Design of a High-Rate, High-Volume
Oil/Water Separator
Joe Stires, * SPE,
Conoco Inc.
Summary
Discussion
At ultra-high water cuts (95% or more), the most difficult production problem may not be getting the oil out
of the ground, but getting oil out of the water. While it is
not uncommon to use large wash tanks to separate the oil
from this type of flowstream, few designs can be tailored
to a specific application. This paper presents one such
design, including the equations used to analyze its performance. This type of analysis can be applied to any
separator to predict what its performance should be.
To take advantage of rising oil prices, many oil companies have increased production from older leases over
the past several years. In 1975, Continental Oil Co.
(now Conoco Inc.) began a program to maximize production from the Big Lake field, Reagan County, TX.
The field was the discovery field of the Permian Basin
region and has been on production since 1923. Production has been primarily from the Grayburg limestone, at
3,000 ft (914 m). This reservoir has a strong water drive,
and water cuts currently average 90% or more. Liquid
productivities are usually more than 3000 BID (477
m 3 I d) per well.
Most wells on our lease in this field were equipped
with high-volume artificial lift in 1975-76 to take advantage of the high productivities of these wells. The leasewide oil production increase from 290 to 525 BID (46 to
83 m 3 I d) was accompanied by an 18,000- BID
(2862-m 3 Id) increase in water. Total water production,
40,000 BID (6359 m 3 /d), exceeded the capacity of the
treating facilities on this lease. As a result, oil carryover
into the produced-water disposal srstem increased, going as high as 700 mg/L (0.7 g/dm ) in some tests. This
meant losses of about 30 bbl (4.8 m 3 ) oil into the
disposal system daily and significant lost revenues. This
un separated oil also caused increased operating costs as
water disposal wells began to plug.
After reviewing these problems, we decided to build a
satellite battery to handle half the produced liquid on the
lease. The central battery was to be modified to increase
its treating and disposal capacity to 32,000 BID (5088
m 3 I d) by installing some type of water-polishing device
between the existing free-water knockouts and the
produced-water disposal system.
Although the capacity of this water-polishing device at
ultra-high water cuts was the primary design criterion,
several other factors had to be considered.
As a result, three secondary design criteria were
developed: that the vessel be built and installed quickly,
that it be reasonably priced, and that it be durable in the
Introduction
The increasing value of oil is making it economically attractive to install high-volume artificial lift equipment in
an oil well, and produce it to a WOR of 125 or more.
However, there are few methods for the design of an
oil/water separator that will handle effectively liquid inputs of 20,000 BID or more at these ultra-high water
cuts. By developing and presenting the design equations
for one such design, this paper describes a foundation for
further work.
Large-volume wash tanks often are used as oil/water
separators or water polishers in high-rate, high-water-cut
applications. Despite widespread use of wash tanks,
there are no design equations available to aid in their
design 1. This paper presents several equations
developed while adapting the API separator to oilfield
use. It also evaluates design performance with field data.
A comparison of actual performance with performance
predicted by reaction kinetics equations shows that, for
the most part, overall performance approached or exceeded predicted performance. Although some flow
characteristics failed to meet the modeled performance,
we conclude that the design equations developed are
valid for design of a high-water-cut, high-rate oil/water
separator.
• Now with Monsanto Oil Co.
0149·2136/82/0010-8307$00.25
Copyright 1982 Society of Petroleum Engineers of AIME
NOVEMBER 1982
2637
CENTRAL AISER
Fig. 1-Cutaway drawing of constant-level skim tank.
0--·1::
D
LOWER
1--INLET
SPREADE~
BLIND
highly corrosive environment. In this case, the presence
of H 2 S in the water aggravated the corrosion problem.
After researching several alternatives, we decided that
converting a surplus tank into a wash tank would be the
fastest and simplest solution. However, when we
reviewed the wash tanks used in this and other operating
areas, we could find no design equations for this type of
vessel. The first step in designing the vessel, then, was
to develop analytical expressions that would allow the
design to meet the primary design criterion. Our approach was to adapt the separator described in the API
Manual on Disposal of Refinery Wastes 2 to a vertical
cylindrical vessel, rather than the horizontal vessel normally used.
