Figure 5-8. Graphical interpretation of determination of flow parameters in a two speed direct indicating viscometer.

As we iaw in Chapter 4, the clay particles present in drilling fluids are highly anisodimensional, and can build a structure at very low solid concentrations beca use of interaction between attractive and repulsive surface forces. At low shear rates the behavior of the clay particles is still influenced by these force*, and. in consequence, the viscosity is relatively high but, as the shear rale increases, the particles gradually align themselves in the direction of flow. and the viscosity then becomes largely dependent on the concentration of all solids present ¡11 the mud.

Because of these phenomena, the degree of deviation from linearity in the consistency curves of drilling muds in the rotary viscometer differs from mud to mud, depending on the concentration, size, and shape of the particles. It is most marked with low-solid muds containing a high proportion of clay particles, or long-chain polymers, and least with high-solid muds containing silt and barite. It is also influenced by the electrochemical environment, which, as discussed in Chapter 4, determines the interparticle forces. Note, for example, in 1 igure 5 9 that the curve for the bentonite flocculated by sodium chloride showed much the greatest deviation from linearity.

Unfortunately, there is no way of determining the linearity of the consistency curves, other than by measurement in a multispeed rotary viscometer. Therefore, the usefulness of the rheological parameters PI7 and YP is limited. In practice, the most common use of these quantities is for the wellsite evaluation of drilling mud performance, particularly as a guide to maintenance treatments. Thus the PV is sensitive to the concentration ol solids, and therefore indicates dilution requirements; the YP is sensitive 10 the electrochemical environment, and hence indicates the need for chemical treatment. The use of P V and YP for these purposes is justified, since in this case the shape of the consistency curve is of no consequence.

P i and YP may also be substituted for \ip and t0, respectively, in Equation 5 12 for predicting laminar flow behavior in pipes, but only for flow at high shear ra tes. When predicting flow behavior at low rates of shear, it is better to calculate the effective viscosity at the rate of shear pievailing in the pipe, which may then be substituted in Poiseulle's equation (5 5). The required value of effective viscosity is best determined from the power law, which is discussed later in this chapter.

As already mentioned, YP does not represent the real yield point. Actually, because of slippage, the consistency curve approaches the stress axis asymptotically, so that the real yield point as defined by Green2 (i.e. the stress required to initiate laminar flow) is indeterminable. For practical purposes the initial gel strength, i.e., the maximum dial deflection observed when the cup is rotated by hand immediately after flow has ceased, is probably the best measure of the real yield point.

Because centrifugal effects become significant at high rotor speeds, rotary viscometers cannot be used to determine rheological properties at very high

Figure 5-9. Behavior of bentonite suspensions in multispeed direct indicating viscometer. u>L marks the rpm above which the curves of a Bingham plastic should be linear. (Data courtesy of Brinadd Company.)

rates of shear. For this purpose a pressurized capillary viscometer, which permits viscosity to be determined over a wide range of shear rates, must be used. This instrument is particularly useful for determining power law parameters, as will be discussed later in this chapter.

The Effect of Thixotropy on Drilling Muds

If the gel strength of a mud is measured immediately after being sheared, and repeatedly after increasingly longer periods of rest, the values obtained will be generally found to increase at a decreasing rate until a maximum value is reached. This behavior is a manifestation of the phenomenon o {thixotropy, originally defined by Freundlich9 as a reversible isothermal transformation of a colloidal sol to a gel. In the case of drilling muds, the phenomenon is caused by the clay platelets slowly arranging themselves in positions of minimum free energy (see Chapter 4) in order to satisfy electrostatic surface charges. After a period of rest, a thixotropic mud will not flow unless the applied stress is greater than the strength of the gel structure. In other words, the gel strength becomes the yield point, t0. If subjected to a constant rate of shear, the clay platelet associations gradually adjust to the prevailing shear conditions, and the effective viscosity decreases with time until a constant value is reached, at which point the structure-building and structure-disrupting forces are in equilibrium. If the rate of shear is increased, there is a further decrease in viscosity with time until an equilibrium value typical of that rate of shear is reached. If the rate of shear is then decreased to the first rate, the viscosity slowly builds up until the equilibrium value for that rate of shear is again reached. Because of these phenomena, Freundlich's original definition of thixotropy has been extended to cover a reversible isothermal change in viscosity with time at constant rate of shear.10

