Improved Estimation and Forecasting Through Residual-Based Model Error Quantification

Abstract

Summary Owing to the complex nature of hydrocarbon reservoirs, the numerical model constructed by geoscientists is always a simplified version of reality: for example, it might lack resolution from discretization and lack accuracy in modeling some physical processes. This flaw in the model that causes mismatch between actual observations and simulated data when “perfect” model parameters are used as model inputs is known as “model error”. Even in a situation when the model is a perfect representation of reality, the inputs to the model are never completely known. During a typical model calibration procedure, only a subset of model inputs is adjusted to improve the agreement between model responses and historical data. The remaining model inputs that are not calibrated and are likely fixed at incorrect values result in model error in a similar manner as the imperfect model scenario. Assimilation of data without accounting for model error can result in the incorrect adjustment to model parameters, the underestimation of prediction uncertainties, and bias in forecasts. In this paper, we investigate the benefit of recognizing and accounting for model error when an iterative ensemble smoother is used to assimilate production data. The correlated “total error” (a combination of model error and observation error) is estimated from the data residual after a standard history-matching using the Levenberg-Marquardt form of iterative ensemble smoother (LM-EnRML). This total error is then used in further data assimilations to improve the estimation of model parameters and quantification of prediction uncertainty. We first illustrate the method using a synthetic 2D five-spot example, where some model errors are deliberately introduced, and the results are closely examined against the known “true” model. Then, the Norne field case is used to further evaluate the method. The Norne model has previously been history-matched using the LM-EnRML (Chen and Oliver 2014), where cell-by-cell properties (permeability, porosity, net-to-gross, vertical transmissibility) and parameters related to fault transmissibility, depths of water/oil contacts, and relative permeability function are adjusted to honor historical data. In this previous study, the authors highlighted the importance of including large amounts of model parameters, the proper use of localization, and heuristic adjustment of data noise to account for modeling error. In this paper, we improve the last aspect by quantitatively estimating model error using residual analysis.