繰り返しラテン超方格法を用いたCO₂地中貯留における坑井配置の大局的最適化

抄録

This study aims at developing a new population-based global optimization algorithm, called iterative Latin hypercube samplings (ILHS), and applying the ILHS to a global optimization of well placement for geological storage of CO₂. The ILHS utilizes a space-filling property specific to the Latin hypercube sampling (LHS) : each independent variable xj(j=1, …, d) is divided into n strata of equal marginal probability and sampled once from each stratum. In the ILHS, the LHS is generated iteratively while a cumulative distribution function for each variable at the current step is updated from the fitnesses evaluated at the previous step. This iterative process enables us to search a global optimum in a derivativefree way. Considering a global minimization of an objective function involving only continuous independent variables, the mathematical formulation of the basic algorithm is described first.
In general, in order to carry out a numerical simulation of CO₂ migration in the subsurface, the target domain is divided into multiple grids and the well placement is indicated by the grid index. Therefore, we need to consider a global optimization of an objective function involving discrete independent variables. Here, a brief handling method toward the application of the ILHS involving discrete independent variables is introduced and we attempt to find an optimal well placement using the ILHS so as to minimize the amount of mobile CO₂. The results for example problems confirm that our proposed algorithm can search an optimal solution effectively within a practical number of simulation runs.