Joint Inversion of Reservoir Production Measurements and 3D Pre-Stack Seismic Data: Proof of Concept Carlos Torres-Verdín, Zhan Wu, Omar J. Varela, Mrinal K. Sen, and Indrajit G. Roy. The University of Texas at Austin, Austin, Texas USA Summary We develop a nonlinear iterative inversion algorithm for estimating three-dimensional (3D) reservoir parameters and initial fluid saturations jointly from pre-stack seismic data and fluid production history. The production measurements and the seismic data are synthetically generated from the output of a multi-phase fluid flow simulator. A Biot-Gassmann rock physics/fluid substitution model is used to enforce a deterministic link between the multi-phase flow parameters and the elastic properties. Iterative nonlinear optimization is used to solve the least- squares minimization problem associated with the inversion. Fluid production measurements are sensitive to initial fluid saturations, fluid properties, porosity, and permeability. Pre-stack seismic data, on the other hand, provide good lateral and vertical control on lithology and fluid distributions. The proposed joint inversion approach, therefore, allows one to effectively integrate the best of the two measurement sets into a consistent 3D distribution of petrophysical variables and fluid saturations. Such distribution can be used for the accurate assessment of in- fill drilling and enhanced-oil-recovery operations. Synthetic test examples are presented with the sole objective to advance a proof of concept for the proposed joint inversion technique. The inversions require large computer resources and hence efficient numerical algorithms. We analyze the relative value of both sets of data and propose an extension of our algorithm to assimilate time-lapse 3D seismic data. Introduction Assessment and prediction of reservoir performance depends on the accurate specification of petrophysical parameters and initial fluid saturations. Simulation of multi-phase fluid-flow behavior is inherently a highly nonlinear problem. The corresponding inverse problem is not only mathematically and computationally challenging, but also highly unstable and non-unique. Therefore, additional independent information is required to stabilize the inverse problem and to reduce the space of solutions. Geostatistical simulation is often used to provide a set of a- priori models based on existing well-log data. In this context, 3D seismic data have been used to guide the geostatistical interpolations through co-kriging and co- simulation techniques. While geostatistical simulation is an efficient interpolation technique, it is meant to honor quantitatively both the fluid production measurements and the 3D seismic data. Practice shows that the amplitude variations of seismic data can be either deterministically and/or non-deterministically (statistically) related to fluid saturation, pore pressure and petrophysical properties. In this paper, we propose a quantitative procedure to incorporate 3D seismic data into the estimation of petrophysical parameters via reservoir history matching. We accomplish this through the use of rigorous nonlinear inverse theory. The inversion is computationally challenging and, with the sole objective of advancing a proof of concept, we present a comprehensive exercise based on the construction of a 3D synthetic reservoir model. We focus our attention the use of pre-stack seismic data as the latter exhibit sensitivity to a larger set of elastic parameters than post-stack seismic data. The inverse formulation advanced in this paper is also suitable for the quantitative interpretation of 4D seismic data. Simulation and Inversion of Multi-Phase Fluid-Flow Measurements and Pre-Stack Seismic Data Reservoir history matching is routinely used to provide a quantitative indication of the spatial distribution of petrophysical parameters in the reservoir. Accordingly, reservoir parameters such as absolute permeability and porosity are adjusted in order to minimize the misfit between the observed and the predicted time record of fluid production measurements. The predicted time record of fluid production measurements is generated from the numerical solution of a set of coupled partial differential equations that describe multi-phase flow phenomena in porous media. Extensive work in this field, however, has shown that a geological and petrophysically sound solution is difficulty to obtain without prior information about the reservoir. History matching is a highly non-linear and non- unique problem that remains intractable without restricting it to satisfy specific a-priori assumptions. By making use of a Bayesian statistical rule, the objective function for the minimization can be written as (Wu et al., 1999 ) ) ( ) ( ) ( ) ( 0 1 1 1 m m C m m d d C d d J M T o obs D T obs − − + − − = − − ,(1) where T k m ) , ( φ = is the vector of reservoir parameters, d is the fluid production data, D C is the covariance of measured data, and M C is the model covariance matrix. The superscript obs is used to identify the time record of