API Separator
The API separator is basically one or more long channels
with a maximum flow area and minimum depth. This
minimizes turbulence and allows oil globules greater
than 0.006 in. (0.15 mm) in diameter to rise to the surface, where they are skimmed off. This type of vessel
was attractive because it was simple and effective, and
could be sized to treat specific inflow rates.
Analysis shows six major components in an API
separator. The preseparator flume and the forebay slow
down flow, reducing turbulence and allowing most of
the gas and sludge to separate out of the flowstream. A
vertically slotted baffle is used to create an even flow
profile into each channel. Several channels are used, and
they are designed to be sufficiently long and shallow for
effective separation at design rates. An oil skimmer and
a sludge-collecting hopper are used to collect these byproducts as they are separated from the water by gravity
and to hold them for removal.
The handling of H 2 S-laden brine in an API separator
presented safety and pollution hazards that were unacceptable. The basic design was rejected on this basis. We
decided, however, that since the strong points of a wash
tank and of the API separator complemented each other,
a better design might result from adapting the API
separator to a wash tank.
2638
--@1 ~~~~~;D TSEL~T:ITH
-
BLIND
.L:L
Fig. 2-Detail of skim tank internals.
Constant-Level Skim Tank
The design shown in Figs. 1 and 2 is an adaptation of the
API separator. The gas boot serves as a preseparator
flume, slowing flow to 0.5 ft/sec (0.15 m/s), downward.
This allows entrained free gas [bubbles of 400 microns
(400 J,tm) or more] to rise out of the flowstream. The line
from the boot to the central riser and the central riser
itself are designed for fluid velocities of 2 to 4 ft/sec (0.6
to 1.2 m/s). These components act together as a forebay,
evenly distributing flow to the upper slots.
The inlet slots in this design are used as a slotted baffle, distributing the water flow evenly across the
spreaders. This set of slots should have enough area to
cause a velocity of 3 ftlsec (0.91 m/s) at design
throughput. While the length and the number of slots can
be varied, each slot should be at least 0.5 in. (13 mm)
across to minimize plugging. The upper end of the slots
should be even with or below the lower lip of the upper
spreader for optimal performance.
The space between the two spreaders is the actual flow
channel in this design. The area of each spreader should
be about half the area of the tank. A space of at least 2 ft
(0.61 m) should remain between the edge of the spreader
and the wall of the tank to provide working room during
construction.
The outlet piping downstream of the exit slots should
be connected to a water leg located outside the tank.
Since the height of the water leg is adjustable, it can be
used to regulate the liquid level. This will maintain a
relatively constant level in the vessel and help to keep the
oil/water interface above the upper spreader. This interface must be kept above the upper spreader for efficient
separation. An oil skimmer should be tied in to the tank
JOURNAL OF PETROLEUM TECHNOLOGY
above the spreader. A continuous skimmer not only will
recover the oil separated by the flowstream but also will
provide a secondary means of controlling the liquid level
in the tank.
A 0.12-psi (0.860-kPa) auxiliary gas source should be
used to maintain a gas blanket in the vapor space of the
vessel. This not only will reduce corrosion in the vessel
but also will reduce the risk of explosion. By using a
cone-bottom tank, the bottom of the tank can be used as
a sludge-collecting hopper. *
While gaslliquid separation should occur primarily in
the gas boot, smaller gas bubbles will be liberated as the
flowstream velocity slows farther downstream. The gas
released by this secondary separation should be routed
into the vapor space of the tank. This is accomplished by
providing vent holes at the top of the central riser and by
placing a vent in each spreader. The vent for the upper
spreader should end just below the top of the tank. The
vent for the lower spreader should end above the top of
the upper slots, just below the upper spreader. The crosssectional area of each vent should be large enough to
keep vapor velocities low. This will prevent the vapor
from lifting water as it moves up the vent.
