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be made to remove the undesirable low-
gravity solids by screening before their particle size is 
reduced within the size range of the API barite 
particles. Hydrocyclones cannot be used alone on 
weighted systems because their cut point falls in the 
particle-size range of the API barite as shown in Fig. 
2.26. However, they sometimes are used in con-
junction with a shaker screen to increase the flow rate 
capacity of the solids removal equipment. A series 
arrangement of a hydrocyclone and a shaker screen is 
called a mud cleaner. It is suited best for muds of 
moderate density (below 15 Ibm/gal). The fine solids 
that pass through the screen can be handled by 
dilution and deflocculation. 
At higher densities, the mud cleaners are much less 
efficient. Much of the coarse solids in the mud 
remain in the liquid stream exiting the top of the unit 
and, thus, bypass the screen. Also, dilution requires 
• 
68 
~ 
~ 
z 
"' u a: 
"' Q. 
(f) 
0 
::; 
0 
(f) 
I MICRON lmm I em 
01 0.1 10 100 1000 •10,000 
2 4 68 2 4 68 2 4 68 2 4 68 2 4 68 2 4 68 
~ r--~ p'-'if-> r 1'-'-~Q Ql< y ) 
----
SILT FINE , COURSE GRAVEL 
SAND SAND ~~~~~ER 200 
DISCARD 
100 MESH 
60 MESH 
20 MESH 
f;ENTRIFUGE DESI TER UNDER fLOW 
OVERFLOW DESANDER UIURFLOW 
TOBACCO SMOKE MILLED FLOUR BEACH 
SAND 
SETTLING RATE OF DRILLED SOLIDS IN 
68°F WATER, FEET PER MINUTE 
.01 0.1 I 10 30 5090 
Fig. 2.26-Particle size range for common solids found in 
weighted water-base muds. 
discarding a large volume of API barite with a 
portion of the old mud and the cost of dilution can 
become quite high. In this situation, centrifuges 
often are employed to separate the particles having 
sizes that fall in the API barite range from the liquid 
and extremely fine solids. In this manner the mud 
stream is divided into (1) a low-density overflow 
slurry (approximately 9.5 Ibm/gal) and (2) a high-
density slurry (approximately 23.0 Ibm/gal). The 
high-density slurry is returned to the active mud 
system, and the low-density slurry usually is 
discarded. An example solids removal system for 
weighted clay /water muds is shown in Fig. 2.27. 
About three-fourths of the bentonite and chemical 
content of the mud is discarded with the fine solids 
when the centrifuge is used. New bentonite and 
chemicals must be added to prevent depleting the 
mud. Also, since some of the API barite and drilled 
solids are discarded in the overflow, the volume of 
mud reclaimed from the underflow will be less than 
the volume of mud processed. A small additional 
volume of new mud must be built in order to 
maintain the total mud volume constant. A material 
balance calculation can be made to determine the 
proper amounts of API barite, clay, chemicals, and 
water required to reconstruct a barrel of mud that 
has been processed with a centrifuge. 
2.3.13.1 Centrifuge Analysis. Consider the flow 
diagram for a centrifuge shown in Fig. 2.28. Dilution 
water and mud enter the centrifuge and a high-
density slurry (pu) containing the API barite exits the 
underflow while a low-density slurry (p0 ) containing 
the low-specific-gravity solids and most of the water 
APPLIED DRILLING ENGINEERING 
Shaker 
OIS<:Ord 
Fig. 2.27-Schematic arrangement of solids-control equip-
ment for weighted mud systems (after Ref. 5). 
Po 
qm qo 
MUD IN 
Pm 
BARITE 
WATER IN 
q., P., qu fa 
WATER q •2 
API BARITE w8 Pm MUD 
CLAY we qm OUT 
ADDITIVE WI 
Fig. 2.28-Fiow diagram of a centrifuge. 
and chemicals exits the overflow. 
