Models for deep bed filtration in the injection of seawater with solid inclusions depend on an empirical filtration function that represents the rate of particle retention. This function must be calculated indirectly from experimental measurements of other quantities. The practical petroleum engineering purpose is to predict injectivity loss in the porous rock around wells. In this work, we determine the filtration function from the effluent particle concentration history measured in laboratory tests knowing the inlet particle concentration. The recovery procedure is based on solving a functional equation derived from the model equations. Well-posedness of the numerical procedure is discussed. Numerical results are shown.

Automatic history matching is based on minimizing an objective function that quantifies the mismatch between observed and simulated data. When using gradient-based methods for solving this optimization problem, a key point for the overall procedure is how the simulator delivers the necessary derivative information. In this paper, forward and adjoint methods for derivative calculation are discussed. Procedures for sensitivity matrix building, sensitivity matrix and transpose sensitivity matrix vector products are fully described. To show the usefulness of the derivative calculation algorithms, a new variant of the gradzone analysis, which tries to address the problem of selecting the most relevant parameters for a history matching, is proposed using the singular value decomposition of the sensitivity matrix. Application to a simple synthetic case shows that this procedure can reveal important information about the nature of the history-matching problem.

An efficient multiscale (MS) gradient computation method for subsurface flow management and optimization is introduced. The general, algebraic framework allows for the calculation of gradients using both the Direct and Adjoint derivative methods. The framework also allows for the utilization of any MS formulation that can be algebraically expressed in terms of a restriction and a prolongation operator. This is achieved via an implicit differentiation formulation. The approach favors algorithms for multiplying the sensitivity matrix and its transpose with arbitrary vectors. This provides a flexible way of computing gradients in a form suitable for any given gradient-based optimization algorithm. No assumption w.r.t. the nature of the problem or specific optimization parameters is made. Therefore, the framework can be applied to any gradient-based study. In the implementation, extra partial derivative information required by the gradient computation is computed via automatic differentiation. A detailed utilization of the framework using the MS Finite Volume (MSFV) simulation technique is presented. Numerical experiments are performed to demonstrate the accuracy of the method compared to a fine-scale simulator. In addition, an asymptotic analysis is presented to provide an estimate of its computational complexity. The investigations show that the presented method casts an accurate and efficient MS gradient computation strategy that can be successfully utilized in next-generation reservoir management studies.

TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractSevere fall of injectivity in porous rock occurs from the practice in offshore fields of injecting sea water containing organic and mineral inclusions. In general, injection of poor quality water in a well curtails its injectivity. The injectivity loss is assumed to be due to particle retention in the porous rock.A model for porous rock damage due to retention in deep filtration during injection of water containing solid particles is formulated. The model contains two empirical functions that affect loss of injectivity -filtration coefficient and damage coefficient versus deposited particle concentration.We show how to solve the inverse problem for determining the first function based on effluent particle concentration measurements in coreflood tests.The second inverse problem is the determination of the formation damage coefficient from the pressure drop history on a core. These two methods allow determining from laboratory tests the information necessary for prediction of well impairment.

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