Influence of Additional Objective Functions on Uncertainty Reduction and History Matching

Abstract

This paper proposes new objective functions to assimilate dynamic data for history matching, and evaluates their influence on the uncertainty conditioning. Representative events are observed and evaluated separately for the available dynamic data. The proposed objective functions evaluate two specific events: (1) the production transition behavior between the historical and forecasting period, and (2) the water breakthrough time. To assess production transition behavior, the deviation between the latest available historical data is compared with the forecast value, at a specific moment, under forecasting conditions. To assess water breakthrough, the irruption time error is measured in addition to the water-rate objective function. The new objective functions are normalized using the Normalized Quadratic Deviation with Sign, for comparison with conventional objective functions (i.e. NQDS-oil production rate). These additional objective functions are included in a probabilistic and multi-objective history matching and applied to the UNISIM-I-M benchmark for validation. Two history-matching procedures evaluate the impact of the additional objective functions, based on the same parameterization, boundary conditions and number of iterations. The first procedure (Procedure A) includes objective functions traditionally used such as fluid rates and bottom-hole pressure, computed using all the historical data points. The second procedure (Procedure B) considers the same as for A as well as the two additional objective functions. The advantages of including the additional objective functions was the supplementary data used to constrain the uncertainties, improving attribute updates. Consequently, Procedure B generated better-matched models considering the historical period and more consistent forecasts for both field and well behavior when compared to available reference data. The addition of the breakthrough deviation improved the quality of the match for water rates because breakthrough deviation is sensitive to reservoir attributes different to those objective functions related to water rate. The production transition error assisted the identification of scenarios that under or overestimated well capacity. Production transition error also improved the transition of the models from the historical to the forecasting period, reducing fluctuations due to the changes in boundary conditions. Despite the increased number of objective functions to be matched, the improved reliability for forecasting is an incentive for further study. Other representative events, such as oil rate before and after the start of water production could be separated and evaluated, for example. The improved reliability for forecasting supports the inclusion of the proposed objective functions in history-matching procedures.