Estimation of Multiphase Flow Functions From Displacement Experiments
- P.C. Richmond (Texas A and M U.) | A.T. Watsons (Texas A and M U.)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Engineering
- Publication Date
- February 1990
- Document Type
- Journal Paper
- 121 - 127
- 1990. Society of Petroleum Engineers
- 5.4.1 Waterflooding, 5.5 Reservoir Simulation, 5.3.2 Multiphase Flow, 1.6.9 Coring, Fishing, 5.6.1 Open hole/cased hole log analysis, 5.1.5 Geologic Modeling
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A recently developed implicit estimation procedure (regression-based method) that uses parameter estimation with B-spline functional representations can determine essentially unbiased estimates of relative permeability functions from dynamic displacement data. In this paper, we extend this method to estimate relative permeability simultaneously with capillary pressure functions. Careful consideration is given to the functional representation of the relative permeability and capillary pressure functions so that the most accurate permeability and capillary pressure functions so that the most accurate estimates of these properties can be obtained. These procedures are demonstrated with laboratory dynamic displacement data.
Macroscopic properties are used to model or to simulate the flow of fluids through porous media. Because of the geometric complexity of natural porous systems, properties describing multiphase flow have not been explained satisfactorily in terms of observable microscopic features. Normally, these properties are estimated from laboratory displacement experiments. We consider the estimation of two-phase relative permeability and capillary pressure curves as functions of saturation.
Both steady-state and unsteady-state displacement experiments have been used to determine relative permeability curves. Steady-state experiments have several disadvantages: they are time-consuming, relatively few points of the relative permeability curves are determining, two fluids must be injected simultaneously, capillary effects may be difficult to eliminate, and they may not provide the values appropriate for simulating a displacement process. Unsteady-state or dynamic displacement experiments are the experiments used to determine relative permeability curves.
The standard explicit-type procedures used to estimate relative permeabilities from dynamic displacement data have serious permeabilities from dynamic displacement data have serious limitations. The most notable is the neglect of capillary pressure effects. The Johnson-Bossler-Naumann (JBN) method, and variations of that method, are based on the Buckley-Leverett model for representing two-phase flow through porous media, which neglects capillary pressure. Experiments normally are run at relatively high flow rates to negate capillary effects in comparison with viscous effects. It has not been established, however, that capillary pressure effects will not significantly affect the accuracy of estimates so obtained, even if scaling criteria are used to choose the flow rate. Another concern is that the microscopic displacement at the extremely high flow velocities required to have viscous forces overwhelm capillary forces may be quite different from that for an experiment run at a velocity more typical of reservoir flow velocities, and the relative permeabilities estimated consequently may have little resemblance to those for the situation of interest. A procedure to estimate relative permeability curves at any flow procedure to estimate relative permeability curves at any flow velocity, particularly the low flow velocities encountered in reservoir flow, is needed.
Archer and Wong developed a different approach to estimating relative permeabilities from displacement data. They used an implicit procedure in which relative permeability curves are adjusted so that, when used to simulate the coreflood experiment mathematically, the computed pressure drop and production match (in some sense) the measured data. They used trial and error to adjust the unknown curves, and no quantitative criterion for the match of the data was reported. Sigmund and McCaffery provided a systematic procedure for adjusting the unknown curves. The relative permeability curves were represented by power-law functions, and permeability curves were represented by power-law functions, and nonlinear regression was used to adjust the exponent for each function to minimize a sum of squared differences between the data and corresponding computed values. Batycky et al. represented the relative permeability curves by those same power-law functions and also chose a scalar multiplier of a capillary pressure curve determined by mercury injection.
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