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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