Blake-Kozeny model

Although the early versions of capillary models, namely, the Blake and the Blake-Kozeny models, are based on the use of V = Vq/s and = LT, it is now generally accepted [Dullien, 1992] that the Kozeny-Carman model, using Vi = VoT/e provides a more satisfactory representation of flow in beds of particles. Using equations (5.36), (5.38) and (5.40), the average shear stress and the nominal shear rate at the wall of the flow passage (equations 5.34 and... 

There are several versions of the Blake-Kozeny model to improve agreement between experimental and predicted results. For example. Equation 2 is the modified Blake-Kozeny model developed by Christopher and Middleman. The tortuosity was assumed to be 25/12 in this model. 

The Blake-Kozeny model assumes that polymer retention on the rock does not alter the permeability of the rock. Modifications of the Blake-Kozeny model have been proposed to account for permeability reduction by correlating the radius of the capillary with the amount of permeability reduction. 

The Blake-Kozeny and modified Blake-Kozeny models have been verified by comparing observed pressure drops with computed pressure drops for flow of non-Newtonian fluids through packed beds. Agreement between predicted and measured pressure drops is within 20%. Thus, it is possible to predict flow behavior through some porous materials from rheological properties and characteristics of the porous media. 

Comparisons were made between polymer mobilities computed from the Blake-Kozeny model (Equation 1), the modified Blake-Kozeny model (Equation 13) and the actual data. Equation 32 is the expression for A derived from the Blake-Kozeny model. ... 

Typical results are shown in Tables 3-5 for the Blake-Kozeny model where polymer mobilities are compared at a frontal advance rate of 1 ft/d. For the conditions of this study, the polymer mobility was underestimated by factors ranging from 1.3 to 6.7. Best agreement was observed at 500 ppm for high permeability cores. Poorest agreement occurs at 1500 ppm and 15.5 md cores. The average reduction in polymer mobility was 0.42 for the Blake-Kozeny model and 0.36 for the modified Blake-Kozeny model. Capillary bundle models consistently predict lower polymer mobilities in porous rocks than observed experimentally. 

K and n obtained from steady shear experiments do not describe flow in porous rocks. This finding has significant impact on simulation of polymer injection rates in potential polymer floods and permeability modification projects. Injection rates predicted using Blake-Kozeny models will be less than can be attained in practice. Therefore, it is necessary to determine... 

The correlations represented by Eqs. 5.26a through 5.26e can be extended to interpolate for polymer concentrations between 1,000 and 2,000 ppm by use of a correlation based on the modified Blake-Kozeny model for the flow of non-Newtonian fluids. 62 Eq. 5.27 is an expression for A bk derived from the Blake-Kozeny model. Note that all parameters are either properties of the porous medium or rheological measurements. Eq. 5.27 underestimates A/ by about 50%. However, Hejri et al. 6 were able to correlate pBK and A for the unconsolidated sandpack data with Eq. 5.28. Eqs. 5.27 and 5.28, along with Eq. 5.24, predict polymer mobility for polymer concentrations ranging from l.,000 to 2,000 ppm within about 7%. 

Using the Blake-Kozeny equation, the screw conveyor reactor can be modeled as rotating equipment in which the fluid is moved by screw rotation. Although 10 small horizontal cylindrical baffles exist in the screw flights, the interaction between the screw and baffles can be ignored. For this case, the rotating reference frame was used instead of the inertial reference frame. 

The Ergun equation was empirically obtained based on a more general form of the dimensionless pressure drop equation, namely, the Blake-Kozeny equation, which was also theoretically derived by Irmay (23). Irmay s model yields... 

The most popular approach is the pipe flow analogy model, also called the capillary tube model or channel model, which approximates the flow through the packed bed by the flow through a bundle of straight capillaries of equal size. Further refinement produced the constricted tube model. In this model, an assembly of tortuous channels of varying cross sections simulates the varying dimensions and curvatures of pores in the packed bed. The major contributions following this approach include Blake (1922), Kozeny (1927),... 

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