Oil/water separation should occur primarily in the
flow channel between the two spreaders. As a result, oil
will build up in the space below the upper spreader and
above the top of the upper slots. Although this oil
blanket will help small oil globules to coalesce and move
out of the flowstream, it could become contaminated
with anaerobic bacteria, which would be a source of corrosion. This can be minimized by treating the inlet
stream with a bactericide at regular intervals. Secondary
oil/water separation will occur in the region outside the
spreaders and in the area below the lower spreader.
Secondary separation also will occur in the quiet space
between the upper spreader and the oil/water interface.
Design Equations
In the API separator, each flow channel is designed to
keep the horizontal velocity at 3 ftlmin (0.015 m/s) or
less at design rates. This will minimize turbulence in
each channel. The channels are designed to be long
enough for an oil droplet 150 microns (150 J-tm) in
diameter to rise from the lowest streamline to the
oillwater interface before it reaches the end of the channel. In this adaptation of the API separator, all the oil
droplets must rise to an elevation equal to the lip of the
top spreader before they are carried out from beneath the
spreader. The length and the width of the flow channel
are approximately constant for any particular size tank,
because the spreader size is a function of tank size. As a
result, calculations must be carried out to determine the
distance between the two spreaders, and the length of the
inlet slots. These distances, h2 and h I (Fig. 2), must be
long enough so that most oil droplets will be captured
beneath the upper spreader at design rates. These
distances can be characterized by a single variable, ii,
which is the average of h I and h 2 •
The design process is similar to that outlined in Chap.
5 of Ref. 2. In this case, it is possible to begin with a
design rate and work up rough values for the length of
the slots and the distance between the spreaders. The
TABLE 1-RETENTION TIME DISTRIBUTION,
CONSTANT-LEVEL SKIM TANK
Reduced Time
Distribution
Function
(ppm)
to
E(t o )
0
85
442
421
276
335
314
297
266
245
197
235
235
100
0.17
0.26
0.35
0.44
0.54
0.65
0.76
0.87
0.98
1.09
1.2
1.31
1.43
2.1
0
0.19
0.99
0.94
0.62
0.75
0.70
0.66
0.59
0.55
0.44
0.52
0.52
0.22
Time
Tracer
t
C
(minutes)
9
14
19
24
29
35
41
47
53
59
65
71
77
100
quickest way to design this vessel is to select a value of ii
and calculate the capacity of the vessel. Then ii should be
iterated until a value is found that will allow the desired
throughput. The design engineer then can select values
of h I and h2 that are compatible with this value of ii.
The upper slots should be designed to cause a velocity
of 3 ftlsec (0.91 m/s) at design rates, and will require
some minimum length to handle the desired throughput.
This gives a minimum value of both h I and h 2 • The two
spreaders can be moved only a limited distance apart
because of the amount of piping and quiet space required
in the tank. This gives a maximum value of h I and h 2 .
Thus, the design of this vessel becomes simply a matter
of determining an optimal value of ii for a desired
throughput.
Using the Stokes equation, droplets of oil as low as
0.006 in. (0.15 cm) in diameter will rise in water at a
velocity of
Ut
.
=0.0241 ( 'Yw-'Yo) ft/mm
J-tw
or
Ut
=0.0122
(1' w~~'Y
0 )
cm/s.
. ............ (1)
The probable flow channel in this design is indicated in
Fig. 2 by dashed lines.
This flow channel will have a length (in feet or meters)
of
L= llz(d 2 -d I)'
The average depth of the channel (in feet or meters) can
be estimated:
ii=llz(h l +h 2 ) . ........................... (2)
The volume of the channel should be
"Gipson, F.W.: personal communication, Conoeo Inc. (1976).
NOVEMBER 1982
2639
400
0
300
~
p=
0
0
0
-
!
"'0
300
o
300
200
400
OiL CAMfO"l£R. INLET
600
700
600
\"lIIl)
Fig. 3-Performance of skim tank at 25,000 BID (3975 m 3/d).