Thixotropy must not be confused with plasticity. As we have already seen, the effective viscosity of a Bingham plastic depends on the rate of shear because ils structural component forms a decreasing proportion of the total resistance to shear as the shear rate increases. The viscosity of a thixotropic fluid depends on time of shearing, as well as rate of shear, because the structural component changes with time according to the past shear history of the fluid. For this reason, thixotropic fluids are said to be "fluids with a memory." Bingham plastics may or may not be thixotropic, depending on composition and electrochemical conditions. A quick test for thixotropy may be made in a viscometer fitted with an x-y recorder, by increasing and then decreasing the rotor speed. If a hysteresis loop is obtained on the recorder, the fluid is thixotropic.

The opposite of thixotropy is rheopexy. The viscosity of a rheopectic fluid increases with time at constant shear rate. Rheopexy in drilling fluids has not been reported

The effect of thixotropy on the evaluation of the rheological parameters of drilling muds was first investigated by Jones and Babson.11 They observed the change in torque with the passage of time, when thixotropic muds were sheared at constant rate in a MacMichael viscometer. Curve 1 in Figure 5 in shows the result when a gelled mud was sheared at a constant rate of I Kc> rpm The torque decreased sharply during the first 15 minutes; then decreased gradually until equilibrium was reached after about one hour. Curve 2 shows the behavior of the mud after the shear rate was increased to 279 rprn. maintained there till equilibrium was reached, and then brought back to rpm. Note that the torque gradually built back to the equilibrium value of Curve 1. Curves 4 and 5 show that approximately the same equilibrium value was obtained at 81 rpm, regardless of whether the mud was pre-sheared at I 19 or 279 rpm. These results confirm that thixotropic muds have an equilibrium value which is typical of the shear rate at which it is measured, and u Inch is independent of shear history.

The equilibrium viscosities of the mud at rates ranging from 189 rpm to 21 rpm are shown by Curve 1 in Figure 5 11. Jones and Babson emphasized that the concepts of plastic viscosity and yield point cannot be applied to this curve because each point represents a different degree of structural breakdown. In other words, the equilibrium curve relates stress to both rate of shear and to the effect of time, whereas flow equations relate stress only to rate of shear. Meaningful values of plastic viscosity and yield poi nt can only be obtained h\ shearing to equilibrium at a specified speed, and then making torque readings as quickly as possible at lower rpm before any thixotropic change takes place. Curves 2 and 3 in Figure 5-11 show these instantaneous values after pre-shearing at 189 and 279 rpm, respectively. For each pre-shear rate, the area between the equilibrium and instantaneous curves defines the flow conditions at any lower shear rate at any point in time.

The effect of shear history on viscosity was also shown by Cheng et a I ■ They pre-sheared bentonite suspensions to equilibrium at rales varying from 700 to 20 reciprocal seconds. In each case the instantaneous curves were obtained at shear rates ranging downward from 700 reciprocal seconds. The results for a 4.8",, bentonite suspension, shown in Figure 5 12, indicate thai the instantaneous effective viscosity at 700 rprn varied from II iu 63 ccntipoises depending on the rate of pre-shearing.

The principles and experimental results discussed above show that the effect of shear history must be taken into account when determining the How parameters of thixotropic muds. For example, muds must be pre-sheared to equilibrium at a standard rate when comparing the flow properties of different muds When the flow parameters arc to be used for the purpose of calculating pressure drops in a well, the mud must be pre-sheared to a condition corresponding to that prevailing at the point of interest in the well

Figure 5-10. Flow behavior of a clay mud in a MacMichael viscometer. {From Jones and Babson.")

Note that the time required for pre-shearing to equilibrium may be longer or shorter than the one hour reported by Jones and Babson. Figure 5 13 shows an extreme case where a very long time was required to pre-shear a flocculated monoionic montmorillonite suspension. Muds brought into the laboratory from a well may also require long pre-shearing times to reduce them to a state of shear similar to that in the well.

Slibar and Paslay13 developed a set of constitutive equations containing five physical parameters which can be used to predict the effect of shear history oil the flow of thixotropic materials. They obtained good correlation between their predictions and the experimental results of Jones and Babson.

The high gel strengths developed by thixotropic muds after prolonged periods of rest create another problem for the drilling engineer. The long-term

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