Optimal Choice of Inversion Parameters for History-Matching with the Pilot Method

There is currently significant interest in the industry towards computer-aided history-matching methods. These methods must lead to a good match of production data, but also satisfy a priori geological constraints. The "pilot-point method" appears to provide a promising solution to the problem, by combining geostatistical techniques with gradient-based optimisation algorithms. In this paper, the optimal choice of location and number of pilot-points is addressed. A new approach is presented, which combines two criteria. The first criterion is sensitivity: pilotpoint locations must be such that a change in pilot-point parameters significantly influences the objective function. The other criterion is uncertainty: if pilot-point values are to be changed in the history-matching process, they must be subject to a high degree of uncertainty. Combining the kriging variance and the results of an eigenvalue/eigenvector analysis of the Gauss-Newton matrix - which is calculated for a regular subset of gridcells - allows a rational choice to be made about the best number and positions for the pilot-points. The performance of the suggested method is evaluated by applying it to a synthetic case study consisting of 5 layers, 3000 gridcells and 6 wells. Matched production data include Well Pressures, Water Cuts and Gas-Oil Ratios. The multiple solutions obtained are used to quantify the uncertainty on production forecasts.