To rise from the lowennost streamline to the uppermost streamline of flow requires a separation time of
fi
t'=- min ............................... (3)
Ut
This separation time will have to be less than the time required for flow to move beyond the spreader (i.e. leave
the flow channel) at design rates, or
Thus, at design rates,
U [7r
2
7r 2
7r
q=-=- d 2 h 2 - - d Ih 1---(h 2 -h 1)
t
h
4
4
12
. (d 22 +d 2d I +d2dJ '
which reduces to
7r
q=--xutx
4
1
(d 2 -d I) ( 2
h
1
- d 2h2+-d 2hl
3
3
2)
+ - d 1h2 +-d1hl cu fi/min,
3
3
or
This equation will not have a unique solution, so
several pairs of h I and h2 can be calculated. If h2 is
maximized (to reduce turbulence), the design throughput
becomes a function of hI. Using the properties of the
system and the design rate, then, h I can be calculated as
the final step in the design process. An example calculation is shown in the Appendix.
2640
100
O~~-~--~--'-----'----~'---'-I
o
20
40
60
80
100
120
RETENTION TIME (r.lUTES)
Fig. 4- Tracer response curve for skim tank at 25,000 BID
(3975
m 3 /d).
Field Testing
A prototype vessel was built and installed in the Big
Lake field in mid-1977. With the above equations, this
vessel has a design water capacity of 48,000 BID (7631
m 3 /d). This rate is 150% of the desired throughput of
32,000 BID (5088 m 3 /d). Initial water throughput was
approximately 25,000 BID (3975 m 3 /d). Figs. 3 and 4
display the results of several tests run at that time to
detennine effectiveness of this design.
Fig. 3 presents effluent water quality as a function of
input water quality. Although slugs ofO.7 to 8 giL (0.7
to 0.8 g/cm 3 ) oil were measured going into the
separator, effluent quality was generally less than 0.175 .
giL (0.0175 g/cm 3 ) oil. Because of the vessel's performance above 0.200-g/L (0.200-g/cm 3 ) input, this curve
shows the effectiveness of the vessel when used as a
free-water knockout or where large slugs of oil are
expected.
To detennine the retention time of water in this vessel,
a tracer was mixed in water and injected into the
flowstream before it entered the gas boot. Samples were
taken at the water outlet and then were analyzed for
tracer material. As indicated in Fig. 4, the peak retention
time was 19 minutes.
The degree of mixing is indicated by the width of the
retention curve at one half the peak height. In this test,
the width of the retention curve was 60 minutes using a
tracer concentration of 200 ppm. This indicates that turbulence and mixing are occurring, but that they are not
affecting perfonnance adversely to any great extent.
Reaction Kinetics Equations
How efficient is this vessel? Is it doing as well as could
be expected? What should the retention time curve look
like? Using the method given by Zemel and Bowman, I
we can compare actual perfonnance with ideal
perfonnance.
Basic reaction kinetics provides several ways to obtain
an approximation of that ideal perfonnance. This will
allow the production engineer to analyze the performance of this or any other reaction vessel.
JOURNAL OF PETROLEUM TECHNOLOGY
Using equations from several reaction kinetics
texts,3-5 the area under the rete~tion time curve in Fig. 4
is:
Ct =
r
Cdt
o
As with any function, the distribution is characterized by
its first and second moments.
For this distribution to be compared effectively with
ideal and actual performance of other vessels, it should
be plotted as a dimensionless curve.
To obtain a dimensionless plot, the ideal mean
residence time is used to reduce both t i and C i to functions of dimensionless time, t D. Thus, for any sample,
or
ti
tD=7
00
.L:c X~ti ppm-min ....................... (5)
o
i
.............................. (10)
and
7
E(tD)=-C i . . . • . . . . . . . . . . . . . . . . . . . . . . . . (11)
The retention time curve becomes the retention time
distribution when
C
E(t) = -minutes -I
Ct
.......................
(6)
is plotted vs. t.
The mean residence time, 7, of a vessel is a key
operating characteristic. If there is no dead space in the
vessel,
V
7=-min, ............................... (7)
q
but the actual 7 for a vessel can be calculated from a
tracer test with the formula
r
Cxtdt
7="-0----
r
Cdt
o
Ct
Reaction engineering texts provide two simple singleparameter models that represent two extremes of flow.
These can be used to obtain clues to which flow regimes
are occurring in the vessel. These two equations also can
be used to predict the retention-time distribution of this
vessel, within the limiting assumptions.
