## The Filtration Properties Of Drilling Fluids

In order to prevent formation fluids from entering the borehole, the hydrostatic pressure of the mud column must be greater than the pressure of the fluids in the pores of the formation. Consequently, mud tends to invade the permeable formations. Massive loss of mud into the formation usually does not occur, because the mud solids are filtered out onto the walls of the hole, forming a cake of relatively low permeability, through which only filtrate can pass. Muds must be treated to keep cake permeability as low as possible in order to maintain a stable borehole and to minimize filtrate invasion of, and damage to, potentially productive horizons. Furthermore, high cake permeabilities result in thick filter cakes, which reduce the effective diameter of the hole and cause various problems, such as excessive torque when rotating the pipe, excessive drag when pulling it, and high swab and surge pressures. Thick cakes may cause the drill pipe to stick by a mechanism known as differential sticking, which may result in an expensive fishing job.

Two types of filtration are involved in drilling an oilwell: static filtration. which takes place when the mud is not being circulated, and the filter cake grows undisturbed, and dynamic filtration, when the mud is being circulated and the growth of the filter cake is limited by the erosive action of the mud stream. Dynamic filtration rates are much higher than static rates, and most of the filtrate invading subsurface formations does so under dynamic conditions. The filtration properties of drilling fluids are usually evaluated and controlled by the API filter loss test,2 which is a static test, and is therefore not a reliable guide to downhole filtration unless the differences between static and dynamic filtration are appreciated, and the test results interpreted accordingly.

* A glossary of notation used in this chapter will be found immediately following this chapter text.

In this chapter, we discuss the principles of static and dynamic filtration, and the best means of correlating between them. The effects of filtration properties on the various drilling and producing problems mentioned in the first paragraph are not discussed in this chapter because there are other factors involved: they will be described in the chapters dealing with the particular problems.

### The Theory of Static Filtration

If unit volume of a stable suspension of solids is filtered against a permeable substrate, and a: volumes of filtrate are expressed, then 1 —x volumes of cake (solids plus liquid) will be deposited on the substrate. Therefore, if Q( be the volume of the cake, and Qw the volume of filtrate:

and the cake thickness (h) per unit area of cake in unit time will be

Now, Darcy's law states

* ■ kP (6 2 dt ßh where k= permeability in darcies, P = differential pressure in atmospheres fi = viscosity of the filtrate in centripoises, h = thickness in centimeters q — volume of filtrate in cubic centimeters, and / = time in seconds. Therefore

Static Filtration

Integrating

From Equations 6/1 and 6/4

Larsen's experimental results showed that for a given pressure, Equation 6/6 may be written:

where qa is the zero error, and C is a constant given by

v Qc

Thus the filtration properties of diverse muds can be evaluated by measuring the filtrate volume accumulating in a standard time and under standard conditions. The conditions recommended by the API2 are:

Time: 30 minutes

Pressure: 100 psi (6.8 atmospheres, 7 kg/cm2) Area of cake: approximately 7 in.2 (45 cm2)

The filtrate volume that would accumulate in 30 minutes can be predicted from the volume, Qw observed at time from the equation:

For example, the 30 minute filtrate volume is sometimes predicted by measuring the filtrate volume at 7.5 minutes, and doubling the value obtained, since v 30/ ^ 73 — 2.

### Relationship Between Pressure and Filtrate Volume

According to Equation 6-6, Qw should be proportional toV/Vand a log-log plot of Qw versus P should yield a straight line with a slope of 0.5, assuming all factors remained constant. Actually, this condition is never met because mud filter cakes are to a greater or lesser extent compressible, so that the permeability is not constant, but decreases with increase in pressure.1'3 Thus:

Qw a Px where the exponent x varies from mud to mud, but is always less than 0.5, as shown in Figure 6-2.

The value of the exponent jc depends largely on the size and shape of the particles composing the cake. Bentonite cakes, for example, are so compressible that jc is zero, and Qw is constant with respect to P. The reason for this behavior is that bentonite is almost entirely composed of finely-divided platelets of montmorillonite, which tend to align more nearly

where yU, and are the viscosities at the filtration pressures in the tests for Q„-i and Qw2, respectively.

Relationship Between Temperature and Filtrate Volume

Increase in temperature may increase the filtrate volume in several ways. In the first place, it reduces the viscosity of the filtrate, and, therefore, the filtrate volume increases according to Equation 6-9. The viscosity of water and of 6% brine are shown over a range of temperatures in Table 6-1, and over an extended range, for water only, in Figure 6-3. It is evident that changes in temperature may have a substantial effect on filtrate volume because of changes in filtrate viscosity. For example, the filtrate volume at 212°F (tOO'C) would be about

1-1 = ! .88 times as large as the volume at 68°F (20°C). V 0.284 6

Changes in temperature may also afTfect filtrate volume through changes in the electrochemical equilibria which govern the degree of flocculation and aggregation, thus altering the permeability of the filter cake. As a result of such effects, filtrate volumes may be higher or lower than predicted from Equation 6-9, but usually they are higher.6 For instance, Byck7 found that, of the six muds he tested, three had 8% to 58% greater filter loss at 175°F (70°C) than had been predicted from the filter loss at 70°F (2rC) by substituting the changes in filtrate viscosity in Equation 6-9. The permeability of the cakes increased correspondingly, with the maximum change being from 2.2 to 4.5 x 10 ~3 md—an increase of over 100%. Filtration rates of the other three muds deviated from the predicted values by only ± 5%, and the permeabilities the cakes remained essentially constant. In more extensive tests, Shremp and Johnson8 showed that there is no way that filter losses at high

Table 6-1

The Viscosity of Water and 6% Sodium Chloride Brine at Various Temperatures

Temperature Temperature Viscosity water Viscosity brine

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