Viscosity Measurements in the Presence of Wall Slip in Capillary, Couette, And Parallel-Disk Geometries

Abstract

Viscosity Measurements in the Presence of Wall Slip in Capillary, Presence of Wall Slip in Capillary, Couette, And Parallel-Disk Geometries Summary- Measurements of viscosities for slurries, cements, gels, foams, and emulsions are often confounded by the presence of slip at solid boundaries. Slip arises from thin regions of low-viscosity fluid at the boundary that result in large velocity gradients near the solid surface. Unless the measurements are corrected for slip, the calculated viscosities will be smaller than the true fluid viscosities. We review available techniques for determining wall slip velocities and viscosities in standard geometries. The earlier techniques of Mooney for capillaries and Couette geometries are presented. In addition, new analyses are presented for Couette and parallel-disk geometries. The new Couette analysis requires only two measurements rather than the three required in Mooney's analysis. Examples showing the application of these techniques are given for the capillary, Couette, and parallel-plate geometries. Experimental techniques to eliminate wall slip by use of rough surfaces are described. Introduction In several applications in the oil and gas industries, complex fluids are used that may exhibit slip at solid boundaries. These include fracturing fluid gels, cements, concentrated emulsions, and clay suspensions. Slip confounds rheological measurements of fluid viscosity and requires special techniques to separate the effect of slip from that of fluid flow. The traditional techniques of correcting for slip in capillary and Couette geometries were developed by Mooney in 1931, but the original paper is not easily accessible. We have recently developed two new techniques: a simplified Couette test and a new test that uses parallel disks with varying gap height. Our goal is to summarize existing techniques for wall-slip analyses and to make the results accessible to researchers in the petroleum industry. Derivations have been largely omitted because they can be found in the original references. in the next section, we present the available analyses in tabular form. Examples of capillary, Couette, and parallel-disk experiments are presented to show how the analyses are applied. Finally, some suggestions for experimental techniques to eliminate slip are presented. Viscosity Measurements In the Presence of Slip For gels, cements, dispersions, and emulsions, "wall slip" is not a true slipping at the boundary, but rather is an apparent slip caused by a region of higher velocity gradient adjacent to the wall. With concentrated suspensions, for example, the presence of the wall reduces the local concentration of suspended particles. When the material is sheared, large velocity gradients are produced in this low-viscosity layer, resulting in apparent slip. In the following analyses, we assume that this wall layer thickness is very small compared with the viscometer dimensions. We can then treat wall slip as a discontinuity in velocity (i.e., actual slip), where the slip velocity is defined as the difference between the velocity of the wall and that of the fluid at the wall. We also assume that once steady state is achieved, the slip velocity is a function of stress only. Often the best way to test for slip is to make measurements with two capillary diameters or two gap sizes in the case of a Couette or parallel-plate geometry. If the calculated viscosities and shear rates superimpose, then slip is not indicated. If they do not superimpose, the slip is occurring and it must be calculated and subtracted from the data to calculate actual viscosities. If slip is not subtracted, the resultant apparent viscosities will be lower than the actual fluid viscosity. Table I shows the equations for capillary, Couette, and parallel-disk measurements, and Figs. 1 through 3 show the three geometries. The figures show the velocity fields that occur in the presence of slip. The use of these equations to calculate slip velocities and viscosities is demonstrated in the following examples for capillary Couette, and parallel-disk geometries. Example: Capillary Method. To illustrate Mooney's capillary method, we will use data on a polyacrylamide solution measured carefully by Cohen and Metzner, In this method, data on flow rate vs- pressure drop are required from at least two capillaries of different diameters. Cohen and Metzner used several capillaries for more accurate results. Their data are reproduced in Fig. 4, where the measured pressure drops have been converted to stress at the wall, oR, through oR =pR/2L. For each wall stress, the value of q(CR)/7rR2 is plotted vs. the radius R as shown in Fig. 5. This gives a straight line for each wail stress, and the (normalized) flow caused by fluid deformation alone, q, is obtained from the slope If only two capillary sizes were used, qn would be calculated as Values of qn are then plotted as a function of wall stress on a log-log scale (Fig. 6), and the fluid shear rates at the wall are calculated: The corresponding viscosities are obtained from and are shown in Fig. 7. Finally, the slip velocity, v, is calculated by plotting the values q(oR)/ R3 vs. 1/R for each wall stress as shown in Fig. 8. SPERE p. 735