The dispersion model assumes that flow is similar to
pipe flow, with mixing caused by turbulence and
molecular diffusion processes. As can be expected where
one variable combines these two effects, the dispersion
coefficient, K, primarily reflects the amount of turbulence encountered during flow. The vessel dispersion
number is K/(vL) , a dimensionless number used to
characterize the amount of mixing during flow. For
small values of K/(vL), [K/(vL)::;; 0.002], turbulence is
negligible and plug flow is described, resulting in a
Gaussian curve centered at t D = 1. As turbulence increases, so does K/(vL), until fully mixed flow occurs as
k/(vL) approaches infinity. Increased mixing causes the
distribution to reach a peak retention time before t D = 1
and results in a lower peak concentration. For this
model,
00
.L:CXt~t
.....;O~--min . . ........................ (8)
Ct
........................ (12)
7 is the first moment of the retention time distribution;
the second moment is its variance, (12 (t) is
r
The tanks-in-series model simply assumes flow
through a series of mixing tanks, each equal in size. The
single parameter describing this system is n, the number
of tanks in this series. For this model,
n(nt D)n-I e -ntD
C(t-T)dt
(12t="-0 _ _-
r
Cdt
o
r
E(tD)=
Ct 2dt
="-0-----_t 2
r
Cdt
(n-l)!
................... (13)
The second moment, the variance, of these functions is
2K
K2
(12(tD)=- +8-- for the dispersion model . (14)
vL
vL
and
o
(12 (t D) = lin for the tanks-in-series model.
I
.... (15)
00
=
~C·I Xt2·~t-72
L..J
I
0
NOVEMBER 1982
. . ................... (9)
Note that as the number of tanks increases to infinity, or
as K gets very small, (12 (tD) approaches zero and overall
flow through the system will approach plug flow.
Because the dispersion model allows for flow back
2641
TABLE 2-COMPARISON OF
PROJECTED vs. ACTUAL PERFORMANCE AT 25,000 BWPD
Ideal
Distribution
Actual
Distribution
0.85 tD (46 min.)
0.78 tD (42 min.)
0.86 tD (46 min.)
tD (54 min.)
0.9
peak retention time
mean retention time
time at one-half peak
concentration
peak concentration
0.35
1.01
0.88
0.85
tD (19 min.)
t D (54 min.)
tD (47 min.)
tD (46 min.)
0.99
RTD
1.0
0.8
-0
w
0.6
~
0.4
0.2
0
0
05
1.5
2
Fig. 5-ldealized residence-time distributions at 25,000 BID
(3975 m 3 /d).
1.4
1.2
TANK IN
SERIES
1.0
'0
0.8
~
UJ
ACTUAL
DISTRIBUTION
0.6
0.4
0.2
0
0
.5
1.5
2
to
Fig. 6-Equivalent residence-time distributions at 25,000
BID (3975 m 3/d).
upstream, the distributions predicted by these two
models differ more and more with increasing deviation
from the plug flow regime. 5
Analysis of Results
Using these equations, the data from the retention time
testing were used to arrive at a retention time distribution
for the vessel (Table 1). This distribution was plotted in
Fig. 5 to predict what the retention time distribution for
flow through the gas boot, suction piping, and spreader
areas of the constant-level skim tank should look like.
2642
Here it was assumed that n=3. From Eqs. 14 and 15, we
calculate that (J2(t D)=0.333, and KlvL=0.115. Between the two predictions is a composite curve. This is
an interpolation predicting what the retention time
distribution should be for the constant-level skim tank
based on the two models. According to this curve, the
peak concentration is predicted to occur at t=0.85tD'
and the time span at one half the peak concentration is 7.
The peak concentration should be about 0.9E(td)' The
variance, (J2, of this vessel, should be 0.333; the mean
residence time is 0.78tD' The actual retention time
distribution for this vessel is plotted in Fig. 6. It can be
seen that the peak concentration actually occurs at
t=0.35tD' From Eq. 8, 7=54.9 minutes (1.01tD) for
this distribution, and we can calculate that
(J2(tD)=0.303. Thus, in this vessel the actual constants
are n=3.29 and KlvL=0.106, using Eqs. 14 and 15.
