Summary

Nine multimillion-cell geostatistical earth models of the Marrat reservoir in Magwa field, Kuwait, were upscaled for streamline (SL) screening and finite-difference (FD) flow simulation.

The scaleup strategy consisted of (1) maintaining square areal blocks over the oil column, (2) upscaling to the largest areal-block size (200 x 200 m) compatible with 125-acre well spacing, (3) upscaling to less than 1 million gridblocks for SL screening, and (4) upscaling to less than 250,000 gridblocks for FD flow simulation. Chevron's in-house scaleup software program, SCP, was used for scaleup. SCP employs a single-phase flow-based process for upscaling nonuniform 3D grids. Several iterations of scaleup were made to optimize the result.

Sensitivity tests suggest that a uniform scaled-up grid overestimates breakthrough time compared to the fine model, and the post-breakthrough fractional flow also remains higher than in the fine model. However, preserving high-flow-rate layers in a nonuniform scaled-up model was key to matching the front-tracking behavior of the fine model. The scaled-up model was coarsened in areas of low average layer flow because less refinement is needed in these areas to still match the flow behavior of the fine model. The final ratio of pre- to post-scaleup grid sizes was 6:1 for SL and 21:1 for FD simulation.

Several checks were made to verify the accuracy of scaleup. These include comparison of pre- and post-scaleup fractional-flow curves in terms of breakthrough time and post-breakthrough curve shape, cross-sectional permeabilities, global porosity histograms, porosity/permeability clouds, visual comparison of heterogeneity, and earth-model and scaled-up volumetrics.

The scaled-up models were screened using the 3D SL technique. The results helped in bracketing the flow behavior of different earth models and evaluating the model that better tracks the historical performance data. By initiating the full-field history-matching process with the geologic model that most closely matched the field performance in the screening stage, the amount of history matching was minimized, and the time and effort required were reduced. The application of unrealistic changes to the geologic model to match production history was also avoided.

The study suggests that single realizations of "best-guess" geostatistical models are not guaranteed to offer the best history match and performance prediction. Multiple earth models must be built to capture the range of heterogeneity and assess its impact on reservoir flow behavior.

Introduction

The widespread use of geostatistics during the last decade has offered us both opportunities and challenges. It has been possible to capture vertical and areal heterogeneities measured by well logs and inferred by the depositional environments in a very fine scale with 0.1- to 0.3-m vertical and 20- to 100-m areal resolution (Hobbet et al. 2000; Dashti et al. 2002; Aly et al. 1999; Haldorsen and Damsleth 1990; Haldorsen and Damsleth 1993). It also has been possible to generate a large number of realizations to assess the uncertainty in reservoir descriptions and performance predictions (Sharif and MacDonald 2001). These multiple realizations variously account for uncertainties in structure, stratigraphy, and petrophysical properties.

Although impressive, the fine-scale geological models usually run into several millions of cells, and current computing technology limits us from simulating such multimillion-cell models on practical time scales. This requires a translation of the detailed grids to a coarser, computationally manageable level without compromising the gross flow behavior of the original fine-scale model and the anticipated reservoir performance. This translation is commonly referred to as upscaling (Christie 1996; Durlofsky et al. 1996; Chawathe and Taggart 2001; Ates et al. 2003).

The other challenge is to quantify the uncertainty while keeping the number of realizations manageable. This requires identifying uncertainties with the greatest potential impact and arriving at an optimal combination to capture the extremes. Further, these models require a screening and ranking process to assess their relative ability to track historical field performance and to help minimize the number of models that can be considered for comprehensive flow simulations (Milliken et al. 2001; Samier et al. 2002; Chakravarty et al. 2000; Lolomari et al. 2000; Albertão et al. 2001; Baker et al. 2001; Ates et al. 2003).

In some situations, often a single realization of the best-guess geostatistical model is carried forward for conventional flow simulation and uncertainties are quantified with parametric techniques such as Monte Carlo evaluations (Hobbet et al. 2000; Dashti et al. 2002).

Using the case study of this Middle Eastern carbonate reservoir, the paper describes the upscaling, uncertainty management, and SL screening process used to arrive at a single reference model that optimally combines the uncertainties and provides the best history match and performance forecast from full-field flow simulation. Fig. 1 presents the details of the workflow used.

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