S. Wang, SPE, R.S. Mohan, SPE, and 0. Shoham, SPE, The U. of Tulsa, and

G.E. Kouba, SPE, Chevron Petroleum Technology Co,

Summary

Gas/Liquid Cylindrical Cyclone (GLCC, copyright, the U. of Tulsa,1994) separator performance can be improved considerably byadopting a suitable control strategy to reduce liquid carry-over intothe gas stream or gas carry-under into the liquid stream. A dynamicmodel for control of GLCC liquid level and pressure with classicalcontrol techniques is developed in this paper for the first time.Detailed analysis of the GLCC control-system stability and tran-sient response indicates that liquid-Ievel control can be achievedeffectively by a control valve in the liquid outlet for gas-dominatedsystems or by a control valve in the gas outlet for liquid-dominatedsystems. Based on the proposed linear-control system model, thesystem performance is simulated with a suitable software designtool. Experimental investigations have been conducted to evaluatethe liquid-Ievel and pressure-control systems. The novel control-

system design approach presented in this paper forms a frameworkfor the GLCC active control-system optimization.

IntroductionThe petroleum industry has traditionally relied on conventionalvessel-type separators, which are bulky, heavy, and expensive incapital, installation, and operation. Compact separators, such as theGLCC, are now becoming increasingly popular because they are

simple, compact, lightweight, inexpensive, low-maintenance, andeasy to install and operate. The development ranking of the variousseparation-technology alternativesl shows that conventional vessel-ty.Pe separators have reached their maturity, except fQrsome minorimprovements that are being incorporated, such as new develop-ments of internal devices and control systems. Potential applica-tions of GLCC include performance enhancement of multiphasemeters, multiphase flow pumps, and desanders through control ofgas/liquid ratio, partial processing, portable well-testing equipment,flare gas scrubbers, slug catchers, downhole separators, preseparators,and primary separators.2.3

The GLCC separator has a simple construction with neithermoving parts nor internal devices. It is a vertically installed pipemounted with a downward-inclined tangential inlet, with outlets forgas and liquid provided at the top and bottom of the pipe. The twophases of the incoming mixture are separated owing to the centrifugal/buoyancy forces produced by the swirling motion and the gravityforces acting on the phases. The liquid is forced radially toward thewall of the cylinder and is collected from the bottom, while the gasmoves to the center of the cyclone and is taken out from the top.

Applications to date have been for GLCC loop configurationsin which the gas and liquid outlets are recombined, such as in amultiphase metering loop. This configuration is self -regulating forsmall flow variations. However, many field applications other thanmetering are characterized by separate gas and liquid outlets.GLCC's used in such configurations must have liquid-Ievel andpressure control so as to prevent, or delay, the onset of liquid carry-over into the gas stream or gas carry-under into the liquid stream.Also, the GLCC loop operation could be improved for large flowvariations through suitable liquid-level control. Different GLCC

control-system strategies are briefly discussed by Wang4 andMohan et al.5

This paper presents, for the first time, a dynamic model for controlof GLCC liquid level and pressure using classical control strategies.The dynamic model is especially significant for GLCC's operatingunder slug flow conditions. The results of a detailed system-stabilityanalysis performed with the dynamic model are also discussed. Thisanalysis showed that system stability could be ensured by appropri-ately designing the controller and control valve. It is concluded thatthe liquid-Ievel control could be achieved effectively by a controlvalve in the liquid outlet for gas-dominated systems or by a controlvalve in the gas outlet for liquid-dominated systems. A control valvein the gas outlet for any inflow condition could achieve GLCC pres-sure control. Based on the proposed linear control-system model, asample control-system design is performed and the system-transientresponse is simulated with suitable software. A design framework forimplementation of the GLCC control system using a dedicated simu-lator is finally presented.

Literature Review

Arpandi et al.6 and Marti et al: have conducted detailed reviews ofthe literature on separation technology, revealing that very littleinformation is available about the optimum design and performanceof the GLCC. Most of the investigations are based on experimentalcorrelation. The existing mathematical models for cyclone separa-tors have been limited to single-phase flow with low concentrationof a dispersed phase. Also, no reliable models are available forcyclonesB (conical or cylindrical) that are capable of simulating afull range of multiphase flows entering and separating in a cyclone.

