Streamline-Based Method With Full-Physics Forward Simulation for History-Matching Performance Data of a North Sea Field
- Bijan Agarwal (Dubai Petroleum Co.) | Martin J. Blunt (Imperial College)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- June 2003
- Document Type
- Journal Paper
- 171 - 180
- 2003. Society of Petroleum Engineers
- 5.2.1 Phase Behavior and PVT Measurements, 4.1.5 Processing Equipment, 5.3.2 Multiphase Flow, 2.2.2 Perforating, 4.3.4 Scale, 5.6.5 Tracers, 5.5 Reservoir Simulation, 5.5.8 History Matching, 5.5.3 Scaling Methods, 5.1.5 Geologic Modeling, 5.6.4 Drillstem/Well Testing, 5.1.2 Faults and Fracture Characterisation, 7.6.2 Data Integration, 5.8.7 Carbonate Reservoir, 4.1.2 Separation and Treating, 5.4.1 Waterflooding, 5.1 Reservoir Characterisation, 6.5.2 Water use, produced water discharge and disposal, 5.4.2 Gas Injection Methods, 5.5.7 Streamline Simulation, 5.8.8 Gas-condensate reservoirs, 1.2.3 Rock properties
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We present a method for history-matching production data using a streamline simulation that captures all the pertinent physics, including compressible three-phase flow with gravity. We use an approach based on the assumption of 1D flow along streamlines to find the sensitivity of water flow rate at production wells to changes in permeability. Although the computation of the sensitivities is approximate, we show, using data from a North Sea field, that the method can provide a reasonable history match and good predictions of future performance for problems with significant effects caused by compressibility and gravity.
Several history-matching methods have been proposed to constrain reservoir descriptions to production data, such as water-cut history (see, for instance, Refs. 1 through 8). These techniques use conventional grid-based simulation to compute sensitivity coefficients, which give the change in production data caused by a change in the permeability or porosity of some portion of the simulation model. Using the sensitivity coefficients, the porosity and permeability are adjusted to create a new reservoir model. When another simulation is performed using this model, a better match to the data should be obtained. If the match is still unacceptable, new sensitivity coefficients are computed and used to modify the reservoir model again. Because the sensitivity coefficients are nonlinearly dependent on the reservoir description, many iterations may be needed before a good history match is obtained. For a finely-gridded model, there are many more matching parameters than data, and the match is nonunique. To overcome the problem of having many poorly determined parameters in the reservoir description, methods that reduce the parameter space, such as the use of recursively refined grids,9,10 gradzone analysis,2,4 and gradual deformation7,8 have been proposed.
Current history-matching methods are still limited, however, by the time taken to perform the forward simulations. Ideally, history matching would start from a statistical ensemble of equiprobable initial estimates of the reservoir description. Each reservoir description, if it is a fine-scale reservoir model, may contain several million gridblocks. Current simulation techniques may take approximately a week to perform a single simulation of this size, making history matching that may require tens to hundreds of iterations on several models impossible in practice. Approaches where history matching is performed on a much coarser grid than the geological model offer appealing savings in computer time. However, the appropriate manner to upscale or downscale single and multiphase flow properties is not obvious. Furthermore, fine-scale details may be important for future prediction of, say, waterflood or gasflood performance. In these cases, history matching on a coarse grid may yield a poor reservoir description with correspondingly inaccurate predictions of future recovery.
Streamline-based simulation offers an attractive alternative to grid-based techniques for history matching for two reasons. The first is that for displacement-type simulations through fine-scale heterogeneous reservoir descriptions, streamline simulation can be considerably faster than comparable grid-based, conventional methods.11 This enables the forward simulations to be performed much faster, allowing matches to be obtained with fine grids. Vasco et al. introduced the use of streamlines in history matching. 12 A streamline simulator that assumed fixed streamlines without gravity was used to perform the forward simulation, while conventional techniques were applied to the computation of sensitivity coefficients. Because the forward simulation was so fast, impressive results were achieved on a number of synthetic and field case histories. There is, however, a second powerful reason for using streamlines in history matching. The time of flight along a streamline can be used directly to compute sensitivity coefficients. The time of flight of a streamline at a producer indicates the water breakthrough time for that streamline. The water cut is the sum of the production along each streamline reaching the well. The time of flight, from Darcy's law, is inversely proportional to the average permeability, assuming that the streamline locations do not change with small changes in permeability. It is then possible to estimate the change in permeability along a streamline necessary to match production history. Independently, three groups have proposed different methods for using streamlines in history matching by calculating the change in permeability necessary to match water production.13-17
These streamline-based history-matching techniques offer considerable promise, but they all suffer from one major limitation: the forward simulations assume incompressible flow without gravity. The theory of streamline-based history matching assumes essentially tracer-like flow - fixed streamlines over time with no gravity or compressibility. This may be a poor approximation for many cases, such as for matching early production history, including periods of primary production, where compressibility is important, or for assessing gas injection schemes, where gravity override is significant. It is possible to obtain a history match from a forward simulation that ignores essential physics. However, the reservoir description obtained may not be representative of the field, and the prediction of future performance will be in error as a consequence.
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