Structure Preserving Inversion: An Efficient Approach to Conditioning Stochastic Reservoir Models to Dynamic Data
Authors: Xue Guoping , Datta-Gupta Akhil 
Published: December 2007

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Abstract
We propose a two-stage approach to data integration that combines elements of geostatistics within the framework of inverse modeling. First, we incorporate static data using traditional stochastic imaging techniques that are robust and computationally efficient. Next, we condition the resulting model to dynamic data using a novel approach called structure-preserving inversion. Unlike traditional inverse methods, the proposed approach involves a gradient-based iterative minimization procedure that perturbs reservoir properties (for example, permeability) only at selected pilot locations to match the production history. The resulting changes in properties at the pilot locations are then transferred to other locations by kriging that preserves the initial structure. Typically only about 10–15% of the grid points are used as pilot locations resulting in orders of magnitude savings in computation time compared to simulated annealing. Selection of pilot locations can be based either on sensitivity studies of the initial model or a priori knowledge of the reservoir under study. Multiple realizations of reservoir models conditioned to static and dynamic data can be generated by starting with different initial realizations.
The proposed approach has been applied to synthetic as well as field examples. The synthetic example is designed to address several key issues such as computational efficiency, selection of pilot locations, convergence of the algorithm, and updating techniques. The field example is from the North Robertson Unit, a low permeability carbonate reservoir in west Texas and includes multiple patterns consisting of 42 wells. Water-cut history from producing wells is used to characterize permeability distribution to demonstrate the feasibility of the proposed approach for large-scale field applications.

Introduction
A reservoir model derived from the static data such as geologic, well, and seismic data, will result in fluid flow predictions that do not necessarily match the observed field production history. Since our ultimate objective is to build a reservoir model for future performance predictions, it is imperative that such models adequately reproduce the past performance history. Thus, the model needs to be further improved by integrating dynamic data such as transient pressure and tracer response and multiphase production history.
The integration of dynamic data into petroleum reservoir characterization has been an area of active research in recent years. Previous work includes incorporation of pressure transient tests, multiwell pressure interference tests, and tracer tests. However, much of the work has been limited to single-phase flow. Recently, Vasco et al. integrated multiphase water-cut history into stochastic reservoir characterization. Integration of multiphase production history is particularly important since it is the most widely prevalent dynamic data.
Conditioning reservoir models to dynamic data typically requires the solution of an inverse problem. Such inversion techniques generally involve perturbing reservoir parameters, for example permeability, at all locations until the model performance predictions match the observed data within some acceptable tolerance. A significant drawback of such schemes is the computational burden associated with large number of parameters, particularly for integrating multiphase production data into field-scale models. Although reparameterization techniques can be used to improve the computational efficiency, the extent of improvement can be problem specific.
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