Mixed-integer Optimization under Uncertainty in Reservoir Development and Management

Resumo

Reservoir geoengineering is usually faced with large-scale optimization problems under uncertainty
arising as part of development planning of smart wells locations, performing separated, jointly, or simultaneously
optimization of well locations and control rates of water injection and hydrocarbon productions. This paper
performs a simultaneous optimization of well locations and production rates under geological uncertainty using
Monte Carlo samples over geostatistical realizations. Those optimization problems are of mixed-integer type.
Traditionally, they have been solved by performing projections between real and integer variables using different
strategies, Whitney and Hill [7]. This work investigates the performance of DSPSA, a discrete version of SPSA,
recently described in Wang and Spall [13], and proposes a discrete variant to be applied in mixed-integer problems
where all control variables are ceiling round, taking advantage of practical field implementations. One-sided
deterministic constraints are imposed to reduce search space. For more general one-sided stochastic non-linear
constraints, see Fonseca [3] and Fonseca et al. [9]. In the class of reservoir problem solved in this paper, functional
and constraints derivatives a never available, mainly because industry solves the reservoir simulation problem
using commercial software as a black box. Additional metaheuristics are used to construct the discrete version of
DSPSA. This work makes a preliminary comparison between the new discrete version, DSPSA-R, with SPSA-Z,
the mixed-integer version of SPSA in Fonseca [3].