Parameter Estimation and Uncertainty Quantification for Core Flooding

Abstract

In light of our depleting fossil fuel reserves and the relatively `cheap' extraction of oil and in spite of the highly nonlinear nature of reservoirs, waterflooding has become big business. In recent times, the use of numerical reservoir simulation has not only become possible but has increasingly been used in the petroleum industry in the forecasting of output and money to be made. However, this numerical modelling and automated history matching is not without its problems. The inner workings of sophisticated commercial reservoir simulators are often taken for granted, i.e., ``black boxes''. These simulators are constructed around a numerical method, with its advantages and disadvantages. Herein, the input settings play a role in the stability and precision of results. For example, the chosen iteration method, grid spacing and time step size or even the choice of iteration parameters, all based on insufficient data, leads simulators to be unreliable and inefficient. Moreover, even under the assumption that such ``black boxes'' are able to produce a true prediction, this is entirely conditional on correctly establishing the current state and conditions. Thus, practitioners have many global settings given, many of which inaccurate. These many uncertainties can lead to costly mistakes.
The aim of this study therefore: is to develop a tool that can quantify the uncertainty of a core flood model and a parameter estimation routine.
Specifically, it investigates whether, given limited incoming data, an uncertain parameter can be estimated and then used to simulate and quantify the uncertainty of the water saturation and oil pressure in the core sample. In this context, we question if it be used to provide a history match of the core sample.
To see how the uncertain input parameters are reflected in a model output, the tool, based on, the IMPES scheme simulates the two-phase flow, and the Ensemble Kalman filter (EnKF) to estimate the parameters. Building on the base twin experiment, a variety of twin experiments were performed to understand the parameter estimation, by presenting and visualizing the uncertainties in the data and states. We investigate the use of the EnKF for history matching and ways to improve are also explored.
Based on the results of this study, it is concluded that the Ensemble Kalman Filter is capable of effective parameter estimation. With modification, it can also be used for history matching and uncertainty quantification. It clearly suggests that the utility of numerical modelling and automated history matching will continue to make contributions to the success of the exploration and extraction of fossil hydrocarbons.