Summary It is well documented that history matching is a problem with possibly nonunique solutions. In the past few years, several automated or semiautomated history-matching algorithms have been proposed. Depending on the algorithm used, it is possible that the final estimated reservoir-property distribution that allows for a good history match may not be geologically realistic. Therefore, there is a need to include other constraints to generate multiple, geologically realistic history-matched realizations. These constraints might, for example, include the variogram, a training image, the distribution of net-to-gross, pore volume, or other geostatistical information about the reservoir. This inclusion is particularly useful because it introduces uncertainty information in the reservoir description when we have limited history from existing wells in the field and intend to drill infill wells or implement a secondary-recovery process. The algorithm proposed in this paper uses multiresolution wavelet analysis to integrate history data with the geostatistical information contained in the variogram proposed for the reservoir. Wavelets allow the representation and manipulation of property distributions at various resolutions at the same time. Using wavelets, information from different sources such as production history and seismic surveys (that would be at different resolutions) can be incorporated directly at the appropriate resolution level. In the first step, we fix the wavelet coefficients sensitive to the history-match data. This has the effect of fixing the field history without fixing individual gridblock properties. In the second step, the remaining free wavelet coefficients are modified to integrate variogram information into the reservoir description. Generating multiple realizations of only the second set of wavelets coefficients results in multiple history-matched, variogram-constrained descriptions of the reservoir. The computational investment is very modest because the history match is done only once. In a number of example cases, different areal Gaussian fields with varying amounts of available production-history data were studied to test the algorithm. It was found that the wavelet coefficients constraining the history can be decoupled from those constraining the variogram. The implication of this observation is that the history data and variogram can be integrated sequentially into the reservoir model—that is, after the initial history match, new information can be added to the model without disturbing the original match to yield multiple history-matched and geostatistically constrained realizations. Introduction Reservoir modeling is essential for forecasting the performance of a reservoir, for reservoir management, for risk analysis, and for making key economic decisions. The purpose of reservoir modeling is to develop a model of the reservoir that closely resembles the actual reservoir based on available information. This model then can be used to forecast future performance and optimize reservoir-management decisions. The more accurate the reservoir model, the better the predictions will be. Therein lies the importance of generating a good reservoir model. History matching is but one step in this direction. Merely achieving a good history match does not ensure sound predictions from the reservoir model; it is therefore essential that all sources of information about the reservoir be used appropriately to come up with a good model. Early automated history-matching procedures were discussed by Jacquard and Jain,1 adapted from variational analysis in electric networking. Since then, there have been several developments of concepts and algorithms along similar lines. In general, the objective is to determine the spatial distribution of a set of gridded reservoir properties such as permeabilities and porosities, given the response of the field in terms of fluid flow to an external impulse such as drainage and injection of fluids, as well as geostatistical data. Production history from existing wells is an important source of information about the reservoir, in terms of the average permeabilities, spatial distribution of permeabilities, net-to-gross, etc. Production history could be in the form of the pressure or saturation distribution in the reservoir in response to injection or production impulses. A good reservoir model must therefore, when run through a flow simulator, give the same response to the same impulse as the real reservoir. Many studies have shown favorable results from integrating dynamic data into reservoir modeling using streamline simulators (e.g., Datta-Gupta et al.2). However, not only does history matching alone not ensure sound production forecast, it also does not guarantee physical consistency and might produce artifacts based on the algorithm used. The results thus obtained might give a perfect history match, but if they are a physical, use of the model will lead to further error in prediction of future performance because the model may not be close enough in a geological sense to the actual reservoir. This situation arises because there may be a number of different solutions to the history-matching problem. In other words, a number of different permeability distributions may be found, all of which give the same response to a given impulse. As such, we need to integrate geostatistical data that will constrain the problem and make the model more realistic. Landa and Horne3 and Landa4investigated the impact of different data on reservoir characterization and uncertainty. Integration of static and dynamic data into reservoir models has been attempted in the Bayesian framework5-7 and with gradual deformation.8 Multiresolution wavelet analysis forms the basis for efficient representation of the field as well as a reduction in the number of parameters to be estimated. As described in the following section, the gridded reservoir-property distribution can be transformed linearly to give a unique set of wavelet coefficients. It has been found9,10 that a specific subset of these wavelet coefficients is sufficient to determine the response of the reservoir to production. The conjecture is that the remaining set can be modified subject to constraints based on geological, seismic, or other subjective information about the spatial distribution of the permeabilities. This study showed that the sets of wavelets constraining the history match and those constraining geostatistical parameters (variograms in particular) can indeed be decoupled and evaluated separately to yield a set of different permeability distributions stochastically. Most history-matching algorithms involve flow simulation at each iteration while minimizing the objective function. The advantage of our new algorithm is that instead of doing repeated history matches, it fixes a set of wavelet coefficients that constrain the history, thereby fixing the history up to some tolerance. The objective function endeavors to enforce a proposed variogram of spatial distribution of the permeabilities. As such, the algorithm takes orders-of-magnitude less time to yield permeability distributions that are constrained by both the history and the variogram of the field.

