Figure 6-14. Dynamic filtration from emulsion mud. {From Ferguson and Klotz.z« Copyright 1954 by SPE-AIME.)

Figure 6-16. Dynamic filtration from lime-starch mud. (From Ferguson and Klotz.24 Copyright 1954 by SPE-AIME.)

Vertical Mud Velocity, fps

Figure 6-17. Dependence of equilibrium dynamic filtration rate on mud flow velocity at 75° F. (From Ferguson and Kioto.™ Copyright 1954 by SPE-AIME.)

Vertical Mud Velocity, fps

Figure 6-17. Dependence of equilibrium dynamic filtration rate on mud flow velocity at 75° F. (From Ferguson and Kioto.™ Copyright 1954 by SPE-AIME.)

experiments the pipe was centered). Annular conditions simulated 6Va" pipe in a 8V2" hole.

In contrast to the above two findings, Peden et al21a 24a observed that dynamic filtration rates decreased with increase in annular velocity when circulating a KC1 polymer mud in a model wellbore. They suggest that the reason was that high annular velocities tended to erode the coarser particles and increase the deposition of the polymer chains, thus decreasing the permeability of the filter cake. It should be noted that flow was turbulent at their highest annular velocity, and that the shear rates at the two lower velocities were much higher than the shear rates normally prevailing at the wall of a wellbore.

Other findings by Vaussard et al24b were:

1. The dynamic rate was reduced by a period of static filtration, but increased if the annular flow rate was increased—markedly so at the onset of turbulence, which occurred at about 1,800 1/min (see Figure 6-17b).

2. Invert emulsion mud cakes were easily erodable, resulting in higher dynamic rates than would have been expected from their API filter losses. Spurt losses were high when the solids content was low.

3. The dynamic rates were independent of rock properties, except for coarse sintered media.

Filtration in the Borehole

The Filtration Cycle in a Drilling Well

In a drilling well, filtration takes place under dynamic conditions while the mud is circulating, and under static conditions when circulation is stopped to make a connection, change bits, etc. A static cake is thus laid down on top of a dynamic one, so the filtration rate decreases and the filter cake thickness increases, as shown between T3 and T4 in Figure 6-12. The amount of filtrate invading the formation under this condition can be calculated approximately from Equation 6-6 by assuming that the dynamic cake was laid down under static conditions, and by obtaining the values of £?„ and i corresponding to the dynamic cake thickness from static test data. Such calculations show that the amount of filtrate invading the formation under static conditions is

rium value. Thus the thickness of the cake increases every dynamic-staiic cycle, but the amount of increase is small.

The growth of the filter cake is limited by mechanical wear when the drill pipe is rotating, and by abrasion when pulling or running pipe, but these effects cannot be quantified.

Filtration Beneath the Bit

Very little filter cake forms on the bottom of the hole because the action of the mud jets is highly erosive, and because every time a bit tooth strikes, a fresh surface of rock is exposed. At one time it was thought that major filtrate invasion took place beneath the bit, but several investigations17 • -4 •2 5•2have shown that beneath the bit, filtration is severely restricted by an internal mud cake that forms in the pores of the rock just ahead of the bit. Indeed, even if the drilling fluid is water, filtration is restricted (although to a lesser degree) as drilled solids plug the pores.17 In their tests in the model well, Ferguson and Klotz24 measured liquid losses through the movements around the bottom of the hole corresponding to filtrate invasion of from 0.04 to 0.64 well radii, as compared to a potential invasion of from 0.3 to 14.3 well radii if no plugging had occurred.

Ferguson and Klotz24 also estimated the amount of filtrate invasion that would take place during the various stages of drilling and completing a hypothetical well, assuming a sand at 7,000 feet and a total depth of 7,500 feet. The results (see Table 6- 5) showed that some 95% of the invasion would take place under dynamic conditions while drilling, and only 6% under static conditions while tripping and completing.

Havenaar27 derived the following equation for filtration through the bottom of the hole while drilling:

where Q is the filtration rate in cm3/sec. n the number of cones on a bit rotating at m times per second, and C is determined from Equation 6- 7, using data from the API filtration test. Table 6-6 compares fiiltration rates calculated by this equation with the experimental data of Ferguson and Klotz. The poor correlation obtained with oil-base mud is probably because cakes of oil-base muds are easily eroded, and Equation 6-15 neglects erosion by the mud jets.

Hassen27a has developed a set of equations describing the various stages of filtration downhole. The parameters for these equations may be determined from dynamic tests in the laboratory. The equations can then be used to calculate downhole filtration rates under the relevant conditions. The method is particu

larly useful for determining the depth of penetration of a water base mud filtrate into a particular formation. Data obtained by this method were in good agreement with data derived from electric logs.

As might be expected from the discussion on Figure 6-17, the filtration rate beneath the bit bears no relation to the API filter loss. This lack of correlation was clearly shown by Horner et al,25 who measured dynamic filtration rates during microbit drilling tests under conditions where nearly all the filtrate came from beneath the bit (see Figure 6 -19). Their results also showed that

Table 6-5 Drilling Schedule and Filtrate Invasion*


Time (hours)

Filtrate volume (ml/in2)

Invasion radius


Invaded zone thickness (inches)

Drill through zone at

5 fph

Drill below zone at 5 fph

Round trip to replace bit

Drill below zone at 5 fph

Pull pipe, log well, run pipe

Condition hole to run casing:

Circulate drilling mud

Pull drill pipe Run casing Cement casing, end of mud filtration

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