CO₂ Water-Alternating-Gas (CO₂-WAG) injection is not only a method to enhance oil recovery but also a feasible way to achieve CO₂ sequestration. However, inappropriate injection strategies would prevent the attainment of maximum oil recovery and cumulative CO₂ storage. Furthermore, the optimization of CO₂-WAG is computationally expensive as it needs to frequently call the compositional simulation model that involves various CO₂ storage mechanisms. Therefore, the surrogate-assisted evolutionary optimization is necessary, which replaces the compositional simulator with surrogate models. In this paper, a surrogate-based multi-objective optimization algorithm assisted by the single-objective pre-search method is proposed. The results of single-objective optimization will be used to initialize the solutions of multi-objective optimization, which accelerates the exploration of the entire Pareto front. In addition, a convergence criterion is also proposed for the single-objective optimization during pre-search, and the gradient of surrogate models is adopted as the convergence criterion. Finally, the method proposed in this work is applied to two benchmark reservoir models to prove its efficiency and correctness. The results show that the proposed algorithm achieves a better performance than the conventional ones for the multi-objective optimization of CO₂-WAG.

Rate-transient analysis (RTA) has been widely applied to extract estimates of reservoir/hydraulic fracture properties. However, the majority of RTA techniques can lead to misdiagnosis of reservoir/fracture information when the reservoir exhibits reservoir heterogeneity and multiphase flow simultaneously. This work proposes a practical-yet-rigorous method to decouple the effects of reservoir heterogeneity and multiphase flow during TLF, and improve the evaluation of reservoir/fracture properties.

A new, general, semi-analytical model is proposed that explicitly accounts for multiphase flow, fractal-based reservoir heterogeneity, anomalous diffusion, and pressure-dependent fluid properties. This is achieved by introducing a new Boltzmann-type transformation, the exponent of which includes reservoir heterogeneity and anomalous diffusion. In order to decouple the effects of reservoir heterogeneity and multiphase flow during TLF, the modified Boltzmann variable allows the conversion of three partial differential equations (PDE's) (i.e., oil, gas and water diffusion equations) into ordinary differential equations (ODE's) that are easily solved using the Runge-Kutta (RK) method. A modified time-power-law plot is also proposed to estimate the reservoir and fracture properties, recognizing that the classical square-root-of-time-plot is no longer valid when various reservoir complexities are exhibited simultaneously. Using the slope of the straight line on the modified time-power-law plot, the linear flow parameter can be estimated with more confidence. Moreover, because of the new Boltzmann-type transformation, reservoir and fracture properties can be derived more efficiently without the need for defining complex pseudo-variable transformations.

Using the new semi-analytical model, the effects of multiphase flow, reservoir heterogeneity and anomalous diffusion on rate-decline behavior are evaluated. For the case of approximately constant flowing pressure, multiphase flow impacts initial oil rate, which is a function of oil relative permeability and well flowing pressure. However, multiphase flow has a minor effect on the oil production decline exponent. Reservoir heterogeneity/anomalous diffusion affect both the initial oil production rate and production decline exponent. The production decline exponent constant is a function of reservoir heterogeneity/anomalous diffusion only.

The practical significance of this work is the advancement of RTA techniques to allow for more complex reservoir scenarios, leading to more accurate production forecasting and better-informed capital planning.