Estimation of Flow Functions During Drainage Using Genetic Algorithm
- Sun Xuefei (University of Houston) | Kishore K. Mohanty (University of Houston)
- Document ID
- Society of Petroleum Engineers
- SPE Annual Technical Conference and Exhibition, 5-8 October, Denver, Colorado
- Publication Date
- Document Type
- Conference Paper
- 2003. Society of Petroleum Engineers
- 5.5.2 Core Analysis, 5.6.2 Core Analysis, 5.5.8 History Matching, 5.3.1 Flow in Porous Media, 5.3.2 Multiphase Flow, 4.1.2 Separation and Treating, 1.6.9 Coring, Fishing, 4.3.4 Scale, 4.1.5 Processing Equipment
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Unsteady state relative permeability experiment followed by automatic history matching has been used in the past for estimating relative permeability and capillary pressure simultaneously. The performance of the automatic history matching largely depends on the simulator, the functional form of the flow functions, and the optimization tool. Newton method, which is commonly taken as the optimization tool for the automatic history matching, may not converge to the global extremum in the presence of high non-linearity. Genetic algorithm (GA) with better global convergence property was used as the optimization tool in this work. Another advantage of GA as an optimization tool is that it requires only function evaluations for the solution searching and not Jacobian or gradient calculations as required by the Newton method. Corey model and piece-wise spline interpolation were utilized to represent the relative permeability. A new coding method in genetic algorithm was developed for piece-wise spline interpolation. In situ saturation data were collected during an unsteady state primary drainage experiment by CT-scanning. Simulation and experimental data were used to test the performance of the algorithm. Test results showed a good match between the simulation data and experimental data for low injection rate primary drainage.
Relative permeability and capillary pressure are two important functions for describing multiphase flow through porous media. 3 They depend on saturation, saturation history, wettability, porous medium microstructure, capillary number and Bond number, in general. Pore network models are being developed to estimate these functions, but most researchers rely on experimental measurements of these functions.
Capillary pressure and relative permeability are usually measured separately.1,2 Capillary pressure is usually measured by the porous plate method, centrifuge method or the mercury porosimetry. The porous plate method is the most accurate, but slow. It may have problems with crude oil if they wet the porous plate or the semi-permeable membrane. The centrifuge method can be used only for drainage, not imbibition. Mercury porosimetry relies on similar wettability between water-oil and air-mercury.
Relative permeability is usually measured by steady-state, unsteady-state or centrifuge methods. The steady-state method can generate accurate data, but it is time-consuming and thus seldom used.3,4 The unsteady state method is fast and more widely used, but the results need to be interpreted.5-8 The JBN method is often used to interpret experimental data in the unsteady-state method, but it ignores capillary pressure. Automatic history matching methods have been used to extract relative permeability from the raw data given the capillary pressure. This method will be discussed in more detail in this paper. The centrifuge method can be used for drainage and it is successful when one of the phases is almost inviscid.
The drawback of determining capillary pressure and relative permeability separately is that the capillary pressure measured in this manner gives a static capillary pressure curve, while it is the dynamic capillary pressure that influences the flow. As pointed out by Bentson, 1,9 the capillary pressure in a dynamic system may be different from that in a static case, for the dynamic capillary pressure is affected by many factors including flow rate, possible variations of the wetting property and micro-heterogeneity. Therefore, simultaneously estimating the capillary pressure and the relative permeability for a given flow system is preferable.
History matching techniques have been developed to estimate relative permeability and capillary pressure simultaneously. 10 Functional forms with a set of parameters are presumed for relative permeability of each phase and capillary pressure. A series of forward simulations is run with the parameters taking a certain set of values. The parameters are automatically tuned by an optimization tool to match the simulation data (generally the pressure drop and the production) with the experimental data.
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