Thus, the flow rate of the overflow is the sum of 
the mud flow rate and water flow rate into the 
centrifuge less the underflow rate: 
qo =qm +qwl -qu. · · · · · · · · ·- · · · · · · · · (2.24) 
The total mass rate into the centrifuge is given by 
mass rate in= qwl Pw +QmPm · 
Similarly, the total mass rate out of the centrifuge is 
given by 
mass rate out= q uPu + Q 0 P0 • 
For continuous operation, the mass rate into the 
centrifuge must equal the mass rate out of the 
centrifuge. Equating the expressions for mass rate in 
and mass rate out gives 
QwJPw +QmPm =QuPu +QoPo· · · · · · · · · · (2.25) 
Substitution of Eq. 2.24 for the overflow rate in 
Eq. 2.25 and solving for the underflow rate, qu, gives 
the following equation. 
qm (Pm -po) -qwl (Po -pw) Qu = ..... (2.26) 
<Pu- Po) 
This equation allows the calculation of the underflow 
rate from a knowledge of ( 1) water flow rate and 
mud flow rate into the centrifuge, (2) the densities of 
the water and mud entering the centrifuge and (3) the 
densities of the underflow and overflow slurries 
exiting the centrifuge. 
The reconstruction of the mud from the centrifuge 
underflow occurs in a pit downstream of the cen-
I 
DRILLING FLUIDS 
trifuge. It is desired to obtain a final mud flow rate 
from the mixing pit equal to the mud feed rate into 
the centrifuge. In addition, the final mud density 
should be equal to the density of the feed mud. A 
knowledge of volume fraction of feed mud, dilution 
water, and API barite in the underflow stream simplifies 
the calculations required for reconstruction of a mud 
with the desired properties. 
Consider the underflow stream to be composed of 
(1) old mud, (2) dilution water, and (3) additional 
barite stripped from the discarded mud. The density 
of the underflow can be expressed by 
Pu =pmfum +Pwfuw +PBfuB• · · · · · · · · · · (2.27) 
wherefum•fuw• andfuB are the volume fraction of 
mud, dilution water, and API barite in the underflow 
stream. Furthermore, if we assume perfect mixing of 
the feed mud and dilution water in the centrifuge, 
then the diluted feed mud in the underflow should 
consist of feed mud and dilution water in the same 
ratio as they existed going into the centrifuge. From 
this assumption we obtain 
qwl 
fuw =fum-· · · · · · · · · · · · · · · · · · · · .. (2.28) 
qm 
Also, since all the volume fractions must sum to one, 
thenfuB can be expressed by 
fuB = 1-fum- fuw = 1- fum- fum qwl · .. (2.29) 
qm 
Substituting these expressions for fuw and fuB into Eq. 
2.27 and solving for fum gives 
(pB-Pu) fum=--------------------
qwl 
PB-Pm+- (pB-Pw) 
qm 
...... (2.30) 
The flow rate of old mud, dilution water, and API 
barite to the pit from the centrifuge underflow are 
given by qufm, qufw, and quf8 , respectively. 
The fraction of the underflow stream composed of 
old mud already has Wyoming bentonite, defloc-
culants, filtration control additives, etc., at the 
desired concentration. Thus, only sufficient additives 
to treat the remaining portion of the mud stream 
from the mixing pit are required. The fraction of the 
mud stream from the mixing pit composed of old 
mud is given by 
fm = qufum . 
qm 
If ci is the desired concentration in pounds per barrel 
of a given additive in the mud stream, then this 
additive must be added to the mixing pit at the 
following mass rate. 
Wi =ciqm ( 1- fm) =ci (qm -qufum) • · · · · (2.31) 
where q m and q u are expressed in barrels per unit 
time. This expression also can be used to obtain the 
mass rate at which commercial clay should be added. 
The volume of water and API barite needed to main-
tain the density of the mud leaving the mixing pit at 
the same density as the mud entering the centrifuge can 
be determined through a balance of the material entering 
69 
and exiting the mixing pit. The total flow rate exiting 
the mixing pit can be expressed by 
WB We n Wi 
q m = q u + q w2 + -- + -- + .E 
PB Pe i=l Pi 
Similarly, the mass rate of material exiting the mixing 
pit is given by 
n 
QmPm =QuPu +qw2Pw + WB +We+ E wi. 
i=l 
Solving these simultaneous equations for unknowns 
q w2 and w 8 yields 
+(pB-Pw), .................. (2.32) 
and 
n WB=(qm-qu-qw2-~- .E ~ )PB· 
Pe i=l Pi 
............................