. 11. Calculate C by Figure 4.2. 12. Calculate C by equation 4.4 and Figure 4~4. 13. Select the lowest of these (CI, Cii, or CIII) as the controlling mechanism. 14. Compute the total volume pumped (V = Vi t). 15. Guess a fracture width (probably in the range 0.1 - 0.4 in.). 16. Correct the width for spurt loss by equation 4.12. 17. Use Figure 4.6 to determine the fracture area. 18. Calculate the fracture radius from the area. 19. Calculate NRE (Reynolds Number) from equation 4.7 if the fracture is to be vertical. 20. Calculate W from Figures 4.7, 4.8, 4.9, or 4.10 using the slurry properties determined using equation 4.11 and Figure 4.11. 77

21. If the calculated width varies significantly from the assumed width, guess a new width and repeat steps 13 -17. 22. Compute the cost using Table 4.3 and using one dollar per hydraulic horsepower. Example Problem Data: Depth of zone to be treated 2000 feet Formation permeability.050 darcys Formation porosity 0.15 Formation Fluid Viscosity 1 cp Fracture Type Desired horizontal 1. Frac. Fluid - Lease Oil Gravity 35 API Viscosity 500 cp Propping agent - sand Concentration 1.5 lbm/gal Pumping Time 60 min. Pack casing to allow single point horizontal entry Casing Size 52 in. 2. Assume that a fluid loss test gives the curve of Figure 4.3 (area of filter = 20 cm ). 3. From Table 4.2, Vi = 25 bbl/min. 4. PP = (2000 ft)(l psi/ft) = 2000 psig. 5. Since a friction loss graph such as Figure 4.12 was not available for this fluid, Pk was assumed equal to 250 psig. 6. From Figure 4.13, fluid head = 0.420 psi/ft. Ph = (0.420)(2000 ft) = 840 psig. 78

7 Ps Pr + PF Ph (4.13) Ps = 2000 + 250 - 840 Ps = 1410 psig 8. HHP = 0.0245 P V1 (4.14) s1 HHP = (0.0245)(1410)(25) HHP = 863 horsepower. 9. P = (62.4) (2000)(-I (32.2) G = 44 32.2 PG = 865 psig AP = P - P AP = 2000 - 865 AP = 1135 psi. 10. From Figure 1, C = 6X10- 3 ft/mhin. 11. From Figure 2, CII = (1110-3 ft/\mi) (3.0 6.6x10-3 f t/\/ll 12. C = 0.0164 m (4.4) III a iI = 0,0164 20 Ca11 = 1.64x10-3 ft/.mi. From Figure 4, Corrected 10 13. C = C 1.7x103 ft/mi-T. 14. V = V1 t V = (25 bbl/min.)(60 min)(42 gal/bbl). V = 63,000 gal. 15. Guess W = 0.15 in. 79

vSp 16. W' = W + 1524a Vp = 2cc (from Figure 4.3) (4.12) WI 0.15 2 = 12 + (15.24)(20) W' = 0.0125 + 0.00656 W' = 0.01906 ft. W' = 0.228 in. 17. From Figure 4.6, A = 150,000 ft2. 18. cr A == 150,000 = 218 ft. 19. Not needed. 20. = (1.5 gal. )(63,000 gal.)((3.44)(62. 4)lbm )=441 ft3 (4.11) c Vs/WA Cs = (441 ft3)(12 in/ft)/(0.228 in)(150,000 ft3) Cs = 0.154 From Figure 4.11, slurry visc./pure frac. fluid visc. = 2 Slurry visc. = (2)(500) = 1000 cp. Q4Cr = (25)(1000)(218) = 5,450,000 From Figure 4.10, W = 0.285 in. Second Trial 15. Guess W = 0.20 0.20 16. WI 12 + 0.00656 W'= 0.01667 + 0.00656 W' = 0.0232 ft. W' = 0.281 in. 17. From Figure 4.6, A = 165,000 ft2 80