Several investigators3.4.5.9 have realized that the performance ofcompact separators could be improved by incorporating suitablecontrol systems. Kolpak9 developed a hydrostatic model for passivecontrol of compact separators in a metering loop configuration. Thismodel provides the sensitivity of the liquid level to the gas and liquidinflow rates. For gasniquid two-phase flow separators that operateunder slug flow conditions, the system dynamics are crucial, espe-cially when a control system is added to the separator. Genceli etal.!O developed a dynamic model for a slug catcher. The systemresponse of slug catchers was found to be quite slow because of thelarge residence time of the big vessel. Roy and Smith!! discussed thecontrol algorithms in digital controllers to meet the goal of averaginglevel control for a single-phase surge tank system. These controlalgorithms are a primary concern in chemical processes, wheresmooth outlet flow from the tank is very important. Galichet et al.!2presented the development of a fuzzy-Iogic controller that maintainsa floating level in a tank (single-phase flow) on top of an atrnos-pheric distillation unit of a refinery. The authors of this paper4.5 havedeveloped a steady-state model for GLCC control and performed asensitivity analysis. Detailed experimental investigations on a newlydeveloped GLCC passive control system demonstrated that thepassive control system improved the GLCC operational envelope ina restricted range of flow conditions.

From the above discussion, it can be noted that compact multiphaseseparation technology research remains critical for the petroleumindustry. Development of this technology can have a tremendousimpact in improving the optimization and productivity of the industry.Previous studies also demonstrate that the performance of compactseparators could be enhanced considerably by incorporating controlsystems. However, for the GLCC, there is an increasing need to

Copyright @ 2001 Society of Petroleum Engineers

This paper (SPE 71308) was revised for publication from paper SPE 49175, prepared for

presentation at the 1998 SPE Annual Technicai Conference and Exhibition, New Orleans,27-30 September. Original manuscript received for review 24 March 1999. Revised man-uscript received 12 December 2000 Manuscript peer approved 19 February 2001.

236June 2001 SPE Journal

kd = dimensionless penneability retainedkda = adjusted penneability retained, fractionkeg = effective gas penneability, mdkt = penneability at final stress, md

kta = adjusted final penneability, mdkg = Klinkenberg absolute gas penneability, mdki = penneability at initial stress, md

kia = adjusted initial penneability, mdko = penneability at zero stress, mdkw = absolute penneability to brine, mdNd = dimensionless porosity retained

Nda = adjusted porosity retained, fractionNeff = effective porosity, fractionNi = porosity at initial stress

Nia = adjusted initial porosity, fractionNt = porosity at final stress

Nta = adjusted final porosity, fractionNo = porosity at zero stress, fractionp = overburden pressure

Pc = capillary pressurep o = initial overburden pressure<1> = net isostatic stress, psi

<1>* = decay constant (3,000), psiPhi Grain Size Scale: d = 2-pmWhere: d = grain diameter in millimeters, then:log d = -phi log 2

d = -0.30l03phiq = rate of flow

AcknowledgmentsWe gratefully acknowledge the contributions of the followingfunding organizations and individuals: Gas Research Inst. andStephen A. Holditch of S.A. Holditch and Assocs. Inc., for theTravis Peak data set; U.S. Dept. of Energy Class III ReservoirProgram, Tidelands Oil Producing Co.; and P. Scott Hara andJulius J. Mondragon for assistance with data generation for theWilmington Field (fault Block IIA) data set.

13. McKee, C.R., Bumb, A.C., and Koenig, R.A.: "Stress-Dependent

Permeability and Porosity of Coal and Other Geologic Formations,"SPEFE (March 1988) 81.

14. Walls, J.D.: "Tight Gas Sands-Permeability, Pore Structure, and Clay,"IPT (November 1982) 2708.

15. Soedder, D.J. and Randolf, P.L.: "Porosity;'Permeability and Pore

Structure of the Tight Mesaverde Sandstone, Piceance Basin,

Colorado," SPEFE (June 1987) 129; Trans., AIME, 283.16. Rhett, D.W. and Teufel, D.W.: "Stress Dependence of Matrix

Permeability of North Sea Sandstone Reservoir Rock," Proc., 33rd U.S.Symposium on Rock Mechanics, Washington, DC (1996) 345.

17. Bruno, M.S., Bovberg, C.A., and Nakagawa, F.M.: "Anisotropic Stress

Influence on the Permeability of Weakly Cemented Sandstones,"Proc., 32nd U.S. Symposium on Rock Mechanics, Washington, DC(1991) 375.

18. Krishnan, GR., Zaman, M.M" and Roegiers, J.C.: "Permeability

Measurements Under Different Stress Paths for a Weakly Cemented

Sandstone," Proc., Second North American Rock MechanicsSymposium, Washington, DC (1996) 1011.

19. Crawford, B" Yale, D., and Hutcheon, R.: "Experimental Yielding of

Compacting Sediments, Coupled Mechanical Deformation and FluidFlow in Granular Reservoir Media," Proc., Ninth IntI. Congress onRock Mechanics, Paris (1998) 747.

20. Archer, J.S.: "Reservoir Characterization and Modelling: A Frameworkfor Field Development," Structural Geology in Reservoir

Characterization, M.P. Coward, T.S. Daltaban, and H. Johnson (eds.),Special Publication No.127 , Geological Society, London (1998) 15-18.

