MULTIVARIATE OPTIMISATION OF HYDRAULIC FRACTURE DESIGN

Abstract

This paper presents a detailed description of a true multivariate optimisation routine for the design of hydraulic fractures. Using the Sequential Unconstrained Minimisation Technique, the optimisation routine intelligently searches for the optimum combination of operator-controllable hydraulic fracture treatment parameters, as opposed to existing simple iterative schemes. Net Present Value (NPV) was used as a measure of the economic impact of hydraulic fracture design on incremental reservoir production revenue. The effects of individual treatment parameters on incremental NPV were investigated for a hypothetical well. The results showed that there was an optimum value for each of the treatment parameters: injection period, injection rate and proppant concentration. For the same hypothetical well, contours of incremental NPV vs two fracture treatment parameters (injection period/injection rate and injection period/proppant concentration) were also constructed. These contours were smooth and continuous and did not show multiple extreme value points. These observations imply that there should be no obvious barriers to the estimation of the optimal hydraulic fracture design using the optimisation routine. Indeed, through visual inspection of the contours in the case of 2 treatment parameters, the optimisation routine consistently arrived at the optimum solution for a given set of inputs. The optimisation routine was extended to 3 treatment parameters (injection period, rate, and proppant concentration) and again consistently arrived at the same optimum solution with different starting positions. The optimisation routine can be extended to any number of operator controllable treatment parameters.