A general method for the scale up of highly detailed, heterogeneous, three dimensional reservoir descriptions is developed and applied. The method entails the nonuniform coarsening of the original detailed description, with finer resolution introduced in regions of potentially high flow rate (as identified through computationally efficient single phase flow calculations) arid coarser, homogenized property descriptions applied throughout the bulk of the model. The method is applied to the simulation of three actual reservoirs and is demonstrated to provide coarsened reservoir models which give simulation results in close agreement with those of the original fine scale description but at considerable computational savings (speedups of nearly two orders of magnitude). In addition, it is shown that the method can provide geologically realistic coarse scale reservoir descriptions, which can be subsequently history matched to field data via geologically sensible modifications. Introduction Through the use of sophisticated geological and geostatistical modeling tools, engineers and geologists can now generate highly detailed, three dimensional representations of reservoir properties. Such models can be particularly important for reservoir management, as fine scale details in formation properties, such as thin, high permeability layers or thin shale barriers, can dominate reservoir behavior. The direct use of these highly resolved models for reservoir simulation is not generally feasible because their fine level of detail (up to millions of grid blocks) places prohibitive demands on computational resources. Therefore, the ability to coarsen these highly resolved geologic models to levels of detail appropriate for reservoir simulation (tens of thousands to one hundred thousand grid blocks), while maintaining the integrity of the model for purposes of flow simulation (i.e., avoiding the loss of important details), is clearly needed. We previously developed and applied such a technique for the scale up of detailed cross sectional models. Given a highly detailed reservoir cross section, this method was designed to generate a coarsened model that is capable of providing simulation predictions in close agreement with results using the original, detailed reservoir description. More specifically, we require agreement in (1) the global pressure-flow rate behavior of the reservoir; (2) the breakthrough characteristics of the displacing fluid and; (3) the post-breakthrough fractional flows of all reservoir fluids. The cross sectional method achieves such a scale up by efficiently identifying the likely regions of high fluid velocities (via single phase flow calculations), which can lead to the early breakthrough of displacing fluids. These regions are then modeled in detail, using a fine scale permeability description, within the coarsened reservoir model. The remainder of the fine scale description is coarsened using a general technique, based on homogenization theory, for the calculation of effective, directional permeabilities. The resulting coarsened reservoir description is able to model both average reservoir behavior as well as some important effects due to extremes in reservoir properties (such as the early breakthrough of injected fluids), without prior knowledge of the global flow field. This indicates that the scaled up model is largely process independent. The method is implemented as an interactive workstation application, with various diagnostics to allow for an assessment of the accuracy of the coarsened reservoir model relative to the original fine scale description.

The fluid motion at a free surface advancing into a mold or duct is appreciably different from its steady state behavior in well-developed flow; this affects the residence time distribution and structure of macromolecular fluids as they are frozen in injection molding processes. In this work such motion is treated numerically and measured precisely for Newtonian fluids. While the three-phase contact line represents a special problem conceptually and analytically, a very simple algorithm is seen to represent the fluid motion in this region accurately.Good agreement is found over wide ranges of the governing dimensionless groups (the Reynolds, Jeffrey, and capillary numbers). Since viscous forces are dominant under the circumstances studied, this finding is not surprising but it confirms the applicability of the numerical methods developed herein to the modeling of these flows under conditions of actual interest. As a result, simulations may be made with confidence to predict flow patterns encountered in practice but difficult to reproduce in laboratory experiments.

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.

A semicontinuous thermodynamic description has been used to model the C7+ fraction for equation of state (EOS) calculations. This semicontinuous description may be used in existing discrete-component EOS programs by picking pseudocomponents in a rigorous a priori fashion dependent only on the properties of the C7+ fraction. Excellent representation of experimental PVT data considered here is obtained with only two C7+ pseudocomponents, although the theory and procedure extend to three or more components.