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```balance. 2
remain static for 10 minutes, the maximum dial
deflection is reported as the 10-min gel. These as well
as other non-Newtonian parameters are discussed in
detail in Chapter 4. However, it is sufficient that the
beginning student view these parameters as
diagnostic indicators that must be kept within certain
ranges.
Example 2.1. A mud sample in a rotational
viscometer equipped with a standard torsion spring
gives a dial reading of 46 when operated at 600 rpm
and a dial reading of 28 when operated at 300 rpm.
Compute the apparent viscosity of the mud at each
rotor speed. Also compute the plastic viscosity and
yield point.
Solution. Use of Eq. 2.1 for the 300-rpm dial reading
gives
Fig. 2.6-Marsh funnel.
11-a =
300 () N
N
APPLIED DRILLING ENGINEERING
300 (28)
300
= 28 cp .
Similarly, use of Eq. 2.1 for the 600-rpm dial reading
gives
11-a =
300 (46)
= 23 cp.
600
Note that the apparent viscosity does not remain
constant but decreases as the rotor speed is increased.
This type of non-Newtonian behavior is shown by
essentially all drilling muds.
The plastic viscosity of the mud can be computed
using Eq. 2.2:
11-p = 8600-()300 = 46-28 = 18cp.
The yield point can be computed using Eq. 2.3:
Ty = 8300 - 11-p = 28-18 = 10 lbf/100 sq ft .
2.1.4 pH Determination. The term pH is used to
express the concentration of hydrogen ions in an
aqueous solution. pH is defined by
pH = log[H + ] , ..................... (2.4)
where [ H + ] is the hydrogen ion concentration in
moles per liter. At room temperature, the ion
product constant of water, K w, has a value of 1.0 x
10- 14 mol/L. Thus, for water
Fig. 2.7-Rotational viscometer.
I
DRILLING FLUIDS
TABLE 2.1-RELATIONS BETWEEN pH, (H+] AND [OH-]
IN WATER SOLUTIONS
[H +I pH [OH] pOH Reaction
1.0x 10° 0.00 1.0x10- 14 14.00 ..
1.0x1o- 1 1.00 1.0x1o- 13 13.00
1.0x 10- 2 2.00 1.0 X 10- 12 12.00
1.0x1o- 3 3.00 1.0x 10- 11 11.00 Acidic
1.0 X 10- 4 4.00 1.0 X 10- 10 10.00
1.0x1o-s 5.00 1.0x 10- 9 9.00
1.0x 10- 6 6.00 1.0x1o- 8 8.00
1.0x1o- 7 7.00 1.0 X 10- 7 7.00 Neutral
1.0x1o- 8 8.00 1.0x 10- 6 6.00
1.0x 10- 9 9.00 1.0x1o-s 5.00
1.0x10- 10 10.00 1.0x1o- 4 4.00
1.0x10- 11 11.00 1.0x 10- 3 3.00 Alkaline
1.0x 10- 12 12.00 1.0 X 10- 2 2.00
1.0x1o- 13 13.00 1.0x1o- 1 1.00
1.0x1o- 14 14.00 1.0x10° 0.00
HzO""H+ +OH-
Kw= [H+] [OH-] =LOx w- 14 .
For pure water, [H+] = [OH-] = 1.0 x w- 7 ,
and the pH is equal to 7. Since in any aqueous
solution the product [H + ] [OH- ] must r~main
constant, an increase in [ H + ] requires a
corresponding decrease in [OH- ]. A solution in
which [H + ] > [OH- ] is said to be acidic, and a
solution in which [ OH - ] > [ H + ] is said to be
alkaline. The relation between pH, [H + ], and
[OH- ] is summarized in Table 2.1.
The pH of a fluid can be determined using either a
special pH paper or a pH meter (Fig. 2.8). The pH
paper is impregnated with dyes that exhibit different
colors when exposed to solutions of varying pH. The
pH is determined by placing a short strip of the paper
on the surface of the sample. After the color of the
test paper stabilizes, the color of the upper side of the
paper, which has not contacted the mud, is compared
with a standard color chart provided with the test
paper. When saltwater muds are used, caution
should be exercised when using pH paper. The
solutions present may cause the paper to produce
erroneous values.
