54 SPE Production & Facilities, February 1996

Although regarded by many as obsolete, gunbarrels (or wash-tanks)are still used for primary oil treating in many areas. This paper de-scribes a modern gunbarrel constructed from an existing 5,000-bbltank. Oil treating without the addition of heat was feasible becauseof the combination of relatively warm produced fluid and lenient ba-sic sediment and water (BS&W) limits. The subject vessel providesgas separation and contains two spreaders that were designed to pro-vide good oil- and water-phase retention and to facilitate solids sepa-ration and removal. The oil-phase spreader has a diameter equal to78% of that of the vessel. It incorporates a unique deep skirt, havinga pattern of restrictive exit ports that imposes uniform radial oil-phaseflow over a wide range of rates and is relatively insensitive to minormisleveling, which is not the case for common serrated-skirt spread-ers. The design of the unique vessel internals permitted assemblywithout welding at the battery site. Differences in the contributionof the water-bath zone of heated and nonheated gunbarrels are dis-cussed, and it is shown that nonheated-vessel designs that increasewater-phase residence time and facilitate convection in the water-bathare the most effective, a result of conservation of intrinsicwell-stream heat. It is also demonstrated that the optimum oil-blanketthickness is a compromise between oil-residence time and oil temper-ature in nonheated vessels that capture water-phase heat. Vessel in-ternals that entrap oil beneath water (such as the oil-phase spreaderof the subject vessel) are subjected to a buoyant force in addition tothe weight of water displaced by steel. This effect is discussed, anddesign equations are developed to calculate the net buoyant force ex-erted upon a specific spreader and the gauge steel from which aspreader must be constructed to preclude floating. An example isincluded that illustrates the application of these equations to the sub-ject vessel.

The gunbarrel (or wash-tank) was devised for field processing at theinfancy of the oil-producing industry. If crude-oil dehydration re-quired increased temperature, energy was added by heating the waterbath by means of an internal firetube, internal steam coils, or externalthermosiphon loop and direct heater. An alternative method was pre-heating the influent fluid. By either process, these vessels were con-siderably less energy efficient than modern heat-treaters. However,during the era of the heated gunbarrel, low-pressure gas had little or novalue. Typically, gunbarrels would have the same diameter as batterystock tanks, but would be somewhat taller to assure gravitational flow.Thus, Lv/dv ratios generally exceeded 1.0. A generic gunbarrel isequipped with a gas separation/fluid inlet device, such as the internallyinstalled flume (or gas boot), illustrated in Fig. 1a, or the external oneshown in Fig. 1b. With either configuration, the fluid stream is nor-mally discharged beneath a serrated spreader having a diameter be-tween one-fourth and one-half that of the tank, which provides a mea-sure of flow distribution of the oil-continuous phase. Normally, thewater-continuous phase is free to short-circuit directly to the water out-let, minimizing energy consumption in the case of a heated vessel.However, it results in the effluent water having approximately the sameoil content as the influent water. The oil outlet is normally a pipe cou-pling installed in the side of the vessel through which oil overflows,maintaining a constant level. An internally or externally installed wa-ter siphon controls the oil/water interface.

Copyright 1996 Society of Petroleum Engineers

Original SPE manuscript received for review Oct. 10, 1994. Revised manuscript receivedJuly 19, 1995. Paper peer approved Aug. 15, 1995. Paper (SPE 28538) first presented at the1994 SPE Annual Technical Conference & Exhibition, New Orleans, LA, Sept. 2528.

Even today, the gunbarrel is often the preferred means of crude-oildehydration in warm climates and/or where produced fluid tempera-tures are high, or where other circumstances make heating unneces-sary or inexpensive. Many current gunbarrels are of larger diameterand have lower Lv/dv ratios than early ones, and have improved inter-nals. This paper describes a modern gunbarrel design that incorpo-rates effective residence time for the water-continuous phase, as wellas improved oil-continuous phase distribution, gas separation, andsolids removal.

