The Benefit of Local Saturation Measurements in Relative Permeability Estimation From Centrifuge Experiments
- J.F. App (U. of Houston) | K.K. Mohanty (U. of Houston)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- September 2002
- Document Type
- Journal Paper
- 288 - 298
- 2002. Society of Petroleum Engineers
- 1.6.9 Coring, Fishing, 5.6.1 Open hole/cased hole log analysis, 5.2.1 Phase Behavior and PVT Measurements, 5.5.8 History Matching
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The standard method for estimating relative permeabilities from centrifuge experiments is to match the production data. This study examines under what conditions local saturation measurements (in addition to production data) can improve the estimation of wetting- and nonwetting-phase relative permeabilities. Synthetic experimental data were obtained through simulation. Three distinct sets of wetting- and nonwetting-phase relative permeability curves at low and high mobility ratios were used to construct the experimental data. The relative permeabilities were then history matched through nonlinear regression using either local saturation and production measurements or only production measurements. Local saturation in conjunction with production measurements can improve the estimation of relative permeabilities from centrifuge experiments. The most significant improvement is in the prediction of the wetting-phase relative permeability at low mobility ratios (e.g., less than 5). For gas/oil systems (with high mobility ratio), the wetting-phase (oil) relative permeability was accurately estimated in all cases using an initial guess based on Hagoort's method with or without local saturation data. Prediction of the nonwetting-phase relative permeability is still difficult under some conditions.
Relative permeability can be measured by three different methods: steady-state, unsteady-state, and centrifuge. The centrifuge method is very attractive because it is relatively fast and data for low wetting-phase saturation can be attained. It is, however, limited to the determination of only the wetting-phase relative permeability, especially at high mobility ratios.
A standard centrifuge experimental data set consists of wetting-phase production measurements at single or multiple angular velocities. At a constant angular velocity, the wetting phase is produced until equilibrium is reached between the capillary pressure and centrifugal force. Wetting-phase production ceases at equilibrium. Relative permeability information is derived from the nonequilibrium data (i.e., during production of the wetting phase). The capillary pressure curve is constructed from the equilibrium data acquired at multiple centrifuge speeds.1,2 Hassler and Brunner3 documented the use of the centrifuge to measure capillary pressure. The capillary pressure curve was determined based on an average wetting-phase saturation within the core at multiple centrifuge speeds. Ayappa et al.4 have provided procedures for calculating the local saturation from the average saturation.
Hagoort5 introduced an analytic method to estimate the oilphase relative permeability in a gas/oil system from centrifuge data. Oil production measurements were used to construct the oil relative permeability curve. Two key assumptions in this development were that: (a) capillary pressure was neglected and (b) mobility of the gas (nonwetting) phase was considered infinite compared to that of the oil (wetting) phase. A numerical model was also developed that considered capillary pressure in an approximate manner (i.e., through the Leverett function).
Numerical methods have been developed to estimate relative permeabilities from centrifuge experiments.6-11 O'Meara and Crump7 developed a semi-implicit method for estimating wettingphase relative permeability and capillary pressure simultaneously from a single experiment in a gas/oil system. Estimation of the oil (wetting-phase) relative permeability and capillary pressure was achieved by history matching the production data. The wetting phase relative permeability was represented by Corey functions. Nordtvedt et al.10 used production data to estimate wetting- and nonwetting-phase relative permeabilities in addition to capillary pressure. The relative permeabilities were represented by B-splines. The significant difference between the two studies is that Nordtvedt et al. estimated both wetting- and nonwetting-phase relative permeabilities. These were evaluated at low (~1) and high (~50) mobility ratios by studying oil/water and gas/oil systems. The mobility ratio, M, is defined for a drainage process as the ratio of the endpoint mobility of the invading (nonwetting) to the endpoint mobility of the displacing (wetting) phase, or
Firoozabadi and Aziz8 proved that history matching production data would not yield a unique set of relative permeabilities. They estimated nonwetting- (gas) and wetting- (oil) phase relative permeabilities by matching production data. They concluded that good matches of production data could be obtained with two different sets of relative permeability relationships. Capillary pressure was included in their model.
Chardaire-Riviere9 et al. attempted to use local saturation measurements to estimate both wetting- and nowetting-phase relative permeabilities in addition to capillary pressure. The local saturation measurements were determined with ultrasonic transducers placed at three locations along the core. Thus, gas was avoided in the system; oil and water were used, and mobility ratios were close to unity. Measurements were made during dynamic operation of the centrifuge. They claimed improved estimation of both capillary pressure and relative permeability by using local saturation as opposed to only production data.
Estimation of relative permeabilities through least-squares regression has been addressed by several authors.7-14 This is an inverse problem where the objective is to minimize the sum of the least square difference between measured data and simulated data from a mathematical model. For the case of relative permeability estimation, the minimization is accomplished by adjusting the parameters in the relative permeability models. With the exception of Chardaire-Riviere et al., only production data has been considered in the regression procedure.
The goal of this work is to determine under what conditions local saturation measurements improve the estimation of wetting- and nonwetting-phase relative permeabilities. This will be investigated at different mobility ratios for gas/oil, oil/water, and gas/ condensate systems. Only single-speed displacements are considered here because the relative permeability can be Bond number dependent, in principle.
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