The rapid increase of concentration in the actual
retention-time distribution seems to indicate the
possibility of short circuiting in this vessel. However,
the mean residence time and the peak tracer concentration were nearly the same as predicted, and no slugging
was observed or recorded.
The retention-time distributions based on these constants are plotted in Fig. 6. Comparing Figs. 5 and 6
shows how similar the actual performance was to the
ideal performance. The variance of the actual retentiontime distribution was only slightly less than the variance
predicted by the models. This is an indication that slightly less mixing and turbulence was occurring than was
expected.
This conclusion is supported by two other comparisons. If the hump in the retention-time curve, which
begins at t= 1.2t D, is ignored as an anomaly, the time
during which measured tracer concentration exceeded
one half of the peak concentration was O. 85t D, which is
slightly less than the value expected. This indicates that
the actual flow regime was closer to plug flow than was
predicted. The lack of turbulence also is indicated by the
value of E(t D) achieved at peak concentration; this was
about 10% higher than was predicted by either flow
model (Table 2).
In a final comparison, the measured mean residence
time of 54.9 minutes occurred at 7= 1. 0 1t D, which is
slightly longer than the 7=0.78tD predicted by the
model. In this distribution, samples taken after t=2t D
could be regarded as coming from an inactive part of the
vessel. If these data points are not considered, 7=47.6
minutes, or 0.88tD for this vessel, which agrees fairly
well with the predicted value.
According to Levenspiel,5 the difference between 7
for this smaller set of data, and the ideal 7 (= Vlq)
represents the amount of inactive volume in the vessel:
7 measured X
Vactive
V
= -----tideal
and
Vinactive
=V -
Vactive
= V ( 1-
t measured
)
.
tideal
This vessel was designed to have a quiet space above
the uppermost spreader. In this vessel, 2 ft (0.61 m) of
space (or 14% of the working volume) was isolated, so
JOURNAL OF PETROLEUM TECHNOLOGY
Tm=0.86Ti could be expected based on this analysis.
The Tm = 0.88 TD that was measured indicated that not
all this volume is inactive.
There is a minor anomaly in the retention-time
distribution curve in Fig. 6, starting at t= 1.2t D. This is
caused by a small amount of liquid following a second
flow path longer than the mainstream flow. This minor
flowstream probably exited the upper spreader through
the vent and then used the dead space for separation purposes, reducing the inactive volume of this vessel.
The major difference between the models and the actual performance, however, occurs in the early part of
the distribution, when the tracer shows a quick and
significant breakthrough. It should be realized that this is
expected at the rates seen in this vessel. High rates prevent mixing with upstream water, so a Gaussian distribution cannot be obtained despite an intermediate vessel
dispersion number of K/(vL) =0. 106. The close agreement between the actual and the predicted peak concentration indicates that there is no short circuiting or slugging occurring.
.Conclusions
Because of continuing problems with wash tanks as
water separation equipment, a commitment was made to
design a high-rate separator based on the API model
separator. The primary design criterion was its effectiveness at rates of more than 25,000 BID (3975 m 3 /d).
Secondary criteria were ease of construction, durability,
and low capital costs.
Once the design equations were developed and approved, the constant-level skim tank was put together
quickly as a result of its simplicity and the availability of
component parts. No moving parts are involved, and
corrosion resistance was built in, giving it the reliability
that was sought. Initial outlay was less than the price of a
free-water knockout with comparable capacity. In addition, operating expenses are nil. Thus, this separator met
the three secondary design criteria.
As for the primary criterion-that it be effective-field
performance indicates that the actual performance of this
vessel nearly matches its ideal performance in most areas
of comparison.
Nomenclature
n = number of tanks in series-of-tanks flow
model
q = volumetric flow rate, BID (m 3 Id)
t D = dimensionless time
t' = minimum required separation time, minutes
T = mean residence time, minutes
U = fluid velocity, ft/min (m/s)
U t = terminal velocity of oil rising in water,
ft/min (mm/s)
V = wetted volume of vessel, bbl (m 3 )
Vc = volume of the actual flow channel, bbl (m 3 )
'Y 0 = specific gravity of oil
'Y w = specific gravity of water
/l-w = viscosity of water, cp (Pa' s)
a 2 (t) = variance of the distribution with respect to
time
Acknowledgments
I am grateful to Conoco Inc. for giving me the opportunity to publish this paper. Special recognition is extended
to F.W. Gipson, 1.1. Stockton, D.D. Caudle, and 1.R .