The gunbarrel described here was developed by modifying an exist-ing ineffective 5,000-bbl (38.7 ft24 ft) bolted, cone-bottom set-tling tank. Before vessel modification, the BS&W and solids con-tent of the effluent 29.3-API oil was essentially the same as theinfluent. After the retrofit, the BS&W content of effluent oil waseasily maintained below 2%. The tank was originally equippedwith a 3.0-ft-diameter internal flume and central crows nest oilcollector, which were retained in the modification. The flume ex-tension functions as a vertical oil/gas separator, with gas capacitybeing governed by maximum-allowable superficial-velocity con-siderations. The gas-capacity formula shown below was extractedfrom Ref. 1, and would be appropriate for calculating maximuminstantaneous gas-flow rates. Appreciable liquid carryover fromthe separator is undesirable because it would result in water and wetoil being dumped on top of clean oil leaving the vessel. The ap-propriate value of K for this equation is the largest one that does notinterfere with meeting pipeline-oil specifications.

qg 67, 858 K d2F pTso gg

0.5

psTz. (1). . . . . . . . . . . . . .

Details of the new gunbarrel design are illustrated in Fig. 2. Thisdesign employs large-diameter oil-phase and water-phase distribut-ing spreaders. These were fabricated from bolted 3,000-bbl tank-deck segments and rafters because this construction method per-mitted assembly without welding at the tank-battery site. The raftersof both spreaders extend from the tank wall to the flume, where theyare bolted to attachment rings welded to the flume. The flume wasremoved from the battery site for installation of these rings. The up-per-spreader rafters were supported at the outer end by attachment torolled-channel steel, which was bolted to the tank wall. The lower-spreader rafters were also attached to the tank wall. However, verticalloading was supported by legs extending to the tank bottom. A ventpipe from near the apex of the lower spreader extends up into theupper spreader, and a second one extends from near the apex of theupper spreader up into the flume dome. The upper spreader has thenormal 1:12 tank-deck pitch and a diameter of 30.0 ft. The lowerspreader was constructed with an 18.8 slope and is 28.5 ft in diame-ter. This was accomplished by using only 19 of the standard 20 tank-deck segments. This increased slope, in conjunction with a jettingsystem, prevents sand accumulation on top of the lower spreader.A steel plate seals the bottom of the flume, which is supported by anangle iron framework from the tank bottom. Incoming fluid exitsthe flume through 16 equally spaced 2-in. round inlet ports located ra-dially around the flume. The bottoms of these holes are at the depthof the bottom of the upper (oil-phase) spreader skirt.

Oil-Flow Regulation. Radial oil-phase flow is imposed within theoil-phase spreader by outflow regulation, using 9/16-in.-diameter re-strictive exit ports in the spreader skirt. Port flow rate is a functionof the interface depression (D), illustrated in Fig. 3, and may be cal-culated from Eq. 2. This equation was derived from Eq. B-4 by con-verting rate to barrels per day.

SPE Production & Facilities, February 1996 55

Fig. 1Typical gunbarrel configurations.

qh 116.6 d2h D (w o)o0.5

. (2). . . . . . . . . . . . . . . . . . .

The 12-in. spreader skirt has three horizontal rows of ports, with 60equally spaced ports per row, located 2-, 4-, and 6 in. from the skirttop (see Fig. 4). No fluid flows through a row of ports until the inter-nal interface is depressed to a lower depth because there is no differ-ential pressure. Fig. 5 is a plot of flow rate exiting the spreader vs.interface depth (Z), measured from the skirt top. This figure is basedon Eq. 2, and the average tank-battery oil gravity (29.3 API) and wa-ter specific gravity (1.02). Curves are presented for each row of portsand for the sum of all rows. It can be seen that good rate regulation(and thus radial flow) is imposed from no flow when Z2 in., up to7,452 B/D when Z12 in., at which point oil spillover at the skirt bot-tom is impending. Since qh is a square root function of D, slight mis-leveling of the spreader would have minimal effect on radial-flow dis-tribution up to the point of spillover. Spillover would likely occuralong a small arc of the spreader skirt unless it was precisely level.Field circumstances dictated the wide range of controlled flow de-signed into the oil-phase spreader, which would be impossible toachieve with a conventional serrated spreader even if precisely level.

