Flow Simulation of Geologic Models
- M.J. King (BP Exploration Ltd.) | Mark Mansfield (BP Exploration Ltd.)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- August 1999
- Document Type
- Journal Paper
- 351 - 367
- 1999. Society of Petroleum Engineers
- 5.1.2 Faults and Fracture Characterisation, 4.1.2 Separation and Treating, 7.2.2 Risk Management Systems, 5.2 Reservoir Fluid Dynamics, 5.4.2 Gas Injection Methods, 5.6.5 Tracers, 5.5.8 History Matching, 1.2.3 Rock properties, 1.6.9 Coring, Fishing, 5.5.3 Scaling Methods, 4.3.4 Scale, 5.5 Reservoir Simulation, 5.1.1 Exploration, Development, Structural Geology, 2.4.3 Sand/Solids Control, 5.1.5 Geologic Modeling, 5.1 Reservoir Characterisation, 5.4.1 Waterflooding
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We report upon our experience in performing flow simulation within detailed three dimensional geologic models. Such models have the potential to significantly improve mechanistic understanding of fluid flow through our reservoirs, especially those influenced by strong contrasts in permeability at multiple scales. We have found that utilizing these static models in a dynamic sense places new requirements upon the models, and forces a reevaluation of the theoretical foundations behind our flow simulators. We review a range of physical and numerical concepts, and provide the required conceptual extensions and new derivations.
The last several years have seen an explosive growth in the ability of the petroleum industry to develop flow simulation models based upon detailed three dimensional geologic descriptions.1-9 As "Shared Earth" models, they provide an integrated repository of static data and a means of visualizing and integrating well and reservoir data at multiple scales.10-12 These models tend to be large and complex, as they include the reservoir structural framework, reservoir zonation and flow units, trends in quality, and local reservoir heterogeneity. Such an integrated data set offers a significant opportunity to improve our mechanistic understanding of fluid flow through our reservoirs, especially those impacted by strong contrasts in permeability and the interaction of complexity at these many scales.13-15
Until recently, such modeling activities have required access to research codes, and specialists to utilize them. But, with a wide range of vendor tools now available, it is possible to build such models within asset teams without the direct involvement of the specialists. However, this does not imply that the underlying technology has matured to the point where it can be used routinely. In the course of an asset study of bypassed oil within the Magnus reservoir, we have repeatedly run into limitations of the available industry tools. This is especially true in the treatment of the geologic model as a flow simulator, e.g., in performing fluid flow simulation on the geologic grid, with that model providing the initialization data. We do not believe that this is a shortcoming of the specific tools, but is instead due to the additional requirements being placed upon our theoretical foundations by these new reservoir modeling applications.
In some instances the theoretical foundations seem to be well developed; we need only to generalize the derivations. This is the case when evaluating well connection factors for wells at arbitrary orientations to the computational grid, now with a (symmetric) full tensor permeability.16-22 Some concepts need only a slight reexamination. How does the definition of tensor permeability differ between the geologic model and a flow simulator?
Other concepts and algorithms have relied heavily upon the existence of a computational grid with an (I,J,K) "shoe box" topology. These are the most in need of reexamination. The most important is the definition of transmissibility if the principle directions of permeability are not aligned with the computational grid. The most "obvious" generalization of the ECLIPSE NEWTRAN equation is not guaranteed to provide positive transmissibilities.23-25 What formulation (or formulations) should we use instead? Similarly, the usual equations for the upscaling of effective permeability from a fine to a coarse grid is strongly dependent upon the shoe box topology of the grid.26,27 How do we formulate the upscaling calculation when the fine grid is not a simple refinement of the coarse grid, or where upscaling regions are irregular in shape?
There are also new requirements placed upon the geologic model. A computational grid and static model which is adequate for defining volumes may be far from optimal for modeling flow. This is demonstrated within the Magnus geologic model at reservoir zone boundaries, where the erosion of one zone by another generates nonconformities across much of the grid. A new gridding algorithm has been implemented, improving our ability to model flow at these boundaries. A simple treatment of transmissibility across the pinched out cells at the zone boundaries is also derived, which greatly simplifies the finite difference formulation at the boundary.
Work was performed as much as possible using standard industry tools. As a result the issues that arise, and the solutions we present, will reflect a compromise between the "correct" or "ultimate" solutions and those that are practical today. Nonetheless, we believe that the conceptual developments and many of the particular solutions we present will be of general applicability.
This paper will first discuss the management of the computational grid at zone boundaries and the transmissibility across pinched-out cells. It will be necessary to include a brief introduction to the modeling requirements posed by the remaining oil study of the Magnus reservoir. Permeability will be discussed next. How does its representation differ between the geologic and simulation models? Transmissibility will be reviewed and two different formulations will be derived. The applicability of each will be discussed. An extension of Peaceman's expression for the well connection factor to full tensor permeability will be provided, although with minimal details of the derivation. The final section of the paper provides two formulations of the upscaling of effective permeability: one for each of the two definitions of transmissibility. Key result equations are listed at the end of each section.
Smedvig's IRAP Reservoir Modeling System (IRAP/RMS version 4.0.7) was used to construct the geologic models.28 TSC's streamline based FRONTSIM simulator was used for the flow modeling.29 BP's TIME OF FLIGHT (TOF) streamline code30-32 was used to visualize the flow solutions. (At the time of this project, industry codes were unable to provide this capability.) A research upscaling code was used for the demonstration examples cited in the last section of this paper, but not for any of the production work.
Managing the 3D Geologic Grid
The issues that we discuss have all arisen in an evaluation of the habitat of the remaining oil of the Magnus sand member (MSM) of the Magnus reservoir.33 The Magnus MSM is a large Upper Jurassic, sand dominated, turbidite reservoir. It was discovered in 1974, commenced production in August of 1983, and was on plateau until January of 1995. Since then, decline has been managed with an active infill drilling program.34
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