Streamline Approach for History Matching Production Data
- Y. Wang (Stanford U.) | A.R. Kovscek (Stanford U.)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- December 2000
- Document Type
- Journal Paper
- 353 - 362
- 2000. Society of Petroleum Engineers
- 5.5.7 Streamline Simulation, 5.1.9 Four-Dimensional and Four-Component Seismic, 5.1 Reservoir Characterisation, 5.1.1 Exploration, Development, Structural Geology, 5.5 Reservoir Simulation, 5.1.5 Geologic Modeling, 5.4.1 Waterflooding, 5.5.8 History Matching, 5.6.5 Tracers, 5.1.8 Seismic Modelling, 5.6.4 Drillstem/Well Testing, 5.3.2 Multiphase Flow, 4.3.4 Scale
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In this study, we propose and develop a streamline approach for inferring field-scale effective permeability distributions based on dynamic production data including producer water-cut curve, well pressures, and rates. The streamline-based inverse approach simplifies the history-matching process significantly. The basic idea is to relate the water-cut curve at a producer to the water breakthrough of individual streamlines. By adjusting the effective permeability along streamlines, the breakthrough time of each streamline that reproduces the reference producer fractional-flow curve is found. Then the permeability modification along each streamline is mapped onto cells of the simulation grid. Modifying effective permeability at the streamline level greatly reduces the size of the inverse problem compared to modifications at the grid block level. The approach outlined here is relatively direct and rapid. Limitations include that the forward flow problem must be solvable with streamlines, streamline locations do not evolve radically during displacement, no new wells are included, and relatively noise-free production data are available. It works well for reservoirs where heterogeneity determines flow patterns. Example cases illustrate computational efficiency, generality, and robustness of the proposed procedure. Advantages and limitations of this work, and the scope of future study, are also discussed.
History matching plays an important role in monitoring the progress of displacement processes and predicting future reservoir performance. Historical production data are routinely collected and they carry much information, although convoluted, that is useful for reservoir characterization and description of reservoir heterogeneity.1,2 In this paper, the concept of streamlines is applied to develop an automatic method for inferring the permeability distribution of a reservoir based on the history of pressure, flow rate, and water cut at producers.
The properties of streamlines are used in deriving the inverse method, so a brief review of streamline methodology follows. Streamline and streamtube techniques are approximate reservoir simulation methods proposed some years ago3-6 that have undergone recent intense study.7-9 They are most accurate when heterogeneity determines flow paths and the recovery process is dominated by displacement (viscous forces) as opposed to gravity or capillarity.10 A streamline is tangent everywhere to the instantaneous fluid velocity field and, for a symmetric permeability tensor, streamlines are perpendicular to isobars or isopotential lines. Streamlines bound streamtubes that carry fixed volumetric flux, and in some cases, flow rate is assigned to streamlines.8,11 For this reason, we use the terms streamline and streamtube interchangeably.
The streamline method assumes that displacement along any streamline follows a one-dimensional solution, and that there is no communication among streamlines. Thus, the flow problem is decomposed into a set of one-dimensional flow simulations linked by common boundary conditions. A streamline must start at a source and end at a sink to maintain continuity. In a streamline-based approach, pressure equations are solved independent of saturation equations. The decoupling of pressure equations from saturation equations speeds up the simulation significantly by reducing the number of times that the pressure field must be updated and greatly reduces the number of equations to solve.
For unit mobility ratio and constant boundary conditions, the streamline distribution remains unchanged throughout the displacement process. Therefore, the pressure field or streamline distribution only needs to be solved once and saturation solutions can be mapped along streamlines. For nonunit mobility ratio, there are two common approaches to treat streamlines. One is to fix the streamline geometry and allow the flow rate to change during the displacement process.12,13 The other is to update the streamline distribution and distribute the flow rate equally among the streamtubes.14,15 In the second case, both the pressure field and streamline geometry must be updated periodically.
For complete descriptions of the various streamline formulations and inclusive reviews of the history of streamlines for predicting reservoir flow, please refer to Refs. 7, 10, 12, and 16.
In this study, the streamline simulator 3DSL of Batycky et al.11 is employed for forward simulation. In short, after solving the pressure field and the streamline distribution, 3DSL assigns equal flow rate to each streamline. Then a one-dimensional saturation solution, either analytical or numerical, is solved along the streamlines. Periodically, the streamline saturation distribution is mapped onto the multidimensional grid, the pressure equation is resolved, and streamline geometry redetermined. There is no detectable reduction in accuracy with this technique for incompressible and viscous determined flows.17
Most approaches to history-matching field data manipulate permeability at the gridblock level, and hence, demand a great amount of computational work because there are many gridblocks in a typical simulation. Integration of production data with reservoir description remains an important issue because of the prevalence of production data and the information that it carries about the reservoir. In this brief review, we focus on work that is most similar to our method to follow. Other approaches to history matching are based upon simulated annealing,18 sensitivity coefficients,19-21 and parameter estimation approaches. 22
Sensitivity coefficient techniques compute the sensitivity of the objective function to the change of permeability of a cell or a set of cells and solve an inverse system that can be very large and somewhat difficult to construct.21,22 Sensitivity coefficient methods might also be computationally expensive if the sensitivity coefficients are evaluated numerically by running multiple simulations. Chu et al.21 developed a generalized pulse spectrum technique to estimate efficiently the sensitivity of wellbore pressure to gridblock permeability and porosity. Other work employed sensitivity coefficients in the integration of well test information, production history, and time-lapse seismic data.22
Vasco et al.20 combined streamlines and a sensitivity coefficient approach while integrating dynamic production data. They employed streamlines to estimate sensitivity coefficients analytically thereby greatly speeding up the procedure. The streamline analysis allowed them to "line up" the first arrival of injected fluid at production wells and then match the production history. This technique remains a gridblock-level optimization approach since all of the cells from the flow simulation are used to describe reservoir heterogeneity.
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