Ronald A. Behrens

Conditional simulation of reservoir heterogeneity with fractals

The displacement efficiency of fluids injected into heterogeneous formations depends on the nature of reservoir-property variations and their spatial correlations. Conditional simulation is a geostatical technique for creating property distributions, with any desired resolution, that have a prescribed spatial correlation structure and that match measured data at their sampling locations. Conditional simulations of reservoir heterogeneities can be used to address the two major issues in characterizing reservoirs for performance modeling: scaling of flow process and properties and dealing with the uncertainty resulting from missing information in reservoir description. The correlation structure emphasized here is a fractal model.

Phase equilibrium calculations for continuous and semicontinuous mixtures

Abstract Significant amounts of computation time are required for phase equilibrium calculations involving mixtures of very many components, such as polymer solutions and petroleum reservoir fluids. In this paper we consider the question of describing such mixtures as a collection of discrete components and a continuum distribution of species represented by a distribution function. We show that (1) the distribution function for the feed in a vapor-liquid calculation will not, in general, represent the coexisting vapor and liquid with equal accuracy, and (2) that to achieve the benefits of a continuous or semicontinuous description of a mixture, one need not rewrite phase equilibrium programs now in use, but instead choose component lumpings based upon Gauss numerical quadrature formulas. The specific Gauss formula to be used depends upon the distribution function which describes the mixture. Further, we have generalized the Gauss quadrature method by considering the case of finite limits of integration, which we show to be important when considering heavy oils. Finally, we show that relatively few pseudocomponents chosen in this way lead to phase equilibrium calculations of an accuracy comparable to that with a very much larger number of pseudocomponents chosen in the conventional way.

Seismic imaging of reservoir flow properties: Time-lapse amplitude changes

Asymptotic methods provide an efficient means by which to infer reservoir flow properties, such as permeability, from time-lapse seismic data. A trajectory-based methodology, much like ray-based methods for medical and seismic imaging, is the basis for an iterative inversion of time-lapse amplitude changes. In this approach a single reservoir simulation is required for each iteration of the algorithm. A comparison between purely numerical and the trajectory-based sensitivities demonstrates their accuracy. An application to a set of synthetic amplitude changes indicates that they can recover large-scale reservoir permeability variations from time-lapse data. In an application of actual time-lapse amplitude changes from the Bay Marchand field in the Gulf of Mexico we are able to reduce the misfit by 81% in twelve iterations. The time-lapse observations indicate lower permeabilities are required in the central portion of the reservoir.

A Multiscale Approach to Production Data Integration Using Streamline Models

We 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.

Incorporating Seismic Attribute Maps in 3D Reservoir Models

We introduce a new geostatistical method to incorporate seismic attribute maps into a 3D reservoir model. The method explicitly honors the difference in vertical resolution between seismic and well log data. The method, called Sequential Gaussian Simulation with Block Kriging (SGSBK), treats the seismic map as a soft estimate of the average reservoir property. Using this method, the average of the cell values in any one vertical column of grid cells is constrained by the value of the seismic map over that column. The result is a model that contains vertical variability driven by well logs and the vertical variogram model and spatial variability driven by the seismic map and the areal variogram model.

Assessing the technical risk of a 4-D seismic project

At the initial stage of any 4-D project, Chevron’s business unit engineers and geoscientists usually ask an obvious question: “Do you think it will work?”

Production Data Integration in Sand/Shale Reservoirs Using Sequential Self-Calibration and GeoMorphing: A Comparison

The stochastic inversion of spatial distribution of lithofacies from multiphase production data is a difficult problem. This is true even for the simplest case, addressed here, of a sand/shale distribution and under the assumption that reservoir properties are constant within each lithofacies. Two geostatistically based inverse techniques, sequential self-calibration (SSC) and GeoMorphing (GM), are extended for such purposes and then compared with synthetic reference fields. The extension of both techniques is based on the one-to-one relationship existing between lithofacies and Gaussian deviates in truncated Gaussian simulation. Both techniques attempt to modify the field of Gaussian deviates while maintaining the truncation threshold field through an optimization procedure. Maintaining a fixed threshold field, which has been computed previously on the basis of prior lithofacies proportion data, well data, and other static soft data, guarantees preservation of the initial geostatistical structure. Comparisons of the two techniques using 2D and 3D synthetic data show that the SSC is very efficient in producing sand/shale realizations matching production data and reproducing the large-scale patterns displayed in the reference fields, although it has difficulty in reproducing small-scale features. GM is a simpler algorithm than SSC, but it is computationally more intensive and has difficulty in matching complex production data. Better results could be obtained with a combination of the two techniques in which SSC is used to generate realizations identifying large-scale features; then, these realizations could be used as input to GM for a final update to match small-scale details.

4D Seismic Monitoring of Water Influx at Bay Marchand: The Practical Use of 4D in an Imperfect World

Multiple seismic surveys over time not intentionally designed for 4D evaluation can be used for imaging fluid. Areas of water influx and areas not yet invaded by water were identified. Reliability estimates were derived for estimates of saturation change as a function of signal-to-noise ratio and scatter in the rock physics relationships. In spite of the deviation from ideal 4D methodology, the results are useful and are making a business impact.

Considerations affecting the scaling of displacements in heterogeneous permeability distributions

Dispersion and convection scaling can be used to model 1D miscible and immiscible flows, respectively, but these scaling techniques fail in multidimensional heterogeneous permeability distributions. The length dependence observed for dispersion induced by correlated heterogeneity in miscible displacement processes precludes the definition of an effective dispersion coefficient. Effective relative permeabilities can be defined that will reproduce the results of the cross-sectional simulations from which they were derived, but complications arise when they are used in areal models

Analysis of time-lapse data from the Alba Field 4C/4D seismic survey

The 1998 Alba 3D Ocean Bottom Cable (OBC) survey was designed to accomplish multiple objectives. The primary goal was to image low impedance reservoir sands with converted wave (PS) reflections; one important secondary goal was to image fluid movement by comparing the OBC data with a 1989 streamer survey. Modelling shows that a strong original oil–water contact reflector should be visible throughout much of the field and that water saturation changes should be observable by analysing the time-lapse differences between the 1989 streamer data and 1998 OBC survey. Differences between the 1989 and 1998 seismic field data confirm that fluid changes are clearly visible near several producing and injector wells. However, extracting additional quantitative saturation information from the seismic data has proven difficult, possibly because of: (a) complex interaction between the fluids, sands and shales within the Alba reservoir; (b) moderate to poor repeatability of the seismic response to reservoir fluids. The focus of this paper is the acquisition and analysis of Alba time-lapse data. We show that production- and injection-related effects are predicted by modelling and observed in the data and then we make an attempt to relate these effects quantitatively to oil production and water injection. Despite the challenges in using the Alba time-lapse data quantitatively, the data have been successfully used qualitatively for well planning risk assessment and for guiding reservoir simulation efforts. Lessons from this work will be used in any future time-lapse surveys at Alba.