Vapor-Liquid-Liquid Equilibrium Modeling of Water/Bitumen/Solvent (C1, C2, C3, and n-C4) Mixtures Using a Cubic-Plus-Association Equation of State

Multiphase equilibrium calculations are important in primary and enhanced oil recovery production mechanisms such as natural depletion, gas injection, and steam injection. Predicting the physical properties of phases under different conditions is necessary for designing optimum recovery techniques. In this work, we report a cubic-plus-association equation of state (CPA EoS) parameterization of vapor-liquid-liquid equilibrium (VLLE) of water/bitumen/solvent (C-1, C-2, C-3, and n-C-4) systems. In this approach, first, the unknown parameters of the EoS are tuned versus the solvent mole fraction in the bitumen-rich phase and saturated bitumen density data. Next, the binary interaction parameters (BIPs) between bitumen and hydrocarbons (C-1, C-2, C-3, and n-C-4) and nonhydrocarbon (CO2 and N-2) solvents are adjusted versus experimental data. The absolute average relative deviation (AARD) values for solubility of C-1, C-2, C-3, n-C-4, CO2, and N-2 are 3.35, 5.58, 4.18, 19.39, 7.43, and 2.36%, respectively, and for the density data, these deviations are 0.52, 0.50, 1.36, 1.99, 0.55, and 0.19%, respectively. In the next step, the cross-association energy and the BIPs between water and bitumen molecules are adjusted under liquid-liquid equilibrium conditions. For these calculations, the AARD values of solubility and saturated bitumen density are 8.35 and 0.36%, respectively. Finally, the obtained parameters are used without further tuning in performing VLLE calculations in the systems composed of hydrocarbon solvents, water, and bitumen. The solubility of C-1, C-2, C-3, and n-C-4 in wet bitumen is predicted with AARD values of 17.17, 18.87, 12.21, and 15.52%, respectively, and the saturated wet bitumen densities are predicted at AARD values of 1.42, 0.79, 1.62, and 1.80%, respectively. Our results revealed that the CPA-EoS is capable of predicting multiphase equilibrium calculations of solvent/bitumen/water systems based merely on binary system parameters, which is an important step forward in eliminating or reducing the need for time-consuming and expensive multiphase/multicomponent laboratory experiments. These results find applications in designing and optimizing solvent-aided and solvent-based bitumen recovery from oil sands.