Reservoir Engineering – Drilling – Equipment, Methods and Materials - A Correlation of the Electrical Properties of Drilling Fluids with Solids Content

The first paper in this series1 outlined practical methods for applying the theory of steady-state flow of an ideal Bingham plastic liquid through a circular pipe and axially through a stationary concentric annulus to the enginekring analysis of friction loss problems. In the present paper the properties of another useful rheological model, the pseudoplastic generalized Newtonian liquid, are considered. The terminology applied to the rheological models is derived from the following classification of rheological models. The term "generalized Newtonian" is a class designation applied to models which do not have yield points but which exhibit a dependence on shear rate. The term "pseudoplastic" applies to a sub-group of models within this class which exhibit a decrease in "viscosity" with increasing shear rate. The term "power model" refers to a mathematical model proposed for describing the behavior of the pseudoplastic liquid. This model is of interest since certain of the salt saturated, oil emulsion, and "low solids" drilling fluids, inverted emulsion- and oil-base drilling fluids, aqueous gels, gelled crudes and blocking agents employed in hydraulic fracturing operations are of this type. The present treatment considers the equations describing steady-state Poiseuille flow through a circular pipe and a stationary concentric annul us, and Couette flow between concentric rotating cylinders for a particular pseudoplastic model. As in the previous paper' it is demonstrated how these equations can be applied to engineering calculations of friction losses. Graphical procedures for recovering the various flow curves and cxample calculations are included. A method for simplifying turbulent-flow correlations is also proposed. PROPERTIES OF PSEUDOPLASTIC GENERALIZED NEWTONIAN LIQUID In contrast to the Bingham plastic the generalized Newtonian liquid is yield point-free. However, in the flow region the relation between stress and rate of shear is not linear as it is with ordinary Newtonian fluids. If the stress increases with shear rate at a less than linear rate the system is called pseudoplastic. While there is no yield point in this system, the Bingham advocates' coined the term pseudoplastic to distinguish this kind of behavior from Bingham plastic behavior. For the pseudoplastic a plot of flow rate vs friction loss or rpm vs torque, from pipe flow or rotational viscometer measurements, respectively, generally has three qualities: (1) it can be clearly extrapolated toward the origin; (2) there is very little slope at the origin. This accounts for the high apparent viscosities at low mixing and pumping rates; and (3) the flow curve possesses a continuous curvature which gradually diminishes as the shear increases. Rheological measurements on a pseudoplastic liquid can be easily misinterpreted as indicating Bingham plastic behavior. A typical case in point is illustrated in Fig. 1. These data were obtained from measurements on an oil-emulsion mud using a commercially available rotational-type viscometer (Model 35 Fann V-G meter). Applying the "two-point"* method3 gives a plastic viscosity of 17 cp and a yield point of 24 lb/100 ft2; at the same time weighting material settles very easily in this system. This illustrates that it is not possible to distinguish between the pseudoplastic and the Bingham plastic from only two data points. It is possible to determine qualitatively which model is more appropriate by a combination of dynamic and static measurements. Experience indicates that the simplest criterion for the Bingham plastic liquid is that the calculated dynamic yield point should be of the same magnitude as the measured gel strengths. For the oil-emulsion drilling fluid illustrated in Fig. 1, a value of 4 lb/100 ft2 was obtained for gel strengths measured