For large scale production optimization problem, gradient based algorithms seem to be the main feasible approach. However, such algorithms have not been widely performed in practice because of the following shortcomings:(i) it is very complicated to commutate the gradient of the objective function by the adjoint method which requires explicit knowledge of the simulator numeric and expertise in simulation development.(ii) Gradient based algorithms are currently restricted to a specific simulator which is mainly for water flooding and can not applied for EOR technology such as polymer flooding. (iii) We need simulator based on fully implicit method to obtain gradient that the calculation is usually huge and slow.
To avoid these difficulties, we intend to apply derivative free method for production optimization. Four typical categories of derivative free algorithm been considered include trust-region interpolation-based method (NEWUOA), direct search method (SID-PSM), evolutionary computation method (PSO) and stochastic approximation method (SPSA) as well. These algorithms can be easily combined with any commercial simulators. Fig. 1 shows the convergence performance of the above four algorithms for a two channel case with 450 control variables. This figure shows that NEWUOA performs best of the four methods with high NPV with fewer reservoir simulations. Fig. 2 shows the final oil saturation distribution before and after optimization using NEWUOA.
Recent publications:
- Zhao, H.; Chen, C.; Do, S.; Oliveira, D.F.B.; Li, G. and Reynolds, A.C.: Maximization of a Dynamic Quadratic Interpolation Model for Production Optimization – accepted for SPE Journal, 2012.