3D Field-Scale Automatic History Matching Using Adjoint Sensitivities and Generalized Travel-Time Inversion

Abstract

3D Field-Scale Automatic History Matching Using Adjoint Sensitivities and Generalized Travel Time Inversion Ahmed Mohamed Daoud; Ahmed Mohamed Daoud Schlumberger Search for other works by this author on: This Site Google Scholar Leonardo Vega Velasquez Leonardo Vega Velasquez Schlumberger Search for other works by this author on: This Site Google Scholar Paper presented at the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, USA, September 2006. Paper Number: SPE-101779-MS https://doi.org/10.2118/101779-MS Published: September 24 2006 Cite View This Citation Add to Citation Manager Share Icon Share Twitter LinkedIn Get Permissions Search Site Citation Daoud, Ahmed Mohamed, and Leonardo Vega Velasquez. "3D Field-Scale Automatic History Matching Using Adjoint Sensitivities and Generalized Travel Time Inversion." Paper presented at the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, USA, September 2006. doi: https://doi.org/10.2118/101779-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 AbstractConditioning geologic models to production data is generally done in a Bayesian framework. The commonly used Bayesian formulation and its implementation have difficulties in three major areas, particularly for large scale field applications. First, the CPU time increases quadratically with increasing model size, thus making it computationally expensive for field applications with large number of parameters; second, the sensitivity coefficients that define the relationship between reservoir properties and the production response typically depend on either the number of model parameters or the number of data points; and third, the calculation of the prior covariance matrix (or its inverse) can be time consuming and memory intensive.We propose a fast and robust adaptation of the Bayesian formulation for inverse modeling that overcomes much of the current limitations and is well suited for large-scale field applications. Our approach is based on a generalized travel time inversion and utilizes the adjoint method for computing the sensitivity of the travel time with respect to reservoir parameters such as porosity and permeability. The sensitivity calculations depend on the number of wells integrated which can be orders of magnitude less than the number of data points or the model parameters. The adjoint sensitivities can be computed from the pressure and water saturation distribution that is readily available from the numerical simulator. For solving the inverse problem, we utilize an iterative minimization algorithm based on efficient singular value decomposition. Prior information is incorporated using an approximation of the square root of the inverse of the prior covariance calculated using a numerically-derived stencil applicable to a wide class of covariance models. Our proposed approach is computationally efficient and more importantly the CPU time scales linearly with respect to model size making it particularly well-suited for large-scale field applications.We demonstrate the power and utility of our approach using synthetic and field examples. The synthetic examples show the robustness and efficiency of this algorithm. The field example is from the Goldsmith San Andres Unit (GSAU) in West Texas and includes multiple patterns consisting of 11 injectors and 31 producers. Using well log data and water-cut history from producing wells; we characterize the permeability distribution, thus demonstrating the feasibility of our approach for large-scale field applications.IntroductionConditioning geological models to production data typically requires the solution of an inverse problem. Such inverse problems are usually ill-posed and their solutions suffer from difficulties in existence, uniqueness, and stability. To remedy these problems, a regularization term, in the form of data-independent prior information is generally added to the objective function in the inverse problem. Two different approaches to incorporate the regularization term have been used extensively in reservoir characterization literatures. One of these approaches is the Bayesian1–7, and the other is the deterministic.8–11 Both approaches have been successfully applied for conditioning geological models to production history and comparison between the two approaches can be found in the literature.12,13 Unlike the deterministic approach, the Bayesian approach associates probability distribution to the prior models and is thus considered well-suited for post-data inference and uncertainty assessment by defining a posterior distribution of models and sampling multiple realizations from this distribution. Keywords: machine learning, reservoir simulation, flow in porous media, Artificial Intelligence, stencil, History, application, calculation, sensitivity, producer Subjects: Reservoir Fluid Dynamics, Reservoir Simulation, Flow in porous media This content is only available via PDF. 2006. Society of Petroleum Engineers You can access this article if you purchase or spend a download.