Buckley-Leverett theory

The mathematical formulation of this model was made by Dever-eux 36) based on the classical Buckley-Leverett theory for two-phase flow in porous media (49) and equations developed by Scheidegger (44). They solve a set of eight equations ... 

In the original Buckley-Leverett theory, gravitational, compressibility and capillarity are ignored. Devereux (36) presents the solution for the case of constant pressure, and the constant-velocity case was derived by Soo and Radke 12). The model requires a knowledge of the capillary retarding force per unit volume of the porous medium, and the relative permeabilities of the oil droplets in the emulsion and the continuous water phase. These relative permeabilities are assumed to be functions of the oil saturation in the porous medium. These must be determined before the model can be used. 

Note that the preceding velocity is the interstitial injection velocity normalized by qt/(A( )), and that it is dimensionless. Lake (1989) and Green and Willhite (1998) used the term specific velocity for the dimensionless velocity. In this book, we follow their terminology. Corresponding to the front of the component C, we assume the water saturation is 8 3. According to the Buckley-Leverett theory (1942), the specific velocity of 8 3 is... 

The waterflood front is given by the classical Buckley-Leverett theory by drawing the tangent to the f versus S. curve from (S c. 0), as shown in Figure 2.16. The corresponding equation is... 

When the injection starts at to = 0, the locations of saturations are given by the Buckley-Leverett theory ... 

The experimental pressure and effluent curves were history matched using an analytic simulation package, "PRIsm [30, 31], which is based on the Buckley-Leverett theory. 

As one would expect, this improvement in displacement efficiency is reflected in a floodout test. Fig. 6 shows the results of such a test on a 1-in. diameter by 1-ft long unconsolidated core from a Louisiana field, using field fluids. According to the simplified form of the Buckley-Leverett theory, this test represents a linear model of the field on a pore volume basis. Thus, this core performance can be considered as a partial representation of the expected field performance. 

According to the Buckley-Leverett (1942) theory, the velocity of the saturation 8 2 is... 

The trapping number defined by Eq. 7.103 for an arbitrary dipping angle is consistent with the conventional Buckley-Leverett fractional flow theory. In the Buckley-Leverett fractional flow equation, the gravity term is multiplied by sina (Leverett, 1941). However, Figure 7.34 shows that the trapped residual saturation predicted by Eq. 7.103 is lower than the experimental data at the same trapping number. This figure compares the relationship between the... 

According to the theory by Buckley and Leverett (1942), the fraction of the displacing water (f ) is... 

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