After the radial-flow regime within the oil-phase spreader, oil globulesexit the 9/16-in. ports in the spreader skirt and rise vertically through thewater bath at a velocity of approximately 0.75 ft/sec to the impact zone

at the oil/water interface, which would effectively be a vertical projec-tion of the spreader skirt. The water bath is very beneficial in the caseof a heated gunbarrel, such as the one described in Ref. 2, because itserves as the heat-transfer medium. However, in the subject unheatedgunbarrel, the principal valve of the water-bath is to conservewell-stream heat, as discussed in a later section. From the oil/water-in-terface impact zone, oil flow would be inward and upward to the oilcollector in an undefined, generally radial flow pattern. Thus, thereare, in effect, two stages of gravity separation. We show in AppendixA that separation capacity is proportional to horizontal cross-sectionalarea (AH) regardless of the direction of bulk flow. Thus, effective sepa-ration is accomplished by efficient use of vessel horizontal area and notdirectly by efficient use of vessel volume. Consequently, separationeffectiveness will not necessarily track with observed residence-timedata when comparing dissimilar vessels because the latter is a measureof volumetric displacement. The functional relationship developed inAppendix A between separation capacity and AH assumed plug flowand that AH does not vary with depth. Real flow differs from plug flowbecause of short circuiting and turbulence, which impede separation.The greater the departure from plug flow, the greater will be the de-crease in separation effectiveness. It is reasonable to assume that thecontrolled radial (horizontal) flow within the oil-phase spreader moreclosely approximates plug flow than the undefined flow regime in theoil blanket. Therefore, any suspended contaminant of constant partialsize that is not removed from the oil while within the spreader wouldnot settle out of the oil phase if introduced at the top of the oil blanket.

Fig. 2Cross-sectional view of vessel internals.

56 SPE Production & Facilities, February 1996

Fig. 3Interface depression within oil spreader. Fig. 4Oil-spreader skirt detail.

However, oil from the spreader enters the oil blanket at the bottom.Therefore, the oil blanket may provide a second stage of separationof indeterminate effectiveness for particles not removed from the oilwhile within the spreader. The greatest contribution of the oil blan-ket, however, is providing residence time for coalescence of smallwater droplets into larger, separable ones.

Spreader-Design Equations. The oil-phase spreader separation-capacity equation (Eq. 3) was derived from Eq. C-2 by convertingrate to barrels per day. Eq. 4, the particle-design-diameter equation,is a rearrangement of Eq. 3.

qMO 2.1603 106d2s d2Fp od2po, (3). . . . . . . . .

and dp 6.8037 104qMO od2s d2Fp o0.5

. (4). . .

These related equations are useful for estimating separation capacity(or design-particle diameter) for removal of either water or solids. Be-cause they describe only spreader performance, they are conservativewhen used to calculate overall vessel performance because they donot include the contribution of coalescence and additional separationoccurring in the oil blanket, which cannot be expressed mathematically.

As previously mentioned, common gunbarrels allow the water con-tinuous phase to short-circuit from the point of liquid entry to thewater outlet, resulting in high-oil and -solids content of the effluentwater. The lower spreader of the subject vessel prevents this. Theapparent water-phase flow path of the subject design is radially out-ward from the flume entry ports to the perimeter of the lower (water-phase) spreader, then radially inward to the water outlet. However,convection will drive some of the warm incoming flow into the wa-ter-bath above the oil-phase spreader, displacing cooler water fromthat area and conserving intrinsic well-stream heat. The low fluidvelocity at the spreader perimeter would provide only moderate re-sistance to this convective current. (In contrast to the subject de-sign, the gunbarrel designs shown in Fig. 1 would result in wastingmost of the heat contained in the water phase.) From the outlet, wa-ter enters an external siphon that controls the oil/water interface.In effect, the spreader area is used twice for oil and solids removalfrom the water phase. In the initial stage of separation, oil dropletsfloat up into the upper (oil-phase) spreader and solids settle to theconical surface of the lower spreader. Once the water phase flowsaround the perimeter of the lower spreader, separated oil dropletswould float up into the apex of the lower spreader and then throughthe vent pipe into the upper spreader. Solids removed in this stagesettle to the tank bottom. The water-phase-capacity equation (Eq.5) was derived by inspection from Eq. 3. Eq. 6 is a rearrangementof Eq. 5 and defines the design-particle diameter as a function ofqMW. The absolute value signs within the specific-gravity term arenecessary because this term would otherwise be negative in the caseof oil separation.