18. Cr =|A = 165,00 229 ft. 19. Not needed. 20. Vs= 441 ft3 cs = (44l)(l2)/(o.281)(l65,ooo) Cs = 0.114 From Figure 4.11, slurry visc./pure frac. fluid visc. = 1.7. Slurry visc. = (1.7)(500) = 850 cp. Q&pC = (25)(850)(229) = 4.87 x 106. From Figure 4.10, W = 0.280 in. (assumed satisfactory within the accuracy of graphs). (Assumed corrected width was 0.281). 21. Fluid cost from Table III; assume fluid is of average cost 0.04 cents/gal. Cost = (0.04)(63,000 gal.) + (8636)($1.00/hp) Cost = 2520 + 863 Cost = $3383.00 81

Nomenclature A = total area of one face of fracture, ft2 2 a = area of filter medium, cm C = a constant which is a measure of the flow resistance of the fluid leaking off into the formation during fracture treatment, ft/ mi. CI = constant C for fracturing fluid viscosity and relative permeability effect, ft/rm/ Tn. C = constant C for reservoir fluid viscosity and compressibility effect, t/II CI iI = constant C for fluid loss additives effect, ft/fmin. CF = compressibility of reservoir fluid, l/psi. CR = radius of a horizontal fracture, ft. E = efficiency, the volume of fracture created expressed as a function of the volume of fluid pumped. Ey = Young's modulus of formation rock, psi. H = height of a vertical fracture, ft. h = depth of formation, ft. HHP = hydraulic horsepower requirement, horsepower. K = permeability of formation to fracturing fluid, darcys. L = length of a vertical fracture measured from the well bore, fto. m = slope of experimental fluid loss line when cm3 fluid loss is plotted versus Jt(time), cc/m-F. NRE = Reynold's Number. AP = difference in pressure between the fluid at the formation face and the fluid in the formation, psi. 82

Nomenclature, Continued P. = fluid friction loss in pipe, psi. P = formation pressure, psig. E = hydrostatic fluid head of fracturing fluid in pipe, psig. hydraulic pressure required to maintain fracture parting, psig. P5 = surface pump pressure, psig. &Q,9Q~& V constant injection rate during treatment, bbl/min, ft3/min, bbl/min. SpGr = specific gravity of fracturing fluid, dimensionless. t = total pumping time, min. V = volume of fracturing fluid pumped, ft3. V = volume of sand injected into fracture, ft3. V spurt loss in fluid loss test, cm SpW = fracture width, ft. or in. W = corrected fracture width, ft. or in. W' = corrected fracture width, ft. or in. 2C~ft 4 F = viscosity of fracturing fluid, cp. A-R = viscosity of reservoir fluid, cp. R / = porosity of formation. p = density of water, lbm./ft3. 83

TABLE 4.1 4.4* Estimates of Young's Moduli of Formation Rocks Type of Rock Probable Value of E (psi) Porous, Unconsolidated to Lightly Consolidated (Friable) Sands 0.5 to 1.5 x 106 Medium-Hardness Sandstone 2 to 4 x 106 Hard, Dense Sandstone 5 to 7.5 x 106 Limestone and Dolomite 8 to 13- x 10 TABLE 4.2 4.6 Injection Rates (Recommended) For Various Tubing Sizes Tubing Size (in.) (Nominal Diam.) Injection Rate (bbl./min.) 1 22 10 3 15 51 25 Superscripts refer to reference from which graph or table was taken. 84

TABLE 4.3 Fracturing-treatment Cost Comparisons for Fluids of Various 4.18 Fracturing-fluid Coefficients Pumped at Different Injection Rates Hydraulic Fracturing Injection Rate, * Treatment, Horsepower, Fluid,++ Total, Bbl/Min C Gallons Dollars Dollars Dollars For a 50,000 sq. ft. fracture:+ 10 10 X 10-3 Impossible $ $ $ 10 5 X 10-3 88,000 735 2,640 5,375 10 1 X 10-3 8,000 735 400 1,135 20 10 X 10-3 Impossible 20 5 X 10'-3 47,000 1,470 1,410 2,880 20 1 X 10-3 5,000 1,470 250 1,720 3o lo100-3 110, 000 2,205 1, 100 3,305 30 5 x 10-3 30,000 2,205 9oo 3,105 30 1x lo-3 - 2,000 2,205 100 2,305 For a 100,000 sq. ft. fracture:+++ 10 10 X 10-3 Impossible 10 5 x 10-3 Impossible 10 1 x 10-3 23,000 735 690 1,425 20 10 10- Impossible 20 5 X 10-3 Impossible 20 1 X 10-3 15,000 1,470 750 2,220 * Assume $0.01 for fluid with C = 10 x 10-3 $0.03 c = 5 x lo-3 $0.05 C = 1 x 10-3 + 3,000 psi, surface pressure and $1.00 per hydraulic horsepower. ++ Fracturing-fluid cost, +++Average width of 0.1 in. 85

