There has been much work done on the optimal well placement and control including some investigates on optimizing well types (injector or producer) and/or drilling order. However, to the best of our knowledge, there are no journal articles on the following problem that is sometimes given to reservoir engineering groups: given a potential set of reasonable drilling paths and a drilling budget that is sufficient to drill only a few wells, find the optimum well paths, determine whether a well should be an injector or a producer and the drilling order that optimizes production. In this work, optimizing production means maximizing the net present value (NPV) of production over the life of the reservoir.
Here, this field development optimization problem is solved using the generally acknowledged Genetic Algorithm (GA). Mixed encodings are used to form the chromosomes. A binary encoding for the optimization variables pertaining to well location indices and well types is proposed to effectively handle the large amount of categorical variables while the drilling sequence is parameterized with ordinal numbers. The same selection procedure is used for the binary encoded parameters and the ordinal encoded parameters, however, different mutation and crossover operations are applied. These two sets of variables are optimized both simultaneous and sequentially. In sequential optimization, the first optimization assumes all wells are drilled at time zero and determines the optimal well locations and types, while the second optimization assumes there is only one drilling rig working on site and optimizes the drilling order based on the optimal solutions obtained in the first optimization. Finally, control optimization can be carried out to further improve the NPV of life-cycle production. The impact of well locations and types, drilling order and control settings on the NPV obtained with simultaneous and sequential optimization are compared.
We test the overall GA workflow on two basic examples, a three-dimensional channelized reservoir where the potential well paths are either vertical or horizontal and the Brugge model where only vertical wells are drilled. As GA is a stochastic algorithm, multiple runs for each problem are done in order to evaluate the average performance and robustness of the algorithm. Results indicate that GA gives good solutions in the following sense: (i) the NPV produced is significantly larger than the NPV of any member of a set of initial guesses; (ii) different runs of GA produce a variety of choices of optimal well paths, but the variation in the estimated optimal NPVs is relatively small; (iii) for problems where wells are under rate controls, GA consistently produces NPVs that are higher than the one obtained with the original gradient-based algorithm developed several years ago, albeit at a higher computational cost.
To the best of our knowledge, this paper presents the first work that focuses on the problem of choosing a set of optimal drilling paths and determining which well should be injector and which well should be producer given a large fixed set of possible drilling paths.