  Large numbers of flow simulations are typically required for determining
optimal well settings. These simulations are often computationally demanding,
which poses challenges for the optimizations. In this paper we present a new
two-step surrogate treatment (ST) that reduces the computational expense
associated with well control optimization. The method is applicable for oil
production via waterflood, with well rates optimized at a single control
period. The two-step ST entails two separate optimizations, which can both be
performed very efficiently. In the first optimization, optimal well-rate ratios
(i.e., the fraction of total injection or production associated with each well)
are determined such that a measure of velocity variability over the field is
minimized, leading to more uniform sweep. In the second step, overall injection
and production rates are determined. The flow physics in the first step is
highly simplified, while the actual physical system is simulated in the second
step. Near-globally-optimal results can be determined in both cases, as the
first optimization is posed as a QP problem, and the second step entails just a
single optimization variable. Under full parallelization, the overall elapsed
time for the ST corresponds to the runtime for 1-2 full-order simulations.
Results are presented for multiple well configurations, for 2D and 3D
channelized models, and comparisons with formal optimization procedures (MADS
and adjoint-gradient) are conducted. Three different fluid mobility ratios (M =
1, 3 and 5) are considered. Optimization results demonstrate that the two-step
ST provides results in reasonable agreement with those from MADS and
adjoint-gradient, with speedups of 5x or more. We also show that the ST is
applicable in the inner-loop in field development optimization, where it will
be especially useful since many different well configurations must be
evaluated.
