A Derivative-Free Approach for the Estimation of Porosity and Permeability Using Time-Lapse Seismic and Production Data

A Derivative-Free Approach for the Estimation of Porosity and Permeability Using Time-Lapse Seismic and Production Data

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Abstract

In this study, we apply a derivative-free optimization algorithm to estimate porosity and permeability from time-lapse seismic data and production data from a real reservoir (Norne field). In some circumstances, obtaining gradient information (exact and/or approximate) can be problematic e.g. derivatives are not available from a commercial simulator, or results are needed within a very short time frame. Derivative-free optimization approaches can be very time consuming because they often require many simulations. Typically, one iteration roughly needs as many simulations as the number of optimization variables. In this work, we propose two ways to significantly increase the efficiency of an optimization methodology in model inversion problems. First, by principal component analysis we decrease the number of optimization variables while keeping geostatistical consistency, and second, noticing that some optimization methods are very amenable to being parallelized, we apply them within a distributed computing framework. If we combine all this, the model inversion approach can be robust, fairly efficient and very simple to implement. In this paper, we apply the methodology to two cases: a semi-synthetic model with noisy data, and a case based entirely on field data.
Content

In this study, we apply a derivative-free optimization algorithm to estimate porosity and permeability from time-lapse seismic data and production data from a real reservoir (Norne field). In some circumstances, obtaining gradient information (exact and/or approximate) can be problematic e.g. derivatives are not available from a commercial simulator, or results are needed within a very short time frame. Derivative-free optimization approaches can be very time consuming because they often require many simulations. Typically, one iteration roughly needs as many simulations as the number of optimization variables. In this work, we propose two ways to significantly increase the efficiency of an optimization methodology in model inversion problems. First, by principal component analysis we decrease the number of optimization variables while keeping geostatistical consistency, and second, noticing that some optimization methods are very amenable to being parallelized, we apply them within a distributed computing framework. If we combine all this, the model inversion approach can be robust, fairly efficient and very simple to implement. In this paper, we apply the methodology to two cases: a semi-synthetic model with noisy data, and a case based entirely on field data. The results show that the derivative-free approach presented is robust against noise in the data.

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