Insights Into Upscaling Using 3D Streamlines
- Adwait Chawathe (ChevronTexaco Overseas Petroleum) | Ian Taggart (ChevronTexaco Overseas Petroleum)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- August 2004
- Document Type
- Journal Paper
- 285 - 296
- 2004. Society of Petroleum Engineers
- 5.5.8 History Matching, 5.1 Reservoir Characterisation, 4.6 Natural Gas, 4.1.2 Separation and Treating, 5.6.1 Open hole/cased hole log analysis, 2.4.3 Sand/Solids Control, 5.5.11 Formation Testing (e.g., Wireline, LWD), 5.5 Reservoir Simulation, 5.5.3 Scaling Methods, 1.2.3 Rock properties, 2 Well Completion, 4.1.5 Processing Equipment, 3.3.1 Production Logging, 4.3.4 Scale, 5.4.3 Gas Cycling, 5.1.5 Geologic Modeling, 1.10.1 Drill string components and drilling tools (tubulars, jars, subs, stabilisers, reamers, etc), 5.5.7 Streamline Simulation
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Large, multimillion-cell geological models are frequently constructed in an effort to "capture" the vertical heterogeneity measured by well logs and the areal heterogeneity inferred by the depositional environments. These criteria often result in fine-scale models at a resolution of 0.1 to 0.3 m vertically and 30 to 100 m areally, resulting in reservoir models on the order of 107 grid cells. Recourse is made to upscaling to obtain coarsened but computationally efficient flow-simulation models. The coarsened models commonly result in no more than 1 to 5% of the original grid size, underscoring the need for judicious upscaling. Of greater importance is demonstrating, for the chosen grid dimensions, that the upscaled representation is both reasonable and optimal in the sense that a significantly better template would be difficult to obtain.
We consider two nonuniformly coarsened models to demonstrate the issues involved and show that the use of 3D streamline methods offers insightful alternatives to decoupled analysis for both the scaleup template design and the pre- and post-diagnostics. We confine ourselves to property-upscaling methods that use local grid information as opposed to estimating upscaled properties based on some global measure. For this class of problems, we demonstrate that the diagnostic phases are necessarily separate from the upgridding and upscaling processes.
Several attempts have been made over the past decade or so to constrain coarse reservoir flow models to observed production data. While many useful models have been built with ad hoc history-matching techniques involving pseudoization of reservoir properties, especially the absolute and relative permeabilities, these techniques often lack an auditable path back to geological and petrophysical inputs.
This makes consensus building difficult in a diverse team environment. As a consequence, many studies prefer instead to use a formalized upscaling method to construct a coarse model from fine-scale geological models that honor raw log properties and variability. With the adoption of geostatistical methods, fine-scale models containing geological entities such as braided channels and alluvial fans are now commonly encountered in the reservoir simulation literature. These beautifully detailed models may capture the depositional and diagenetic nuances of the reservoir, but from a simulation standpoint, they demand a prohibitive number of grid cells. These models can have grids in excess of 10 million cells. Although impressive, current computing technology limits us from simulating such multimillion-cell models on practical time scales. In fact, the routine demands simulation of grids that are one order lower in magnitude. This requires a translation of the detailed grids to a coarser, albeit computationally manageable, level without compromising the anticipated reservoir performance. This translation is commonly referred to as upscaling.1
Most upscaling techniques can be described in the following steps:
(a) Template design, whereby potential high-fluid-throughput zones are identified. Generally, upscaling methods are based on a nonuniform template design, which selectively coarsens low-throughput cells while attempting to retain increased resolution in the high-flux areas.2,3
(b) Renormalization and homogenization, whereby a group of fine cells within each template are coarsened into one cell by estimating equivalent upscaled properties.4-6
(c) Attempting some form of post-scaleup diagnostics to provide an indication of the adequacy of the upscaling process.
Unfortunately, the nonlinear nature of the flow problem and the size of the models usually preclude true 3D flux and effective permeability calculations for both the initial template design and the pre- and post-scaleup diagnostic phases. As a compromise, many methods use a series of decoupled unit-mobility flow simulations through 2D slices.2,3 While offering significant speed and computational efficiencies, this decoupling can have a serious impact on the template design and the pre- and post-scaleup diagnostic phases. Fluxes in a 3D grid can exhibit significant out-of-plane flow components, with the result that even if the homogenization/renormalization phase proceeds exactly, the scaleup diagnostics obtained by making strong decoupling assumptions can often be inadequate and misleading.
Verifying the adequacy of a given scaleup template and scaled properties is a central issue in any reservoir study, so when diagnostic discrepancies occur, it is not clear whether there is a problem with the diagnostic itself, the adequacy of the scaled-up model itself, or both. This problem increases with severe levels of upscaling. For practical problems, the original model size and the available computational resources dictate the level of upscaling or coarsening. Therefore, the verification problem described is really one of finding and demonstrating the optimal scaleup to a predetermined sized model. This paper seeks to highlight and address issues related to these problems by demonstrating that the use of 3D streamline methods can provide a useful insight into the nature of the flux distributions for realistic well completions, thereby suggesting alternate scaleup templates and providing more-reliable diagnostic measures.
This paper uses 3D streamlines to investigate the quality of upgridding and upscaling, but previous studies conducted by Portella et al.7 have actually used streamlines (streamtubes) to upgrid/upscale grids using the semianalytical theory for oil recovery. More contemporary studies conducted by Samier et al.8 use 3D streamlines to compare and contrast available upscaling techniques, but they do not question whether an optimal template, which will provide equivalent results, exists for all the algorithms tested in the study. This could potentially explain the large discrepancy in the predicted-oil rates that they have reported in their paper. In a different flavor of using streamlines in the context of upscaling, Tran et al.9 have used streamline-based coarse-scale inversions to condition reservoirs models to production data. All in all, there is a consensus about using streamline methods for upscaling, but to our knowledge, this is the only paper that uses streamlines to assess the quality of upgridding and upscaling.
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