## 9 2 92 92 92

5-5% bentonite 1% Na tannate 104 5-5% monionic Na montmorillonite 99-7

Time in Minutes

Figure 5-15. Relation between gel strength and time for Californian bentonites. (From Garrison.â„˘ Copyright 1939 by SPE-AIME.)

it appears, therefore, that there is a need for a method of predicting .long-term gel strengths, so that circulation breakdown pressures can be estimated more accurately.

### Pseudoplastic Fluids

Pseudoplastic fluids have no yield point; their consistency curves pass through the origin. The curves are nonlinear, but approach linearit) at high shear rates. Thus, if stress readings taken at high shear rates are extrapolated back to the axis, there appears to be a yield point similar to that of a Bingham plastic: hence the name pseudoplastic. (See Figure 5-19.)

Suspensions of long-chain polymers are typical pseudoplastics. At rest, the chains are randomly entangled, but they do not set up a structure because t he electrostatic forces are predominately repulsive. When the fluid is in motion, the chains tend to align themselves parallel to the direction of flow; this tendency increases with increase in shear rate, so that the effective viscosity decreases.

The consistency curve of the pseudoplastic flow model is described by an empirical equation, known as the power law~ viz:

K is the viscosity at a shear rate of 1 sec "1, and logically should be expressed in dyne/cm/sec, but in the oil industry it is expressed in lb/100 ft2, n is the flow behavior index, and indicates the degree of shear thinningâ€”the less the value of n, the greater the shear thinning characteristic.

Actually, the power law describes three flow models, depending on the value of n:

1. Pseudoplastic, n< 1, the effective viscosity decreases with shear rate.

2. Newtonian, n = 1, the viscosity does not change with shear rate.

3. Dilatant, n > 1, the effective viscosity increases with shear rate.

Since Equation 5 31 may be written

(Text continued on page 213, )

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