qMW 2.1603 106d2sw d2Fp wd2pw, (5). . . . . . . .

and dp 6.8037 104qMWWd2sw d2Fp w0.5

. (6).

Use of these equations for overall vessel water capacity would beconservative because they do not account for the separation occur-ring beneath the lower spreader, or from water driven by convectioninto the area above the oil-phase spreader. The flow regime beneaththe lower spreader will assume some effective thickness. Oil drop-lets smaller than the design diameter (defined by Eq. 6) may be re-moved from water near the top of this flow stream, but not deep inthe flow stream. The reverse would be true of solid particles. Itis recommended that Eq. 5 be used to estimate vessel-water capac-ity, realizing that the results will be somewhat conservative.

We previously mentioned that the primary contribution of the oilblanket was providing residence time for coalescence of small waterdroplets into larger, separable ones. Therefore, it might seem thata very low oil/water interface (thus a large oil-blanket volume andsmall water-bath volume) would be desirable. However, oil-phaseretention time is not the only factor to be considered. Maximizingoil temperature also aids coalescence. A significant water-bathvolume will enhance the previously mentioned convection process.The only energy available to maintain oil temperature above ambi-ent is that intrinsic to the well-stream. At any specific fluid temper-ature, vessel heat loss to the atmosphere can be estimated with Eq.7, which was adapted from an equation presented in Ref. 3. Recom-mended values of k are presented in Table 1.

Q k dv Lv TL TA. (7). . . . . . . . . . . . . . . . . . . . . . . . . .

Fig. 5Effect of interface depression on spreader-flow capactiy.

SPE Production & Facilities, February 1996 57

TABLE 1VALUES OF HEAT LOSS CONSTANT (k)Wind Velocity

(mph)kBare Steel(BTU/hr ft2 F)

0 2.965 3.12

10 4.2020 5.00

The magnitude of liquid-temperature distribution within a vesselwould be very small and the average temperature would be applica-ble to Eq. 7, regardless of the relative volumes occupied by oil andwater. Heat will flow from the water into the oil blanket, and facili-tating the convection process of diverting influent water into the wa-ter-bath by raising the oil/water interface will increase oil-blankettemperature, illustrated in the following example.

Heat-Loss Example. It is assumed that the subject gunbarrel isuninsulated and that the inflow is 2,000 BO and 8,000 BWPD at atemperature of 100F. Ambient air temperature is 40F and windvelocity is 10 mph (thus k4.20 Btu/hr ft2 F). In the first case,it is assumed that all produced water short-circuits the vessel. Thus,the oil provides all of the atmospheric heat loss. Assuming an oilspecific-heat capacity of 0.5 Btu/lbmF, a 70.7F average tank-liq-uid temperature is calculated with Eq. 7. In the second case, it isassumed that all of the water is diverted into the water-bath and thatwater leaving the vessel is at the average tank-liquid temperature.The resulting liquid temperature would be 94.8F. Oil processedat 94.8F would likely meet pipeline specifications and that pro-cessed at 70.7F would not. Thus, it is desirable to capture as muchheat as possible from the water by inducing convection in the wa-ter-bath. An additional benefit of maintaining a high oil/water in-terface is that oil temperature is less affected by short duration de-creases in ambient air temperature because more heat is stored. Theforegoing discussion demonstrates that the optimum oil-blanketthickness is a compromise between oil-residence time and oil tem-perature in nonheated vessels that capture water-phase heat.

