[1] We develop a novel method of parameterization for spatial hydraulic property characterization to mitigate the challenges associated with the nonlinear inverse problem of subsurface flow model calibration. The parameterization is performed by the projection of the estimable hydraulic property field onto an orthonormal basis derived from the grid connectivity structure. The basis functions represent the modal shapes or harmonics of the grid, are defined by a modal frequency, and converge to special cases of the discrete Fourier series under certain grid geometries and boundary assumptions; therefore, hydraulic property updates are performed in the spectral domain and merge with Fourier analysis in ideal cases. Dependence on the grid alone implies that the basis may characterize any grid geometry, including corner point and unstructured, is model independent, and is constructed off-line and only once prior to flow data assimilation. We apply the parameterization in an adaptive multiscale model calibration workflow for three subsurface flow models. Several different grid geometries are considered. In each case the prior hydraulic property model is updated using a parameterized multiplier field that is superimposed onto the grid and assigned an initial value of unity at each cell. The special case corresponding to a constant multiplier is always applied through the constant basis function. Higher modes are adaptively employed during minimization of data misfit to resolve multiscale heterogeneity in the geomodel. The parameterization demonstrates selective updating of heterogeneity at locations and spatial scales sensitive to the available data, otherwise leaving the prior model unchanged as desired.Citation: Bhark, E. W., B. Jafarpour, and A. Datta-Gupta (2011), A generalized grid connectivity-based parameterization for subsurface flow model calibration, Water Resour. Res., 47, W06517,

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As the role of reservoir flow simulation increasingly impacts existing operations and field development decisions, it follows that rigor, fitness and consistency should be imposed on the calibration of reservoir flow models to dynamic data through history matching. Although a wealth of history matching techniques exist in the petroleum literature that propose novel algorithms or share case studies, seldom does the content guide the modeler in fit-for-purpose reservoir model calibration for an operating asset. To evaluate the applicability of these diverse techniques against standards required for reservoir management, an internal study was performed to benchmark four assisted history matching (AHM) techniques commonly promoted in the oil and gas industry. The techniques were vetted against a comprehensive suite of modeling requirements for multiple asset classes, integrating a variety of historical dynamic data types through the calibration of reservoir properties that control flow behavior from the field to inter-well scale. The methods benchmarked were: (1) Design of Experiments (DoE)-based, (2) Ensemble Kalman Filter and Ensemble Smoother, (3) Genetic Algorithm and (4) Generalized Travel Time Inversion. This manuscript focuses solely on the DoE-based technique.In order to consistently benchmark the techniques, a set of standards was defined against which each was evaluated to determine its suitability for widespread history matching applications. The standards involve: the capacity to parameterize (and therefore calibrate) a diversity of reservoir flow model attributes, the capacity to integrate different types of dynamic data, the level of independence from the flow simulator and the capability to provide probabilistic outcomes for predictive uncertainty assessment. Of the four techniques, the DoE-based approach uniquely satisfied all requirements. Its history matching workflow has the flexibility to incorporate any form of reservoir model parameter and to assimilate a history matching error metric for any individual or group of historical data types; therefore, benchmarking established DoE-based techniques as unambiguously the most compliant with generic asset modeling requirements. The approach was also identified as the most straightforward, both theoretically and in practical computation, and therefore applicable to the broadest range of practitioners. Perhaps most importantly, the approach demonstrated the capacity for accurate quantification of uncertainty (or non-uniqueness) in reservoir quality resulting from an exhaustive, although approximate, exploration of model parameter space and the associated history matching error metric(s).This manuscript compiles the results and insights gained from benchmarking of the DoE-based techniques through the proposal of a comprehensive assisted history matching workflow. The workflow is designed for generality while providing best practices that guide the modeler in fit-for-purpose application. Limitations of the workflow are also recognized. Key components includ...

We have developed an efficient approach of petroleum reservoir model calibration that integrates 4D seismic surveys together with well-production data. The approach is particularly well-suited for the calibration of high-resolution reservoir properties (permeability) because the field-scale seismic data are areally dense, whereas the production data are effectively averaged over interwell spacing. The joint calibration procedure is performed using streamline-based sensitivities derived from finite-difference flow simulation. The inverted seismic data (i.e., changes in elastic impedance or fluid saturations) are distributed as a 3D high-resolution grid cell property. The sensitivities of the seismic and production surveillance data to perturbations in absolute permeability at individual grid cells are efficiently computed via semianalytical streamline techniques. We generalize previous formulations of streamline-based seismic inversion to incorporate realistic field situations such as changing boundary conditions due to infill drilling, pattern conversion, etc. A commercial finite-difference flow simulator is used for reservoir simulation and to generate the time-dependent velocity fields through which streamlines are traced and the sensitivity coefficients are computed. The commercial simulator allows us to incorporate detailed physical processes including compressibility and nonconvective forces, e.g., capillary pressure effects, while the streamline trajectories provide a rapid evaluation of the sensitivities. The efficacy of our proposed approach was tested with synthetic and field applications. The synthetic example was the Society of Petroleum Engineers benchmark Brugge field case. The field example involves waterflooding of a North Sea reservoir with multiple seismic surveys. In both cases, the advantages of incorporating the time-lapse variations were clearly demonstrated through improved estimation of the permeability heterogeneity, fluid saturation evolution, and swept and drained volumes. The value of the seismic data integration was in particular proven through the identification of the continuity in reservoir sands and barriers, and by the preservation of geologic realism in the calibrated model.

Summary Assisted history matching (AHM) using design of experiments (DOE) is one of the most commonly applied history-matching techniques in the oil and gas industry. When applied properly, this stochastic method finds a representative ensemble of history-matched reservoir models for probabilistic uncertainty analysis of production forecasts. Although DOE-based AHM is straightforward in concept, it can be misused in practice because the work flow involves many statistical and modeling principles that should be followed rigorously. In this paper, the entire DOE-based AHM work flow is demonstrated in a coherent and comprehensive case study that is divided into seven key stages: problem framing, sensitivity analysis, proxy building, Monte Carlo simulation, history-match filtering, production forecasting, and representative model selection. The best practices of each stage are summarized to help reservoir-management engineers understand and apply this powerful work flow for reliable history matching and probabilistic production forecasting. One major difficulty in any history-matching method is to define the history-match tolerance, which reflects the engineer's comfort level of calling a reservoir model “history matched” even though the difference between simulated and observed production data is not zero. It is a compromise to the intrinsic and unavoidable imperfectness of reservoir-model construction, data measurement, and proxy creation. A practical procedure is provided to help engineers define the history-match tolerance considering the model, data-measurement, and proxy errors.