The pH meter is an instrument that determines the
pH of an aqueous solution by measuring the elec-
tropotential generated between a special glass
electrode and a reference electrode. The elec-
tromotive force (EMF) generated across the specially
formulated glass membrane has been found em-
pirically to be almost linear with the pH of the
solution. The pH meter must be calibrated using
buffered solutions of known pH.
Example 2.2. Compute the amount of caustic
required to raise the pH of water from 7 to 10.5. The
molecular weight of caustic is 40.
45
c#~'f'
•• -~ ...... ~·. ·' :aw
Fig. 2.8-Two methods for measuring pH: pH paper (left) and
pH meter (right).
Solution. The concentration of OH- in solution at a
given pH is given by
= lO(pH- 14).
The change in OH- concentration required to increase
the pH from 7 to 10.5 is given by: .l[OH- ]=[OH -h
-[oH-11-
.:l [OH- ] = 10(10.5- 14) _ 10o -14)
= 3.161 X 10- 4 mol/L.
Since caustic has a molecular weight of 40, the weight
of caustic required per liter of solution is given by
40(3.161 X 10- 4 ) = 0.0126 g/L.
2.1.5 The API Filter Press - Static Filtration. The
filter press (Fig. 2.9) is used to determine (1) the
filtration rate through a standard filter paper and (2)
the rate at which the mudcake thickness increases on
the standard filter paper under standard test con-
ditions. This test is indicative of the rate at which
permeable formations are sealed by the deposition of
a mudcake after being penetrated by the bit.
The flow of mud filtrate through a mudcake is
described by Darcy's law. Thus, the rate of filtration
is given by
r!!J. = k A t:..p
-- , .................... (2.5)
dt 11- hmc
where
•
46
MUD SAMPLE
Fig. 2.9-Schematic of API filter press.
dVJ!dt = the filtration rate, cm 3 Is,
k = the permeability of the mudcake, darcies,
A = the area of the filter paper, cm2 ,
Ap = the pressure drop across the
mudcake, atm,
1-' = the viscosity of the mud filtrate, cp, and
h me = the thickness of the filter (mud) cake, em.
At any time, t, during the filtration process, the
volume of solids in the mud that has been filtered is
equal to the volume of solids deposited in the filter
cake:
fsm V m = fsehmeA •
where fsm is the volume fraction of solids in the mud
andfse is the volume fraction of solids in the cake, or
fsm (hmeA + Vf) = fsehmeA ·
Therefore,
h = fsm Vr
me A (fse - fsm ) .... (2.6)
Inserting this expression for hme into Eq. 2.5 and
integrating,
v2 k J
:J_ = - A 2 ( ~ - I) t:.p t ,
2 1-' fsm
or
Yt
A Y,J. . . ..... (2. 7)
APPLIED DRILLING ENGINEERING
SPURT LOSS
v
Fig. 2.1 0-Example filter press data.
The standard API filter press has an area of 45 cm2
and is operated at a pressure of 6.8 atm (100 psig).
The filtrate volume collected in a 30-min time period
is reported as the standard water loss. Note that Eq.
2. 7 indicates that the filtrate volume is proportional
to the square root of the time period used. Thus, the
filtrate collected after 7.5 min should be about half
the filtrate collected after 30 min. It is common
practice to report twice the 7 .5-min filtrate volume as
the API water loss when the 30-min filtrate volume
exceeds the capacity of the filtrate receiver. However,
as shown in Fig. 2.10, a spurt loss volume of filtrate,
vsp, often is observed before the porosity and
permeability of the filter cake stabilizes and Eq. 2.7
becomes applicable. If a significant spurt loss is
observed, the following equation should be used to
extrapolate the 7 .5-min water loss to the standard
API water loss.
V3o =2(V7_5 - ~p) + Vsp· .............. (2.8)
The best method for determining spurt loss is to plot
Vvs. Yt and extrapolate to zero time as shown in Fig.
2.10.
In addition to the standard API filter press, a
smaller filter press capable of operating at elevated
temperature and pressure also is commonly used.
The filtration rate increases with temperature
because the viscosity of the filtrate is reduced.
Pressure usually has little effect on filtration rate
because the permeability of the mudcake tends to
decrease with pressure and the term .J kt:.p in Eq. 2. 7
remains essentially constant. However, an elevated
pressure is required to prevent```