The subject vessel was initially water filled, and the lower spreader isproperly vented and always totally submerged in water. Consequently,the buoyant force applied to the lower spreader will equal the weightof the water displaced by steel (Ww/s). This amounts to approxi-mately 13.26% of spreader weight for 1.02 specific gravity brine. Theupper spreader is also properly vented and submerged in water but en-traps oil. Therefore, it is subjected to a buoyant force in addition toWw/s, which is a function of the depth of the oil/water interface withinthe spreader and consequently a function of oil-flow rate. Eqs. D-8through D-10 are expressions for the buoyed weight of the top spreader(including the oil entrapment effect), the weight per square foot of sheetsteel required to preclude an unrestrained spreader from floating inthe event it becomes oil filled, and the oil/water-interface depth at theneutral point (if one exists), respectively.

The following example demonstrates how these equations wereused in the design of the subject gunbarrel, and that buoyancyshould always be considered in the design of vessel internals thatcan entrap oil beneath water. First, Eq. D-9 was used to determinethe gauge of sheet steel required to prevent the spreader from float-ing should it become completely oil-filled. Substituting values of1.25-, 1.0-, 15.0-, and 1.5 ft for hc, hs, rs, and rF, respectively, re-sulted in Wu12.855 lbm/ft2. Table 2 (extracted from Ref. 4)shows that 00 gauge (11/32-in.) steel would be needed to meet thiscriteria. Sheet steel of this thickness would be difficult to get andwork with. For these practical reasons, it was decided to use -in.steel weighing 10.00 lbm/ft2. Eq. D-8 was then used to determinethe buoyed spreader weight under oil-filled conditions by settingZ12 in. This calculation resulted in a net upward force of 1,974lbf. Consequently, it was necessary to bolt the spreader to the raf-ters (which were secured to the tank wall and flume) to preclude thepossibility of spreader floating. It was determined that the resultant

TABLE 2SHEET STEEL DATA

Gauge No.Thickness

(in.)Wu(lbm/ft2)

00 11/32 13.7500 5/16 12.5001 9/32 11.2502 17/64 10.6253 1/4 10.0004 15/64 9.3755 7/32 8.7506 13/64 8.1257 3/16 7.5008 11/64 6.8759 5/32 6.25010 9/64 5.62511 1/8 5.00012 7/64 4.375

force on the spreader would be neutral when the oil/water interfacewas located 8.1235 in. from the top of the skirt (Z8.1235 in.) usingEq. D-10. With the interface at this depth, all three rows of exitports would be in operation, and a resultant oil-flow rate of 5,264B/D may be calculated with Eq. 2 or observed from Fig. 5. Thus,the net force on the spreader will be downward so long as the oil-flow rate does not exceed this value.

1. Insufficient gas separation capacity could result in water andwet oil being dumped on top of clean oil leaving the vessel.

2. An improved oil-phase spreader has been developed that pro-vides uniform radial distribution over a wide range of flow rates andis relatively insensitive to minor misleveling.

3. Effective separation is accomplished by efficient use of vesselhorizontal area, and not directly by efficient use of vessel volume.Consequently, separation effectiveness will not necessarily trackwith observed residence-time data when comparing dissimilar ves-sels because the latter is a measure of volumetric displacement.

4. The value of the water-bath in a nonheated gunbarrel is to con-serve intrinsic well-stream heat, whereas for a heated vessel it is theheat-transfer medium.

5. The oil blanket may provide a second stage of separation of in-determinate effectiveness for particles (water or solids) not removedfrom the oil while within the spreader.

6. The greatest contribution of the oil blanket is providing resi-dence time for coalescence of small water droplets into larger, sepa-rable ones.

7. Raising the oil/water interface will increase oil-blanket tem-perature in nonheated gunbarrels designed to conserve water-phaseheat.

