Constraint handling for gradient-based optimization of compositional reservoir flow

The development of adjoint procedures for general compositional flow problems is much more challenging than for oil-water problems, due to significantly higher complexity of the underlying physics. The treatment of nondifferentiable constraints, an example of which is a maximum gas rate specification in injection or production wells, when the control variables are well-bottom-hole pressures, poses an additional major challenge. A new formal approach for handling these constraints is presented and compared against a formal treatment within the optimizer employing constraint lumping and a simpler heuristic treatment in the forward model. The three constraint-handling methods are benchmarked for three example cases of increasing complexity. Moreover, the new approach allows the optimizer to converge to optimal solutions exhibiting higher objective values, since unlike the formal lumping-based methods, where a pressure reduction suggested by the optimizer propagates through the smoothing function to all well rates, it handles constraints individually on a per well and per time step basis. The numerical examples show that the new formal constraint-handling approach allows the optimizer to converge significantly faster than formal lumping-based techniques independently of the initial guess used for the optimization.