REFERENCES 4.1 "Optimum Fluid Characteristics for Fracture Extension,' G. C. Howard and C. R. Fast, API Drilling and Production Practice, 1957. 4.2 "Factors Controlling Fracture Extension," G. C. Howard and C. R. Fast, Con. Min. and Met. Bul., Vol. 54, No. 586, Feb. 1961. 4.3 "Hydraulic Fracture Design," D. D. Hunt, H. R. Crawford, ASME Paper No. 59-PET-45 for meeting Sept. 20-23, 1959. 4.4 "Widths of Hydraulic Fractures," J. K. Perkins, L. R. Kern, Jour. Petroleum Technology, Vol. 13, No. 9, Sept. 1961. 4.5 "Theoretical Principles of Hydraulic Fracturing of Oil Strata," S. A. Christianovitch, Y. P. Zhetov, G. I. Barenblatt, G. K. Maximovitch, World Petroleum Congress, Fifth-Proc., New York, New York, June 1959, Sec. II. 4.6 "Fracture Treatments in S. E. New Mexico," R. L. Essary, World Oil, Vol. 154, No. 4, March 1962. 4.7 "New Fracture-Acid Method Looks Good," Oil and Gas Jour., Vol. 57, No. 23, June 1, 1959. 4.8 "Walnut Shells Give Good Assist in Meramec Fractures," B. G. Alexander, J. M. Wagner, Oil and Gas Journal, Vol. 60, No. 43, October 22, 1962. 4.9 "Fluid and Propping-Agent Injection Schedule for High Capacity Fractures," B. B. McGlothlin, J. L. Huitt, J. W. Jennings, Oil and Gas Journal, Vol. 59, No. 38, Sept. 18, 1961, pp. 86-92. 4.10 "New Fracture Propping Process Uses Aluminum Pellets," J. E. Kastropo Petroleum Engr., Vol. 32, No. 12, Nov. 1960. 4.11 "Evaluation and Selection of Fracture Propping Agents," J. L. Huitt and B. B. McGlothlin and J. F. McDonald, Petr. Engr., Vol. 31, June 1959. 4.12 "Propping Fractures with Aluminum Particles," L. R. Kern, R. E. Wyant, T. K. Perkins, AIME Paper No. 1573G, prepared for meeting October 2-5, 1960. 86

4.13 "Sand Concentration for Maximum Fracture Flow Capacity," Antonio Romero-Juarez, AIME Paper No. 1574G, prepared for meeting October 2-5, 1960. 4.14 "Fractures and Craters Produced in Sandstone by High Velocity Projectiles," J. S. Rinehart, and W. C. Maurer, AIME Paper No. 1534G prepared for meeting October 2-5, 1960. 4.15 "Implosion Technique Improves Fracturing Performance," D. D. Setser, World Oil, Vol. 150, No. 4, March 1960. 4.16 "Some Results of Fracturing with the Single-Point Entry Technique," V. N. Swift, W. E. Bauman, J. W. Jennings, and J. L. Huitt, AIME Paper No. 1570G prepared for meeting, October 2-5, 1960. 4.17 "Stimulation Treatment Selectivity Through Perforation Ball Sealer Technology," R. W. Brown, R. G. Loper, Petroleum Engr., Vol. 31, No. 6, June 1959. 4.18 "Economics of Hydraulic Fracturing Using Wall-Building Additives," F. J. Shell, 0. K. Bodine, API Drilling and Production Practice, 1960. 4. 19 "Flow Charts Pinpoint Pressure Losses of Frac. Fluids," W. B. Bleakley, Oil and Gas Journal, Vol. 60, No. 42, October 15, 1962. 87

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