History Matching of the PUNQ-S3 Reservoir Model Using the Ensemble Kalman Filter

History Matching of the PUNQ-S3 Reservoir Model Using the Ensemble Kalman Filter Yaqing Gu; Yaqing Gu The University of Oklahoma Search for other works by this author on: This Site Google Scholar Dean S. Oliver Dean S. Oliver The University of Oklahoma Search for other works by this author on: This Site Google Scholar Paper presented at the SPE Annual Technical Conference and Exhibition, Houston, Texas, September 2004. Paper Number: SPE-89942-MS https://doi.org/10.2118/89942-MS Published: September 26 2004 Cite View This Citation Add to Citation Manager Share Icon Share Twitter LinkedIn Get Permissions Search Site Citation Gu, Yaqing, and Dean S. Oliver. "History Matching of the PUNQ-S3 Reservoir Model Using the Ensemble Kalman Filter." Paper presented at the SPE Annual Technical Conference and Exhibition, Houston, Texas, September 2004. doi: https://doi.org/10.2118/89942-MS Download citation file: Ris (Zotero) Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentAll ProceedingsSociety of Petroleum Engineers (SPE)SPE Annual Technical Conference and Exhibition Search Advanced Search AbstractThe problem of reservoir characterization through automatic history matching has been extensively studied in recent years. Efficient applications have, however, required either an adjoint or a gradient simulator method to compute the gradient of the objective function or a sensitivity coefficient matrix for the minimization. Both computations are expensive when the number of model parameters or the number of observation data is large. The codes for gradient-based history matching methods are also complex and time-consuming to write.This paper reports the use of the Ensemble Kalman Filter (EnKF) for automatic history matching. EnKF is a Monte Carlo method, in which an ensemble of reservoir models is used. The correlation between reservoir response (e.g. water-cut and rate) and reservoir variables (e.g. permeability and porosity) can be estimated from the ensemble. An estimate of uncertainty in future reservoir performance can also be obtained from the ensemble.The methodology of EnKF consists of a forecast step and an assimilation step. A finite-difference, 3-D, 3-phase black-oil reservoir simulator is used for stepping forward the reservoir states. However, unlike the traditional history matching, the source code of the reservoir simulator is not required, which allows this method to be used with any reservoir simulator. Moreover, this forward step is well suited for parallel computation since the time evolution of ensemble reservoir models are independent, hence the ensemble of reservoir models can be advanced in time simultaneously using multiple processors. Only the data assimilation step, i.e. the computation of Kalman filter, requires communication between processors.The assimilation of the data in EnKF is done sequentially rather than simultaneously as in traditional history matching. By so doing the reservoir models are always kept up-to-date, which is important and practical when the frequency of data is fairly high as, for example, the data from permanent sensors.The PUNQ-S3 reservoir model is used to test the method in this paper. It is a small-size (19×28×5) reservoir engineering model that was developed by a group of companies, institutes and universities in the European Union to compare methods for quantifying uncertainty assessment in history matching. One conclusion is that EnKF can sometimes provide satisfactory history matching results while requiring less computation work than traditional methods.IntroductionThe process of adjusting the variables in a reservoir simulation model to honor observations of rates, pressures, saturations, etc., at individual wells is called history matching. In many cases, general geological information also needs to be honored, for example, the variance-covariance structure of the model parameters. Thus to do the history matching, one typically attempts to minimize the square of the mismatch between all measurements and computed values, and/or the square of the mismatch of the current model parameters and the prior model parameters. Although the process can now be largely automated, a large computational effort is still required, either in objective function evaluation (non-gradient based minimization method), or in gradient computation (gradient-based minimization method). If the gradient-based minimization methods are employed, the adjoint method may be required to compute the gradient of the objective function. The adjoint system is highly dependent on the source code of the reservoir simulator, however, and hence it is not flexible, that is if we want to use a different simulator, development of an adjoint code requires considerable work. On the other hand, the increase in deployment of permanent sensors for monitoring pressure, temperature, resistivity, or flow rate has added impetus to the related problem of continuous model updating. Since the data output frequency in this case can be very high, to simultaneously use all recorded data to generate a reservoir flow model is not practical. Instead, it has become important to incorporate the data as soon as they are obtained so that the reservoir model is always up-to-date. Both the heavy computational burden and the high data sampling frequency require a new kind history matching method. Keywords: permeability, reservoir simulation, reservoir simulator, theoretical data, production data, modeling & simulation, porosity, application, assimilation step, ensemble kalman filter Subjects: Reservoir Simulation, History matching This content is only available via PDF. 2004. Society of Petroleum Engineers You can access this article if you purchase or spend a download.