8. Oil-blanket temperature is less affected by short duration de-creases in ambient air temperature when a high oil/water interfaceis maintained because more heat is stored.

9. Optimum oil-blanket thickness is a compromise between oil-residence time and oil temperature in nonheated vessels that capturewater-phase heat.

10. Buoyancy should always be considered in the design of vesselinternals that can entrap oil beneath the oil/water interface.

AH horizontal area, L2, ft2Ah spreader skirt port area, L2, ft2As oil-phase spreader surface area, L2, ft2C discharge coefficient, dimensionless

dF flume diameter, L, ftdh diameter of exit ports in spreader skirt, L, in.

dp design diameter of oil, water, or solids particle, L,cm

ds oil-phase spreader diameter, L, ftdv vessel diameter, L, ft

58 SPE Production & Facilities, February 1996

Fig. 6 Effect of (a) radial flow and (b) vertical flow direction on separation.

dsw water-phase spreader diameter, L, ftD distance from an oil-phase-spreader port down to

the internal oil/water interface, L, in.Fbc buoyant force resulting from water being displaced

by oil in the conical portion of the oil-phasespreader, mL/t2, lbf

Fbs buoyant force resulting from oil accumulationwithin the oil-phase-spreader skirt, mL/t2, lbf

g acceleration of gravity, L/t2, 32.174 ft/sec2h differential head, L, ft

hc altitude of cone frustum portion of oil-phasespreader, L, ft

hs height of oil-phase-spreader skirt, L, ftk constant from heat-loss equation (Eq. 7), m/t3T,

BTU/hr ft2 FK separator performance constant, L/t, ft/secL height, L, ft

Lv vessel height, L, ftp absolute operating pressure, m/Lt2, psia

ps absolute standard pressure, m/Lt2, psiaq flow rate, L3/t, ft3/sec

qg gas capacity, scf/Dqh port flow rate, L3/t, B/D

qmo oil capacity, L3/t, ft3/secqMO oil capacity, L3/t, B/DqMW water capacity, L3/t, B/D

qo oil-flow rate, L3/t, B/DQ heat-loss rate, mL2/t3, BTU/Hr

rF flume radius, L, ftrs oil-phase spreader radius, L, fttr residence time, t, sec

ts particle settling time, t, secT absolute gas temperature, T, oRTA ambient air temperature, T, oF

TL liquid temperature, T, oFTs absolute standard temperature, T, oRvb bulk-flow velocity, L/t, ft/secvs average fluid velocity at the oil-phase skirt, L/t,

ft/secvt terminal velocity of a settling particle, L/t, ft/sec

Vc volume of cone frustum portion of oil-phasespreader, L3, ft3

W oil-phase spreader weight in air, mL/t2, lbfWb resultant buoyed weight of oil-phase spreader,

mL/t2, lbfWbw buoyed weight of oil-phase spreader immersed in

water, mL/t2, lbfWu unit mass of sheet steel, m/L2, lbm/ft2

Wun value of Wu required to preclude an unrestrained,oil-filled spreader from floating, m/L2, lbm/ft2

z supercompressability factor, dimensionlessZ distance from oil-phase-spreader skirt top to

internal oil/water interface, L, in.Zn value of Z resulting in neutral force, L, in.o oil specific gravity, dimensionlessp particle specific gravity, dimensionlesss steel specific gravity, dimensionlessw produced water specific gravity, dimensionlesso dynamic viscosity of oil continuous phase, m/Lt,

cpw dynamic viscosity of water continuous phase,

m/Lt, cpg gas density at separation conditions, m/L3, lbm/ft3o oil density at separation conditions, m/L3, lbm/ft3

I thank Conoco for the opportunity to work on this project and LarryGaertner for his input and construction supervision. The contribu-tion of Bob Adam with Tank Tec Inc. of working out various fabrica-tion details is gratefully acknowledged.