Cowden for their contributions to this project.
References
l. Zemel, B. and Bowman, R.W.: "Residence Time Distributions in
Gravity Oil-Water Separations," paper SPE 6527 presented at the
1977 SPE California Regional Meeting. April 13-15.
2. Manual on Disposal of Refinery Wastes, "Oil-Water Separator
Process Design," API, Dallas (1969) Chap. 5.
3. Himmelblau. D.M. and Bischoff, K.B.: Process Analysis and
Simulation-Deterministic Systems, John Wiley & Sons Inc., New
York City (1967).
4. Levenspiel, 0.: Chemical Reaction Engineering, John Wiley &
Sons Inc., New York City (1972) 280-90.
5. Hill, e.G. Jr.: Introduction to Chemical Engineering Kinetics and
Reactor Designs, John Wiley & Sons Inc., New York City (1977)
395-40 I, 283, 287.
SI Metric Conversion Factor
bbl
x 1.589 873 E-Ol
m3
APPENDIX
Example Calculations
Design parameters:
'Yw = 1.029 at 120°F (49°C),
'Yo = 0.810 at 120°F (49°C),
= 0.006 cp (6xlO- 3 Pa's),
q = 32,000 BID (5088 =m 3 Id) design rate;
expect surging, and
U t = 0.884 ft/min (4.5 mm/s). . ..... (A-I)
/l-w
C = concentration of tracer chemical in
flow stream , ppm
C t = total amount of tracer injected into
flowstream, ppm/min
d = diameter (see Fig. 2 for appropriate
subscripts), ft (m)
E(t) = retention-time distribution of C with respect
to t, minutes - 1
E(t D) = retention-time distribution of C with respect
to tD
h = height (see Fig. 2 for appropriate
subscripts), ft (m)
fi = average height
K = effective (or longitudinal) dispersion coefficient, sq ft-min (m2-min) .
L = equivalent length of flow channel, ft (m)
NOVEMBER 1982
Gas boot: Design for surging to 48,000 BID (7631
m 3 /d) at u=0.5 ft/s (0.15 m/s), d=34 in. (86 cm),
h=tank height+(2xd)+2 ft=24 ft (7.3 m).
Forebay riser: For velocity < 6 ftl s (1. 830 ml s),
d 1 :e:: 9.8 in. (25 cm).
Exit slots: For q=32,000 BID (5088 m 3 /d), use area of
100 sq in. (645 cm 2) or less to ensure velocity of at least
3 ft/s (0.9 m/s). Assume eight slots [2 ftxO.5 in. (0.6
mX 1.3 cm)] starting 1 ft (0.3 m) below top of spreader
for both inlet and outlet slots.
Using a 21-ft and 16-inx 16-ft (6.6-mx4.9-m) tank
with 1,000-bbl (l59-m 3 ) nominal capacity, a spreader
2643
with approximately half the cross-sectional area would
have d 2 =0.707 x21.6= 15.25 ft (4.6 m).
Estimated h2 =8 ft (2.4 m), .............. . (A-2)
11=5.0 ft (1.5 m),
L= V2 (d 1 +d 2 )=7.l25 ft (2.2 m), and
t'=minimum required retention time,
5.66 min ............... . (A-3)
2644
then
q=maximum allowable throughput,
48,705 BID (7738 m 3 /d) . . . . . (A-4)
JPT
Original manuscript received in Society of Petroleum Engineers office July 17, 1979.
Paper accepted for publication June 5, 1980. Revised manuscript received Sept. 2,
1982. Paper (SPE 8307) first presented at the 1979 SPE Annual Technical Conference and Exhibition held in Las Vegas Sept. 23-26.
JOURNAL OF PETROLEUM TECHNOLOGY