Abstract
Optimizing placement and trajectory of wells is a computationally demanding, and hence time-consuming task due to the high number of simulations typically required to achieve a local optimum. In this work, we combine three remedies for speeding up the workflow; firstly, we employ a flow-diagnostics (see [1] ) proxy for the objective e.g., net-present-value; secondly, we implement an efficient adjoint for computing approximate sensitivities with respect to the placement/trajectory parameters (as suggested in [2] ); and finally, we include a version of the generalized reduced gradient (GRG) method (see [3] ) for efficient constraints handling of the control optimization problem.
The suggested flow diagnostic proxy is based on a single (or a few) pressure solutions for the given scenario and the solution of several inter-well time-of-flight and steady-state tracer equations, typically achieved in a few seconds for a reservoir model of medium size. Although the proxy may not be a particularly good approximation of the full reservoir simulation response, we find that for the cases considered, the correlation is very good and hence the proxy is suitable for use in an optimization loop. The adjoint simulation providing control gradients and placement sensitivities is of similar computational complexity as the forward model (a few seconds). The version of the GRG used here amounts to treating all individual well constraints (e.g., bhp and rates) as control variables and update only those that are active for a given control step. This means that individual well constraints can be enforced within the flow diagnostics computations, and hence every iteration becomes feasible without sacrificing gradient information.
We present numerical experiments illustrating the efficiency and performance of the approach for well-placement problems involving trajectories and simulation models of realistic complexity. The suggested placements are evaluated using full simulations. We conclude by discussing the limitations and possible enhancements of the methodology.
The suggested flow diagnostic proxy is based on a single (or a few) pressure solutions for the given scenario and the solution of several inter-well time-of-flight and steady-state tracer equations, typically achieved in a few seconds for a reservoir model of medium size. Although the proxy may not be a particularly good approximation of the full reservoir simulation response, we find that for the cases considered, the correlation is very good and hence the proxy is suitable for use in an optimization loop. The adjoint simulation providing control gradients and placement sensitivities is of similar computational complexity as the forward model (a few seconds). The version of the GRG used here amounts to treating all individual well constraints (e.g., bhp and rates) as control variables and update only those that are active for a given control step. This means that individual well constraints can be enforced within the flow diagnostics computations, and hence every iteration becomes feasible without sacrificing gradient information.
We present numerical experiments illustrating the efficiency and performance of the approach for well-placement problems involving trajectories and simulation models of realistic complexity. The suggested placements are evaluated using full simulations. We conclude by discussing the limitations and possible enhancements of the methodology.