1. Powers, M.L.: New Perspective on Oil and Gas Separator Performance,SPEPF (May 1993) 77.

2. Williams, A.R.: A Wash-Tank Design, API, Drill & Prod. Prac. (1953)272.

3. Spec. 12L, Vertical and Horizontal Emulsion Treaters, third edition, API,Washington, DC (1986) 20.

4. Engineering Handbook of Conversion Factors, National Tank Co., Tulsa,OK (1991) 156.

5. Powers, M.L.: Analysis of Gravity Separation in Freewater Knockouts,SPEPE (Feb. 1990) 5258; Trans., AIME, 289.

6. Vennard, J.K.: Elementary Fluid Mechanics, third edition, John Wiley& Sons, Inc., New York City (1954) 304.

! "# $

The following demonstrates that gravity separation capacity is inde-pendent of the direction of bulk flow in vessels for which AH doesnot vary with depth. Plug flow is assumed in all cases, and all velo-cities (regardless of direction) are considered positive.

Radial Flow. Fig. 6a depicts the radial (horizontal) flow regimewithin the oil-phase spreader. For complete separation, the waterdroplet (or sand grain) shown at the top of the interior cylinder (rep-resenting the flume) must reach the base of the exterior cylinder(representing the intersection of the oil/water interface and thespreader skirt), before the bulk flow exits through the spreader-skirtports. At capacity, the particle would take the path shown. Thetime required for the particle to settle to the interface is presented inEq. A-1.

SPE Production & Facilities, February 1996 59

ts Lvt. (A-1). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Flow rate may be expressed as Eq. A-2.

q ds L vs. (A-2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Residence time equals volume divided by rate (Eq. A-3).

tr d2s d2F L

4 ds L vs

d2s d2F4 ds vs

. (A-3). . . . . . . . . . . . . . . . . . .

At capacity tstr. Equating Eqs. A-1 and A-3 yields Eq. A-4. Sub-stituting this expression for vs into Eq. A-2 yields the separation ca-pacity equation (Eq. A-5).

vs d2s d2F

4ds Lvt, (A-4). . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

and qmo d2s d2Fvt4 AHvt. (A-5). . . . . . . . . . . . . . . . . .

Ref. 5 shows that Eq. A-5 is also valid for linear horizontal flow.

Vertical Flow. Fig. 6b depicts vertical oil-phase flow in a separationvessel. Separation can occur only if the water droplet (or sand grain)shown within the cylinder has a terminal velocity exceeding the up-ward bulk-flow velocity. Thus, at capacity, vbvt. By inspection,qAHvb. Therefore, qmoAHvt. This expression is identical to Eq.A-5, the capacity formula for horizontal flow. The foregoing illus-trates that gravity separation capacity equals the product of horizontalcross-sectional area and particle terminal velocity in a plug-flow re-gime, and is independent of bulk-flow direction.

! " % $ #&

Flow rate through the oil-phase-spreader skirt ports would obey thecommon orifice flow equation (Eq. B-1), which was extracted fromRef. 6.

q CAh(2gh)0.5. (B-1). . . . . . . . . . . . . . . . . . . . . . . . . . . . .

In this equation, h pertains to the flowing fluid (oil phase), andis developed by the interface depression, D, illustrated in Fig. 3.The equation for h (Eq. B-2) is obvious from inspection of Fig. 3.

h D(w o)12o. (B-2). . . . . . . . . . . . . . . . . . . . . . . . .

Eq. B-3 was derived by substituting Eq. B-2 into Eq. B-1.

q CAhgD(w o)6o0.5

. (B-3). . . . . . . . . . . . . . . . . .

Eq. B-4 is the result of assigning values of 0.6 and 32.174 ft/sec2

to C and g, respectively, and substituting dh2/576 for Ah in Eq. B-3.

q 7.578 103d2h D(w o)o0.5

. (B-4). . . . . . . . . . . .

! "

'

Eq. C-1 (adapted from Eq. 1 of Ref. 5) expresses Stokes law for asettling particle in oil.

vt 178.74p od2po. (C-1). . . . . . . . . . . . . . . . . . . . .

