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Recently, streamline-based flow simulation models have offered significant potential in integrating dynamic data into highresolution reservoir models. A unique feature of the streamlinebased production data integration has been the concept of a traveltime match that is analogous to seismic tomography, allowing the use of efficient and proven techniques from geophysics. In this paper, we propose a generalized travel-time inversion method for production data integration that is particularly well-suited for large-scale field applications with gravity and changing conditions. Instead of matching the production data directly, we minimize a travel-time shift derived by maximizing a cross-correlation between the observed and computed production response at each well. There are several advantages of our proposed method. First, it is general and extremely computationally efficient. The traveltime sensitivities can be computed analytically with a single forward streamline simulation that can be much faster than a conventional reservoir simulator. Second, it is robust and the minimization is relatively insensitive to the choice of the initial model. Finally, it is field-proven because we utilize established techniques from geophysical inverse theory.We demonstrate the power and utility of our proposed method using synthetic and field examples. The synthetic examples include a large-scale 3D example with a quarter-million grid cells involving infill drilling and pattern conversions. The field example is from the Goldsmith San Andres Unit (GSAU) in West Texas and includes multiple patterns with 11 injectors and 31 producers. Starting with a reservoir model based on well-log and seismic data, we integrate water-cut history for 20 years in less than 2 hours on a PC.

[1] In this paper, we use a two-stage Markov chain Monte Carlo (MCMC) method for subsurface characterization that employs coarse-scale models. The purpose of the proposed method is to increase the acceptance rate of MCMC by using inexpensive coarse-scale runs based on single-phase upscaling. Numerical results demonstrate that our approach leads to a severalfold increase in the acceptance rate and provides a practical approach to uncertainty quantification during subsurface characterization.

Abstract. An asymptotic approach to the solution of the transport equation, in the limit of rapid spatial and temporal variation, produces an extremely efficient formalism for the inversion of tracer data. The technique provides tracer concentration sensitivities to porosity, permeability, and pressure gradient variations in just a single simulation run. The calculated sensitivities compare well with those derived using a numerical perturbation method, at a fraction of the computational requirements. An application to a conservative tracer test at Hill Air Force Base in Utah indicates the efficiency and utility of the approach for characterizing three-dimensional variations in flow properties. On the basis of tracer concentration histories at 12 multilevel samplers and three extraction wells, some 44 tracer curves in all, significant small-scale variability in permeability is inferred. In general, the permeability is found to decrease as the lower boundary of the aquifer is approached. The permeability trends we find are consistent with tracer swept volume calculations based upon a moment analysis. IntroductionThe understanding and analysis of solute transport is becoming increasingly important for a broad spectrum of applica- In this paper we describe an asymptotic formulation which

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TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractWe propose a multiscale approach to data integration that accounts for the varying resolving power of different data types from the very outset. Starting with a very coarse description, we match the production response at the wells by recursively refining the reservoir grid. A multiphase streamline simulator is utilized for modeling fluid flow in the reservoir. The well data is then integrated using conventional geostatistics, for example sequential simulation methods. There are several advantages to our proposed approach. First, we explicitly account for the resolution of the production response by refining the grid only up to a level sufficient to match the data, avoiding over-parameterization and incorporation of artificial regularization constraints. Second, production data is integrated at a coarse-scale with fewer parameters, which makes the method significantly faster compared to direct fine-scale inversion of the production data. Third, decomposition of the inverse problem by scale greatly facilitates the convergence of iterative descent techniques to the global solution, particularly in the presence of multiple local minima. Finally, the streamline approach allows for parameter sensitivities to be computed analytically using a single simulation run and thus, further enhancing the computational speed.The proposed approach has been applied to synthetic as well as field examples. The synthetic examples illustrate the validity of the approach and also address several key issues such as convergence of the algorithm, computational efficiency, and advantages of the multiscale approach compared to conventional methods. 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 the proposed approach for large-scale field applications.

Conventional multiple regression for permeability estimation from well logs requires a functional relationship to be presumed. Because of the inexact nature of the relationship between petrophysical variables, it is not always possible to identify the underlying functional form between dependent and independent variables in advance. When large variations in petrological properties are exhibited, parametric regression often fails or leads to unstable and erroneous results, especially for multivariate cases.In this paper, we describe a nonparametric approach for estimating optimal transformations of petrophysical data to obtain the maximum correlation between observed variables. The approach does not require a priori assumptions of a functional form, and the optimal transformations are derived solely based on the data set. Unlike neural networks, such transformations can facilitate physically based function identification. An iterative procedure involving the alternating conditional expectation (ACE) forms the basis of our approach. The power of ACE is illustrated using synthetic as well as field examples. The results clearly demonstrate improved permeability estimation by ACE compared to conventional parametric-regression methods.

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