Interpolating or Extrapolating Drilling Fluid Viscosities to Reference Temperatures
Authors: Stiff Henry A. 
Published: December 2007

Currently, Farm viscosity measurements are made on drilling fluid at a convenient temperature. Since it is frequently useful to compare viscosity determinations or to estimate viscosities at the temperature in the hole, a method is desirable for interpolating or extrapolating Farm readings from measured temperatures to reference temperatures. The method presented is simple, involves a minimum of calculation presented is simple, involves a minimum of calculation and is believed to be accurate enough for most practical purposes. practical purposes. Effective viscosity, mu, can be defined as the ratio between tau (stress) and gamma (shear rate).
(1)
If the relationship is linear or the shear rate is constant, the effect of temperature T can frequently be expressed by an empirical equation such as
(2)
where a and b are constants. Combining Eqs. 1 and 2 gives(3)
Reducing to logarithmic form results in
(4)
Since the Fann readings R and R represent values of r at constant values of gamma, linear equations can be written for each of these terms expressing the effect of temperature as(5)
(6)
where A is a constant [A = (a + log gamma )] denoting the intercept and b is a constant representing the slope. Thus, a plot of Fann readings at several temperatures should make it possible to obtain these values at other temperatures. By this method the apparent viscosity (U), plastic viscosity (P) and yield (Y) of a mud can be interpolated or extrapolated to any desired temperature.
Fig. 1 presents a plot of the log of the Farm readings at 600 and 300 at various temperatures for a typical water-base mud. Also shown are similar data for a typical oil-base mud. It can be seen that the data plot in accordance with theory at temperatures from plot in accordance with theory at temperatures from 70 deg. to 170 deg. F. To date, a number of both water-and-oil-base muds have been tested in the laboratory and in the field. With few exceptions they behaved in this manner within this temperature range, Thus, any temperature from 70 deg. to 170 deg. F may be used as a reference. A few experiments at higher temperatures indicate that, at least in some cases, reference temperatures considerably above 170 deg. F can be used without significant error.
Procedure Procedure
Obtain about 1,500 cc of mud from the flow line. Screen into an enameled beaker or similar container. Fill the Fann viscometer cup and begin cooling the remaining mud by partially submerging the beaker in cold water. Run the viscometer for 15 seconds at 600 rpm, then take readings at R and R. Read the mud temperature in the viscometer immediately and discard the contents of the cup. In cold weather the cup should be insulated by wrapping with paper or cloth. When the mud in the beaker has cooled 100 to 15 deg. below the temperature of the first reading, stir with a stirring rod and repeat Steps 2 and 3. Again, stir and repeat Steps 2 and 3 when the temperature of the mud in the beaker has cooled 20 deg. to 300 below the temperature at which the initial read. ing was made. On semi-log paper plot R and R against temperature. If a straight line can be drawn through the R points and another through the R points, the data can be interpolated or extrapolated to other temperatures.
P. 1248