Modeling Paraffin Wax Deposition from Flowing Oil onto Cold Surfaces

Abstract

Paraffins with large molecular weights precipitate out of solution when temperature decreases, forming a three-dimensional network of crystals that can impede oil flow in a pipe, which is undesirable during crude oil production. One way to assess the potential and severity of a paraffin wax deposition is to employ a first principle mathematical model that can predict the growth rate and evolution of paraffin wax gel or deposit as a function of time. In this thesis, a wax deposition model that includes transient heat transfer and transient mass transfer that are coupled was developed. The model takes the cold finger geometry as a basis and assumes that the heat and mass transfer occur primarily in the radial direction and negligible in other directions while allowing for the possible effects of yield stress on the deposition through a critical solid wax concentration at the deposit-fluid interface, Cpi. This new parameter is the precipitated wax concentration needed to withstand the shear stress imposed by the flow at the interface and reflects the dependence of the deposit yield stress on precipitate concentration and the fluid shear stress at the interface. Wax is taken to be a pseudo one-component that can exist in either a molecular (soluble) or precipitated state. Precipitation is described by a first order reaction where the rate law is given by the product of a rate coefficient and the difference between the local soluble wax concentration and the local solubility limit. Precipitated waxes are assumed to not diffuse and can revert back into soluble waxes if the local soluble wax concentration becomes lower than the local solubility limit. Model predictions were found to be in good agreement with experimental data obtained using a cold finger apparatus. A model oil with a relatively high concentration of wax (in this work composed of 10wt% n-C28 in n-C12), was found able to form gels at a very low precipitated wax concentration where the effect of Cpi is insignificant (close to zero), thus as a result the rate of advancement of the gel-oil interface is dominantly controlled by the heat transfer rate. However, even after reaching a steady-state thickness, n-C28 in the bulk oil continues to diffuse into the gel, densifying the gel. This observation signifies that mass transfer must be taken into account regardless of whether heat or mass transfer is controlling the growth rate. It was also found that after reaching the maximum gel thickness, the gel-oil interface can also retreat back and approaches a new steady-state location which is reached at a much slower rate of days to weeks. This retreat of the front was found to be the result of the depletion of wax in the bulk oil. Experiment performed using a dilute wax model oil (in this work composed of 0.8wt% n-C36 in mineral oil) revealed that its gel growth rate is controlled dominantly by mass transfer. In a dilute wax model oil, the concentration of precipitated waxes is so small that a stable gel is unable to form until mass transfer carrying wax molecules from the bulk oil to the cold surface have accumulated sufficient precipitated waxes around the vicinity of the surface. In this regard, the parameter Cpi in the model becomes significant (Cpi greater than zero).