21. Griffiths, J.C.: Scientific Method in Analysis of Sediments, McGraw

Hill Book Co" New York City (1967) 508.22. Taylor, J.M.: "Pore-Space Reduction in Sandstones," Bull. Am. Assoc.

Petroleum Geol. (1950) 34,701.23. Davies, D.K" Vessell, J.M" and Auman, J.B.: "Improved Prediction of

Reservoir Behavior Through Integration of Quantitative Geological and

Petrophysical Data," SPEREE (April 1999) 149.24. Clelland, W.D. and Fens, T.W.: "Automated Rock Characterization

with SEM/Image Analysis Techniques," SPEFE (December 1991) 437.25. API RP40, Recommended Practice for Core Analysis, second edition,

API, Washington, DC (1998).26. Walder, I. and Nur, A.: "Permeability Measurements by the Pulse

Decay Method: Effects of Poroelastic Phenomena and Non-Linear PorePressure Diffusion," lnt. I. Rock Mechanics and Mining Sciences

(1986) 23,225.27. Jones, S.C.: "Two-Point Detenninations of Permeability and PV vs. Net

Confining Stress," SPEFE (March 1988) 235.28. Timur, A.: "Pulsed Nuclear Magnetic Resonance Studies of Porosity,

Movable Fluid, and Permeability of Sandstones," IPT (June 1969);

Trans., AIME, 246.

SI Metric Conversion Factors

ft x 3.048* E -01 = min. x 2.54* E + 00 = cmpsi X 6.894757 E + 00 = kPa

psi2 X 4.7538 E + 01 = kPa2

.Conversion factor is exact. SPEJ

John P. Davies is a reservoir engineer in the Mid-ContinentDiv. of Chevron U.S.A. Inc., Houston. e-mail: jopd@chevron.com. He specializes in the integrated analysis andsimulation of complex, fractured, and nonfractured reser-voirs. He holds BS and PhD degrees in petroleum engineeringfrom Texas A&M U. and an MS degree in petroleum engi-neering from the U. of Texas at Austin. David K. Davies is areservoir scientist and President of David K. Davies andAssocs. Inc., Houston. e-mail: dkdavies@earthlink.net. Hespecializes in all aspects of reservoir description, evaluation,and characterization. Davies holds BS, PhD, and DScdegrees in geology from the U. of Wales, Swansea, and anMS degree in geology from Louisiana State U. He is a pastSPE Distinguished Lecturer.

References

1. Zimrnennan, R. W.: Compressibility of Sandstones, Elsevier, New York

City (1991) 173.2. Fatt, I. and Davis, D.H.: "Reduction in Penneability witb Overburden

Pressure," JPT (December 1952) 16; Trans., AIME, 195.3. McLatchie, A.S., Hemstock, R.A., and Young, J.W.: "The Effective

Compressibility of Reservoir Rock and Its Effects on Penneability,"JPT (June 1958) 49; Trans., AIME, 213.

4. Wyble, D.O.: "Effect of Applied Pressure on tbe Conductivity, Porosity,

and Penneability of Sandstones," JPT (November 1958) 57; Trans.,

AIME, 213.5. Dobrynin, V.M.: "Effect of Overburden Pressure on Some Properties of

Sandstones," SPEJ (December 1962) 360; Trans., AIME, 225.6. Vairogs, J. et al.: "Effect of Rock Stress on Gas Production From Low-

Penneability Reservoirs," JPT (September 1971) 1161; Trans., AIME, 251.7. Thomas, R. W. and Ward, D.C.: "Effect of Overburden Pressure and

Water Saturation on Gas Penneability of Tight Sandstone Cores," JPT

(February 1972) 120.8. Jones, F.O. and Owens, W.W.: "A Laboratory Study of Low-

Penneability Gas Sands," JPT (September 1980) 1631.9. Wei, K.K., Morrow, N.R., and Brower, K.R.: "Effect of Fluid,

Confining Pressure, and Temperature on Absolute Penneabilities of

Low-Penneability Sandstones," SPEFE (August 1986) 413.10. Seeburger, D.A. and Nur, A.: "A Pore Space Model for Rock

Penneability and Bulk Modulus," J. Geophysical Res. (1984) 89,527.11. Jamtveit, B. and Yardley, B. W.D.: Fluid Flow and Transport in Rocks:

Mechanisms and Effects. Chapman and Hill Co" London (1997) 319.12. Tiab, D. and Donaldson, E.C.: Petrophysics: Theory and Practice of

Measuring Reservoir Rock and Fluid Transport Properties, GulfPublishing Co., Houston (1996) 706.