Substituting Eq. C-1 into Eq. A-5 reduces to the following expres-sion for qmo as a function of dp .

qmo 140.38d2s d2Fp od2po. (C-2). . . . . . . . . . . . .

! "% #& %

The surface area of the oil-phase spreader consists of a cylinder anda frustum of a cone. Using well-known formulas, this area can beexpressed as follows.

As 2rs hs (rs rF)h2c (rs rF)20.5

. (D-1). . . . . . .

The equation for spreader weight in air (Eq. D-2) was derived bymultiplying the surface area (expressed in Eq. D-1) by Wu , the unitweight of sheet steel in lbm/ft2. Table 1 presents the thickness andWu for tank steel of various gauge numbers.

W Wu2rs hs (rs rF)h2c (rs rF)20.5. (D-2). . The buoyed weight of the spreader immersed in water is given by

Eq. D-3, which follows from Eq. D-2.

Wbw Wu 1ws 2rshs (rs rF)h2c (rs rF)2

0.5. (D-3). . . . . . . . . . . . . . . . . . . . . The volume of liquid contained within the oil-phase spreader is

analyzed as two components, (1) a frustum of a cone minus a smalldiameter cylinder (which will always be oil filled), and (2) a spooldefined by the spreader skirt and flume (which will contain an o/winterface, the level of which being determined by qo). The volumeof the first component is expressed in Eq. D-4.

Vc hc3r2s rs rF 2r2F. (D-4). . . . . . . . . . . . . . . . .

The buoyant force resulting from water being displaced from theconical component by oil is shown in Eq. D-5, which follows fromEq. D-4.

Fbc 62.37(w o)hc3r2s rs rF 2r2F. (D-5). . . . .

Eq. D-6 describes the buoyant force resulting from oil accumula-tion within the spreader skirt.

Fbs 62.37 Z r2s r2F(w o)12. (D-6). . . . . . . . . . . . .

The resultant buoyed weight of the oil-phase spreader follows.

Wb Wbw Fbc Fbs. (D-7). . . . . . . . . . . . . . . . . . . . . . . . .

Eq. D-8 was derived by substituting Eqs. D-3, D-5, and D-6 intoD-7.

Wb Wu 1 ws2rs hs [rs rF]h2c (rs rF)20.562.37(w o)hc3r2s rs rF 2r2F Zr2s r2F12

(D-8). . . . . . . . . . . . . . . . . . . . .

In the event Wb becomes negative, the spreader will float unlessit is attached to the tank. The maximum buoyant effect occurs athigh qo , when the spreader is oil filled and spillover is impending.Eq. D-8 may be used to calculate Wb under this condition by settingZ=12 hs.

Eq. D-9 was derived from Eq. D-8 by setting Wb0 and Z=12 hs,and solving for Wu . The result is Wun .

Wun 62.37(w o)hc3r2s rs rF 2r2F hsr2s r2F

1 ws2rs hs [rs rF]h2c (rs rF)20.5(D-9). . . . . . . . . . . . . . . . . . . . .

If application of Eq. D-8 indicates that a net upward force couldoccur, the value of Z resulting in a neutral force may be computedwith Eq. D-10. This equation was derived from Eq. D-8 by settingWb0 and solving for Z.

Zn

Wu 1 ws2rs hs [rs rF]h2c (rs rF)20.55.1975(w o)r2s r2F

60 SPE Production & Facilities, February 1996

4hcr2s rs rF 2r2F

r2s r2F. (D-10). . . . . . . . . . . . . . . . . . . . . . .

( % $

g/cm3Btu 1.055 056 E00kJcp 1.0* E03Pasft 3.048* E01m

ft2 9.290 304* E02m2ft3 2.831 685 E02m3F (F32)/1.8Cin. 2.54* E00cmlbf 4.448 222 E00N

lbm 4.535 924 E01kgmile 1.609 344* E00km

psi 6.894 757 E00kPaR 5/9 K

*Conversion factor is exact. SPEPF

! " # $ % " & $ $ " ' % & ())* # & " ())+ " &" " , $

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