Simulation and Optimization of Foam EOR Processes

Abstract

Chemical enhanced oil recovery (EOR) is relatively expensive due to the high cost of the injected chemicals such as surfactants. Excessive use of these chemicals leads to processes that are not economically feasible. Therefore, optimizing the volume of these injected chemicals is of extreme importance. We intend to maximize the long-term cumulative oil production (Qo,cum) through optimizing the volume of the injected surfactant (represented by the switching time between surfactant and gas slugs) in a surfactant-alternating-gas (SAG) process in a 3D reservoir using a commercial simulator. Evaluating the correctness and accuracy of the numerical simulator is an essential step towards achieving reliable results. However, since no analytical solution exists for a real 3D displacement (with gravity), the performance of the simulator in 1D is evaluated against the exact analytical solutions provided by the method of characteristics (MOC). The MOC has proved useful in highlighting key mechanisms and strategies for improving foam performance. We extended the MOC to foam flow with oil and examined the effects of foam quality, initial oil saturation So(I), and foam sensitivity to high oil saturation (So) and low water saturation (Sw) on oil recovery in 1D. In the cases examined, our analysis revealed the following insights. Regardless of whether foam is sensitive to Sw, if foam is destroyed by oil at the initial condition, the displacement is nearly as inefficient as if no foam were present at all. In real foams, foam bubbles collapse at the residual water saturation (Swr) because of high capillary pressure. The failure to represent this mechanism properly in models leads to misleading prediction of success in SAG foam processes. Incorporating foam collapse at Swr results in the failure of a gas-injection cycle of a SAG process, regardless of the reservoir initial condition and foam sensitivity to Sw and So, for the relative-permeability models we examined. A foam flood is successful for any initial condition if foam is only weakened (not killed) by low Sw and not affected by So. Based on this study, it is not recommended to start foam EOR at early stages of the reservoir life for a foam formulation that is sensitive to high oil saturation, because high So(I) causes the foam EOR process to fail. Thus, the effect of low Sw and high So on foam must be well understood and represented accurately to avoid spurious decisions leading to failure based on unrealistic foam models and parameter values. The MOC solutions developed earlier are utilized to evaluate the performance of the simulator in 1D. In finding an accurate numerical solution that matches the MOC solution, some displacements were found to be more sensitive to the choice of time-step (?t) and gridblock size (?x) than others. For instance, if a part of the solution (e.g., rarefaction wave, constant-state region) is in the proximity of the foam/no-foam boundary at which drastic changes in gas mobility occur, the simulator may exhibit oscillations across the boundary with an improper choice of ?t and ?x and fail to find to the correct solution. Moreover, an inappropriate choice of ?t and ?x leads to erroneous results that might be hard to identify in 3D in the absence of the MOC solutions. One needs to look for symptoms, such as gridblocks with unexpected high/low saturation/pressure, to identify artifacts and find a proper choice of ?t and ?x by performing sensitivity analysis on these parameters. Insights achieved from this analysis led to applying simpler physics for the foam model in the 3D simulations to ensure finding the correct solution. The effect of the switching time (ts) between surfactant and gas slugs on Qo,cum was examined for 3D simulations of a SAG process in scenarios varying in the active constraint on the injection well and the end-time constraint. For all the scenarios, the highest oil recovery was obtained at a value of ts for which the foam front was on the verge of breaking through to the production well, but has not yet broken through, at the end of the simulation. Moreover, the cumulative oil production was impaired once foam appeared in the production well. Therefore, if foam can be destroyed in the proximity of the production well, the optimal oil recovery increases. On the other hand, for an injection well operating at a constant prescribed bottomhole pressure, injecting surfactant into the reservoir did not necessarily lead to improved Qo,cum over a gas flood. Further, increasing ts did not result in higher Qo,cum under certain conditions. In addition, injecting less gas as a result of increasing ts did not lower Qo,cum in many occasions. An investigation was conducted on the capability of a gradient-based optimization routine applied to foam EOR processes. We concluded that an inappropriate choice of the relative tolerance for the adjoint linear solver is the source of getting wrong gradients in our problem, and a very tight relative tolerance was required for the simulator to obtain accurate gradients in certain problems. We applied two types of foam models in this investigation: a linear model introducing gradual changes in gas mobility and a nonlinear model leading to abrupt changes in gas mobility. For the linear foam model (both in 1D and 3D simulations), the local and global trends of the objective function (Qo,cum) were analogous and the optimization routine was capable of finding the optimum switching time (ts,opt). However, replacing the linear foam model with the nonlinear foam model introduced inconsistencies between the local and global trends of the objective function and fluctuations in the adjoint gradient, in both 1D and 3D simulations. For the nonlinear foam model, the local and global trends were analogous and the adjoint gradient was free of fluctuations only at switching times for which the entire reservoir was swept by foam within the simulation period. For the 1D-nonlinear foam model, the gradient-based optimization routine was not suitable for finding ts,opt, unless the initial guess is larger than ts,opt. For the 3D-nonlinear foam model, there were major differences between the local and global trends of the objective function in the neighborhood of the optima that would seriously challenge the performance of the optimization routine. As a result, a gradient-based optimization routine was not suitable for finding ts,opt. Overall, it is shown that accurate representation of the physics of the process in the simulation model and also careful examination of the mechanisms controlling the displacement process elucidate many valuable aspects of the foam EOR processes. Their inaccurate representation in simulations or neglecting them may result in a prediction of success for a process that will be unsuccessful in a real reservoir. Moreover, formation of foam may introduce abrupt changes in gas mobility that might challenge the performance of the simulator and also the gradient-based optimization routines.