The usual procedure in history matching is to adopt a Bayesian approach with an objective function that is assumed to have a single simple minimum at the "correct" model. In this paper, we use a simple cross-sectional model of a reservoir to show that this may not be the case. The model has three unknown parameters: high and low permeabilities and the throw of a fault. We generate a large number of realizations of the reservoir and choose one of them as a base case. Using the weighted sum of squares for the objective function, we find both the best production-and best parameter-matched models. The results show that a good fit for the production data does not necessarily have a good estimation for the parameters of the reservoir, and therefore it may lead to a bad forecast for the performance of the reservoir. We discuss the idea that the "true" model (represented here by the base case) is not necessarily the most likely to be obtained using conventional history-matching methods. Reservoir Model and Objective FunctionWe use a simple 2D cross-sectional model of a layered reservoir, as shown in Fig. 1. 57 The model is 2D, with no-flow boundary conditions. Water is injected on the left side, and a production well is located on the right. There is a single, normal fault at the midpoint between the two wells. The reservoir contains six alternating layers of good-and poor-quality sands with high and low permeabilities, respectively. The porosities of the good-and poor-quality sands are 0.30 and 0.15, respectively. We also assume that the three good-quality layers have identical properties, and the three poor-quality layers have a different set of identical properties. The thickness of the layers has an arithmetic progression, with the top layer having a thickness of 12.5 ft, the bottom layer a thickness of 7.5 ft, and with a total thickness of 60 ft. The width of the model
We use a simple 2D model of a layered reservoir with three unknown parameters: the throw of a fault, and high and low permeabilities. Then consider three different cases where in each case two parameters are kept fixed and the third one is varied within a specific range. Using a weighted sum of squares of the difference in production for the objective function, we plot it against the varying parameter for each case. It mainly shows a complex function with multiple minima. We see that geological Fsymmetry_ and also vertical spreading are some sources of non-monotonicity in the production and transmissibility curves. These result in a multi-modal objective function and consequently non-unique history matches. The behaviour of the system in the forecast period is also studied, which shows that a good history matched model could give a bad forecast.
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