Nonlinear constrained production optimization based on augmented Lagrangian function and stochastic gradient

• The method is based on an augmented Lagrangian function.
• SGFD algorithm is applied for optimizing nonlinear constrained production.
• SGFD shows a better convergence compared to GPSA algorithm.
• A real reservoir case proves the availability of the method.

In the oil and gas industry, reservoir simulation provides reliable information regarding processes which occur in the interior of a reservoir during oil or gas field development. And production optimization could be achieved through a robust reservoir simulation program. In this paper, a new method based on an augmented Lagrangian function and the Stochastic Gradient and the Finite Difference (SGFD) for nonlinear constrained production optimization is proposed. The method can accelerate computation and improve accuracy of the approximate gradient. The approximate gradient is very close to the true gradient and shows a better convergence compared to the Gaussian distribution Simultaneous Perturbation Stochastic Approximation (GPSA) method. Through the test of a real reservoir, the injection and production rates have been constrained successfully, which enhances oil or gas recovery and offers the best net present value (NPV). This method also offers theoretical support for the smart field system.