Determination of optimal location for the injection (and production) wells is a critical step in reservoir development plan in order to produce higher hydrocarbon at lower cost. Finding optimal well locations is an optimization problem on discrete variables (well gridblock indices) and is normally done with a non-gradient based method such as genetic algorithm. A novel idea is presented to convert the discrete optimization problem into a problem on continuous variables. The idea is to put several number of wells in all part of the reservoir and then optimize the net present value (NPV) with respect to the rate of the hypothesized wells. The NPV includes an additional term to account for the cost of the \drilling of a well”. As the cost of “drilling a well” is detracts from the NPV, when NPV is maximized with respect to the wellrate, the rate of some wells will be driven to zero and hence these wells are eliminated from the system. Since well rate is continues, adjoint gradient can be implemented for the optimization process while the gradient projection method is used to ensure the linear constraints to be satisfied. Non-linear constraints such as BHP constraints can be imposed explicitly in an ad hoc procedure.
Recent publications:
- Zhang, K.; Li, G.; Reynolds, A.C.; Yao, J. and Zhang, L.: Optimal Well Placement Using an Adjoint Gradient, Journal of Petroleum Science and Engineering, 2010.
- Forouzanfar, F.; Li, G. and Reynolds, A.C.: A Two-stage Well Placement Optimization Method Based on Adjoint Gradient – paper SPE 135304, SPE Annual Technical Conference and Exhibition held in Florence, Italy, 19-22 September 2010.