Summary
Computer models of oil reservoirs have become increasingly complex in order to represent geological reality and its impact on fluid flow. Memory and CPU time limitations by finite-difference (FD)/ finite-volume (FV) simulators force a coarser resolution of reservoir models through upscaling.
Upscaling can lead to significant difficulties in reservoir studies:while the fine-scale geological model is built from petrophysical, log, and seismic data, its dynamic behavior is never checked. As a result, a coarse-scale reservoir study can be linked to a fine-scale geological model, but the two might be inconsistent in their dynamic behavior.Conversely, the upscaled model cannot be properly tested because the flow and production behavior at the fine-scale level are not available. There is no reference solution for guiding important decisions for building a consistent upscaled model.A large number of sector models are required in designing optimal well patterns.
Streamline simulation is now an attractive alternative to overcome some of these drawbacks because it offers substantial computational efficiency while minimizing numerical diffusion and grid-orientation effects. It allows the integration of fine-scale geological models into the reservoir engineering workflow.
In this paper, we demonstrate the usefulness and efficiency of a streamline simulator in the reservoir engineering workflow. We evaluate its speed, memory requirements, and scalability using tracer and black-oil-test data sets on an SGI Origin 2000™* (250 MHz MIPS). Our data are based on real fields and range from 200,000 to 7 million cells, with cells as small as 30×30×0.5 m. Streamlines allowed us to check the validity of a large geological model and to optimize well patterns with more than 30 producers and injectors. We demonstrate how streamline-based simulation has matured from a research tool to an industrial application providing real benefits to engineers as a complementary tool to existing conventional simulation technology based on FVs.
Introduction
Dynamic flow simulation is still a bottleneck in most integrated reservoir studies that attempt to reconcile the geological model with seismic data and well data. Three-dimensional, high resolution (3DHR) seismic data, as well as improved 3D static modeling tools, produce models that are ever more detailed and allow significantly more faults than the previous generation of static models. Today's fine-scale models are commonly in the range of 1 to 10 million cells. On the other hand, flow simulation technology based on FVs or FDs is mature. Any improvements are expected mainly from parallel processing of key modules, such as the simultaneous solution of the linearized flow equations or PVT calculations. As a result, only relatively small dynamic models (100,000 active cells) can be considered in routine engineering studies. Dynamic flow simulation also has suffered from recent cost cutting by reserving large-scale computing power (machines with more than 1,000 processors) for seismic processing while shifting most other simulations to PC clusters with a limited number of processors (8 to 32).
Upscaling fine-scale geological models remains a reality for most studies, causing significant deterioration in the geological model. In many cases, the fine-scale and coarse-scale models do not superimpose, with coarse blocks being traversed by fine-scale faults. Under realistic reservoir conditions, rigorous upscaling becomes difficult, forcing the engineer to make dubious approximations (fault location and transmissivity, layer resampling, etc.). The fact that these approximations often cannot be quantified because a fine-scale reference solution is not available makes matters worse. A methodology that allows for solutions to the original geological model is therefore desirable, allowing some quantification of errors caused by upscaling. Streamline-based reservoir flow simulation is one alternative currently available.1,2
Streamline Simulation vs. FV Simulation
Streamline-based flow simulation has made significant advances in the past 10 years. Today's simulators are fully 3D1,3 and account for gravity1,4 as well as for complex well controls. Most recent advances also allow for compressible flow and compositional displacements.5,6 A number of recent publications demonstrate how streamline-based simulation is now coming into the mainstream.7–14
FV methods are based on the fundamental concept that fluids are moved from cell to cell. The problem with this methodology is an exponential increase in CPU time, with a linear increase in model size. The reason for this is that larger models dramatically reduce timestep sizes (both in implicit and explicit modes) because of reduced cell volumes and (often) increased heterogeneity. This means that locally higher fluxes have to be pushed through blocks with smaller volumes. Routine solutions of million-cell models with FV or FD technology are, therefore, out of reach for most practical applications. Even with significant simulation power, a single solution can take weeks. Data debugging and sensitivity calculations under these circumstances can become difficult.
Streamline-based simulation is an attractive alternative because of the fundamentally different approach in moving fluids. Instead of moving fluids from cell to cell, streamline simulation breaks up the reservoir into 1D systems, or tubes. The transport equations are then solved along the 1D space defined by the streamlines using the concept of time of flight (TOF).15,16 By decoupling the transport problem from the underlying 3D geological model, fluids can be transported much more efficiently. Large timesteps can be taken, numerical diffusion is minimized, and CPU time varies nearly linearly with model size.
Description of the Streamline Simulator
Modern streamline-based simulation rests on five key principles:tracing streamlines in a velocity field;15writing the mass conservation equations in terms of TOF;16numerical solution of conservation equations along streamlines;17periodic updating of the streamlines;18,2 andoperator splitting to account for gravity.4 Details of the methodology can be found elsewhere;1 we give only a brief overview here.
