Polywater and Reservoir Engineering
- L.B. Davidson (Getty Oil Co.)
- Document ID
- Society of Petroleum Engineers
- Journal of Petroleum Technology
- Publication Date
- October 1971
- Document Type
- Journal Paper
- 1,263 - 1,263
- 1971. Society of Petroleum Engineers
- 5.1 Reservoir Characterisation, 5.3.1 Flow in Porous Media
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Research by Deryagin and Fedyakin during the last decade showed that a solid surface can influence the properties of an adjacent liquid to depths on the order properties of an adjacent liquid to depths on the order of a micron. In particular they found that viscosity increases substantially near the solid-liquid interface.
In many porous materials pore throats on the order of a few microns are quite common. Consequently, "wall effects" may significantly alter viscosity of fluid flowing through such materials and it becomes important to determine how seriously current models of flow in porous media are affected by this phenomenon. phenomenon. As a simple illustration of the role played by "wall effects," consider flow through a single capillary of radius r. Assume that the viscosity at the center of the tube has a constant value , and near the tube wall a constant value . The viscosity changes from to at the radial position us. The "permeability" of the tube is defined for a Newtonian fluid by:
where eff is an effective viscosity for flow through the tube. If there were no "wall effect" eff would equal .
To measure the single-tube "permeability" it is customary to carry out flow tests at constant pressure drop, p, and to compute "permeability" using the viscosity of the bulk fluid, . Let this computer "permeability" be denoted as k calc. Then
Xr = and X = .
Then it is not difficult to show that for a Newtonian fluid
4 = X + (1 - X )Xr ..............(3)
The deviation between the calculated and effective values is a linear function of the ratio X . The slope of the line tends to zero as Xr increases. As a particular example, suppose Xr = 0.5 and the viscosity particular example, suppose Xr = 0.5 and the viscosity is twice as large as the usual value . Then the calculated "permeability" of the tube is equal to 53.1 percent of the effective value. percent of the effective value. This simple example shows that the near-surface structuring of liquid could significantly influence flow behavior in porous materials. Whether or not this is actually true depends on the depth of the liquid structuring, the magnitude of changes in fluid properties resulting from the structuring, and the percent of area available to flow that is affected by structuring. The last factor is determined by the pore-size distribution of the system.
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