Scale Formation in Reservoir and Production Equipment During Oil Recovery: An Equilibrium Model

Abstract

Summary This paper presents a reliable model for the solubility products ofscale-forming minerals. Our model solubilities are in relatively good agreement(±5% to 10%) with the most reliable solubilities in aqueous solutions of up totwice the seawater concentration at temperatures of 20 to 150°C and pressuresup to 40 MPa. An equilibrium model for the reactions responsible for scaleformation is developed. The CO2 equilibria between the gas, oil, andwater phases and in the water phase itself are considered. By combining ahydrodynamic model for the transport of water through an oil reservoir duringwaterflooding with the proposed equilibrium model, we can estimate the amountof precipitate formed in the reservoir. Introduction Many inorganic salts and amorphous materials may be found as solid materialsadhering to the inner walls of tubing, pumps, and other production equipmentduring oil recovery. In the present work, however, we consider only the mostcommon and troublesome scales found: CaCO3, CaSO4, CaSO4·2H2O, SrSO4, and BaSO4. To predict the conditions under which these minerals may form scale, onemost know the solubility products of these salts and how these solubilityproducts vary with composition, temperature, and pressure. We reviewed literature on models for activities of the most commonscale-forming minerals. A quasitheoretical solubility model is proposed herethat can predict reasonable solubilities in temperature, pressure, andcomposition regions where experimental data are available. The solubility modelthen was used to calculate the amount of precipitate formed at equilibrium whentypical formation water and seawater are mixed under conditions that maycompare with conditions found during waterflooding operations. Solubility Models for Some Scale-Forming Minerals The solubility product of a salt MX·nH2O,Ksp(MX), which dissolves in water according to Equation 1 is defined by Equation 2 where CM2+ and CX2- are themolal concentrations of the M2+ and X2- ions of thecompletely dissociated MX salt in the aqueous phase in equilibrium with solid MX. The solubility product defined in this way may vary with the composition ofthe aqueous phase. The thermodynamic solubility product, however, which is independent ofconcentration, is defined as Equation 3 where ?M2 and ?M2- are the twoionic activity coefficients and a H2Ois the water activity. A reasonable model for the activity coefficient of the precipitating salt, together with experimental data of the temperature and pressure variations ofthe thermodynamic solubility product, is thus sufficient to give a reasonableestimate of the solubility of any scale-forming mineral under variousconditions. Pressure Dependence of Solubility. Very little is known about the pressure variation of the solubility ofscale-forming minerals. The published data lack the necessary accuracy to showthe expected trends when solubility is measured as a function of pressure. Thisis a result of the experimental difficulties involved in obtaining accuratesolubilities of these very insoluble salts. The reaction volume of Eq. 1, however, is connected to the thermodynamicsolubility product of the MX salt through the relation Equation 4 where p=pressure, R=gas constant, T=absolutetemperature, ?V01=standard molal volume change, and ? c01=standard compressibility change for Eq. 1. The two standard states are pure, solid MX, and an ideal 1 M solutionof MX. The pressure variations of the activity coefficients (infinite dilutionreference state) may be obtained from Equation 5 where Vi and ci are the partial molalvolume and compressibility of Component i, respectively, and Vi and ci are the same quantities for i in the ideal 1 M solution. By combining Eqs. 4 and 5, we can calculate the pressure dependence of thesolubility product: Equation 6 where ?V1 and ?c1 are the real volumeand compressibility changes for Eq. 1. Table 1 gives the ?c1 values for CaCO 3, CaSO4, CaSO4·2H2O, SrSO 4, and BaSO4 in pure water andseawater. In our calculations, linear extrapolations with ionic strength are used tocalculate ?c1 values outside the experimental ranges. Thetemperature variations observed in ?c1 values1are neglected in the present calculations because data for salt solutions areavailable only up to 25°C. The justification for this approximation is found in Eqs. 4 and 6, where the ?c1p/RT term is about 10% ofthe total pressure variation of ln Ksp at 20.3 MPa. The volume changes of Eq. 1 are known as functions of temperature atinfinite dilution in pure water and in seawater.1,2 These data, together with data obtained in our laboratory on the direct volume changes of Eq. 1, are used to obtain an equation that can describe how?V1 varies with temperature and ionic strength, I, ofthe saturated solution. For all the systems investigated. Equation 7 could be used in the temperature range of 0 to 200°C. Table 2 givesthe different coefficients in Eq. 7, and Table 3 gives the volume dataof the solid minerals. Millero1 predicted solubilities of SrSO4 andCaCO3 in aqueous solutions at pressures up to 100 MPa using partialmolar volume, compressibility data, and Eq. 6. His results agreed well withexperimental solubilities at high pressures for both minerals. Pressure Dependence of Solubility. Very little is known about the pressure variation of the solubility ofscale-forming minerals. The published data lack the necessary accuracy to showthe expected trends when solubility is measured as a function of pressure. Thisis a result of the experimental difficulties involved in obtaining accuratesolubilities of these very insoluble salts. The reaction volume of Eq. 1, however, is connected to the thermodynamicsolubility product of the MX salt through the relation Equation 4 where p=pressure, R=gas constant, T=absolutetemperature, ?V01=standard molal volume change, and ? c01=standard compressibility change for Eq. 1. The two standard states are pure, solid MX, and an ideal 1 M solutionof MX. The pressure variations of the activity coefficients (infinite dilutionreference state) may be obtained from Equation 5 where Vi and ci are the partial molalvolume and compressibility of Component i, respectively, and Vi and ci are the same quantities for i in the ideal 1 M solution. By combining Eqs. 4 and 5, we can calculate the pressure dependence of thesolubility product: Equation 6 where ?V1 and ?c1 are the real volumeand compressibility changes for Eq. 1. Table 1 gives the ?c1 values for CaCO 3, CaSO4, CaSO4·2H2O, SrSO 4, and BaSO4 in pure water andseawater. In our calculations, linear extrapolations with ionic strength are used tocalculate ?c1 values outside the experimental ranges. Thetemperature variations observed in ?c1 values1are neglected in the present calculations because data for salt solutions areavailable only up to 25°C. The justification for this approximation is found in Eqs. 4 and 6, where the ?c1p/RT term is about 10% ofthe total pressure variation of ln Ksp at 20.3 MPa. The volume changes of Eq. 1 are known as functions of temperature atinfinite dilution in pure water and in seawater.1,2 These data, together with data obtained in our laboratory on the direct volume changes of Eq. 1, are used to obtain an equation that can describe how?V1 varies with temperature and ionic strength, I, ofthe saturated solution. For all the systems investigated. Equation 7 could be used in the temperature range of 0 to 200°C. Table 2 givesthe different coefficients in Eq. 7, and Table 3 gives the volume dataof the solid minerals. Millero1 predicted solubilities of SrSO4 and CaCO3 in aqueous solutions at pressures up to 100 MPa using partialmolar volume, compressibility data, and Eq. 6. His results agreed well withexperimental solubilities at high pressures for both minerals.