This paper focuses on an automated way to generate multiple history-matched reservoir models with the inclusion of both geological uncertainty and varying levels of trust in the production data, using wavelet methods. As opposed to previously developed automated history-matching algorithms, this methodology not only ensures geological consistency in the final models but also includes uncertainty in the production data.A data distribution, such as a permeability field, can be (reversibly) transformed into wavelet space in which it is fully described by a set of wavelet coefficients. It was found that different subsets of the collection of wavelet coefficients can be constrained separately to (a) the production history and (b) the geological constraints. This means that the history match need be performed only once, after which multiple realizations can be generated by adjusting only the second subset of coefficients.The ability to include both geological and production-data uncertainty into the reservoir model automatically is of great consequence to reservoir modeling and, hence, to reservoir management, risk analysis, and making key economic decisions. A more complete and realistic reservoir model will lead to better reservoir production and development decisions.

TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractThis paper focuses on an automated way to generate multiple history-matched reservoir models with the inclusion of both geological uncertainty and varying levels of trust in the production data, using wavelet methods. As opposed to previously developed automated history-matching algorithms, this methodology not only ensures geological consistency in the final models, but also includes uncertainty in the production data.A data distribution, say a permeability field, can be (reversibly) transformed into wavelet space where it fully described by a set of wavelet coefficients. It was found that different subsets of the collection of wavelet coefficients can be constrained separately to: (a) the production history, and (b) the geological constraints. This means the history match need only be performed once, after which multiple realizations can be generated by adjusting just the second subset of coefficients.The ability to include both geological and production data uncertainty into reservoir model automatically is of great consequence to reservoir modeling and hence to reservoir management, risk analysis and making key economic decisions. The more complete and realistic reservoir model will lead to better reservoir production and development decisions.

TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractThis work develops a generalized wavelet-based methodology for stochastic data integration in complex reservoirs models. This is an extension of our earlier work for simpler reservoir descriptions (Sahni 2003; Horne 2005, 2006). A single history-matched reservoir permeability model is combined with a stochastic geological description to obtain multiple equiprobable reservoir descriptions using wavelet transforms of the parameter distribution (permeability). In this paper the algorithm has been extended and generalized to be usable with commercial reservoir simulation software and to enable handling of complex three-dimensional models and production scenarios. We also conducted a study of sensitivity coefficient distributions, thresholding and averaging techniques, and a comparison of different Haar wavelet implementations.Wavelet coefficients of reservoir parameter distributions are decoupled into sets of history-matching and geologic coefficients and modified independently. Inverse transformation of these coefficients yields multiple reservoir model results, all of them matched to history. A significant reduction in time is obtained for stochastic modeling of reservoirs by use of this decoupling of production data and other parameters, since only a single history match is required.Thus the proposed algorithm addresses the issue of stochastic modeling of complex reservoirs by integrating all available sources of information. From a single history-matched model we obtain a set of distinct equiprobable reservoir models that can then be used to evaluate uncertainty and make future production predictions and reservoir management decisions.

This paper describes the use of Assisted History Matching (AHM) techniques as a systematic and efficient process for integrating dynamic data (production data) into a reservoir model. As a proof of concept the AHM process was applied to obtain a history match for flowing bottom-hole pressure (FBHP) and gas-oil ratio (GOR) data in the Chayvo field (Sakhalin-1).The AHM workflow developed for this case study consisted of three key components: 1) Quality of match measures 2) Uncertainty Analysis (using Design of Experiments) 3) Static Connectivity MeasurementsTools and workflows were developed to modify the properties of the simulation model and to make static (Shortest-pathbased) connectivity measurements on them. Quantitative quality-of-match measures were developed and used as the response to a change in values of history match parameters. Uncertainty Analysis methods were used to maximize the information obtained from a limited number of single-well sector model simulation runs in order to identify key factors that drive the history match for the Chayvo field.Basic parameters thought to impact HM were the horizontal and vertical permeabilities in three major facies -Upper Shoreface (USF or EOD 3, good quality sand), Middle Shoreface (MSF or EOD 2, intermediate quality) and Lower Shoreface (LSF or EOD 1, low quality). Permeability thickness (KH) information from well tests was used as a constraint on average permeability. This reduced the total number of independent parameters to five. The ranges (maximum and minimum bounds) of these parameters were obtained in consultation with geoscientists. A series of experimental designs were executed, each successive design including more details in the model. Vertical permeability in the MSF and the permeability contrast between MSF and USF were found to be the two major factors that had the largest impact on the quality of the history match. These two factors were then varied systematically to get an improved history match for the sector model.The generation of workflow scripts allowed the history matching process to be executed efficiently, saving the time required for repeated manual input. Also, correlations were found to exist between the static connectivity measurements and the quality-of-match measures derived from simulation results. These indicated that models within a certain range of static drainage volumes for each well were more likely to yield a good quality of match. These correlations could be used to screen future simulation and geologic models. The design of experiments analysis gives a good indication of the key history matching parameters, thereby guiding an understanding of underlying mechanisms and also reducing the number of factors to be considered to improve the match.The learnings from history matching on the sector model were applied to the full-field geologic model resulting in a significant improvement in the well-by-well and the overall field-match to production data. Additional changes required to match individual wells were primarily localized.