June 2001 SPE Journal235

Pressure Controller

0 1Pressure

Transducer,~ Control Valve

..

develop appropriate control strategies, that are different from thoseof the conventional separators, because the GLCC residence time isvery small. Also, no dynamic models are currently available forcontrol-system design of GLCC. Thus, the overall objective of thisinvestigation is to expand the state of the art of GLCC technologythrough development of suitable control strategies.

Dynamic Modeling and Stability Analysis

System Definition. A schematic of the GLCC control system isshown in Fig. I. The GLCC separator has a two-phase flow inletand single-phase gas and liquid outlets. A level sensor, such as adifferential pressure transducer, is used to determine the dynamicliquid level in the GLCC. The actuating signal from the level sensoris sent to the liquid-level controller, which in turn controls thevalve opening of the liquid outlet correspondingly for normal liquidflow conditions. However, for very large liquid flow conditions,the liquid level may rise even when the liquid leg valve is com-pletely open. During that circumstance, liquid carry-over could beavoided through building up backpressure in the GLCC by closingthe gas outlet valve. The maximum gas and liquid discharge rates13are determined by the capacity of the liquid and gas discharge legs,as given below:

Gas Outlet

Level Controller

...0

~ Control Valve

~

= 0. 002228C: [ p -PLout

V. (1)'Lout

Multiphase FlowLiquid-Level

Transducerand

Liquid Outlet

x=CvN7FDPY.1- (2' Fig. 1-Schematic of GLCC control system.'"ut

'I ,TZ

two-phase flow in the inlet pipe, especially under slug flow condi-tions. This causes the GLCC pressure and liquid level to fluctuateduring operation. These fluctuations affect the perfonnance of theGLCC because the liquid carry-over and gas carry-under mecha-nisms depend strongly on the liquid level in the GLCC. The objec-tive of the control system is to smooth the fluctuations of pressureand liquid level in the GLCC, thereby improving its perfonnance.

A simple block diagram of the control system is given in Fig. 2.The respective sensor measures the controlled parameter (in thiscase the pressure or liquid level in the GLCC) and sends the actu-

where PLoDt and p=the liquid discharge pressure and the GLCCpressure, respectively. CG and Cv=the flow coefficients of the liquidand gas control valves, respectively. N7=the numerical constant,Fp=the piping geometry factor, and Y=the expansion; x=the ratioof pressure drop to upstream absolute static pressure, and JIG andJlL=the gas and liquid specific gravities, respectively.

The GLCC pressure and liquid-level or liquid-discharge ratecan be considered as the controlled parameters. The liquid andgas inlet flow rates usually fluctuate because of the occurrence of

Liquid-Level

Transmitter/Sensor

Liquid Rate In

{

i

I i .iquid LevelI

~Level

Set Point

9~ -)-

iquid

Out """/

Rate r '\.: ~ Relation

GLCC

Pressure

~

Set Point

g.: ~ --)0

GasOut ~~

Rate '\j

Liquid ~d\ .J GasRate In ,\.0 ' Rate In

Fig. 2-Block diagram of the control system,

June 2001 SPE Journal237

ating signal to the corresponding transmitter. The transmitter con-verts the information into a pneumatic pressure signal between 3and l5 psig. The error, the difference between the set-point pres-sure and the actual pressure from the transmitter, is sent to the con-troller. The controller sends the corresponding actuating pressuresignal to the control valve through the pneumatic lines so that it canbe opened or closed accordingly.

where the discharge rates of the liquid and gas leg can be deter-mined from Eqs. I and 2, and

7rd21-VG =vGset -(h-hse,) (10)

Controller Equations. There are three basic types of controllers:proportional (P), integral (I), and derivative (D). PI (proportional-integral), PD (proportional-derivative), and Pill (proportional-integral-derivative) are three combinations of controllers. The mainpurpose of the integral controller is to eliminate the offset thatoccurs in proportional controller systems when not operating at thedesign conditions. The derivative controllers can improve thesystem response because they predict the future and take actionaccordingly. In this study, the PI controller was chosen for the pres-sure control and a PD controller for the liquid-Ievel control toensure a stable system. The mathematical description of a PI con-troller is given by

e+~ fedttr ,

(11)

In Eq. 11, pc=pneumatic pressure to be sent to the controlvalve, po=the initial pressure at the controller, Kc=the controllergain, e=the error, tr=the reset time, and tr=Kcli, where li =theintegral time.

A transmitter linearly converts the measured value of the con-trolled variable into a pneumatic pressure signal ranging from 3 to 15psig. The conversion for the pressure control transmitter is as follows:

PTrnin=3 psig

pTmax= 15 psig

if P~Pmin, and"f >1 P-Pmax,

Mathematical Model. The assumptions for the dynamic modelingare as follows:

.Zero time lags for the liquid and gas discharge legs.

.Constant GLCC temperature and gas-compressibility factor.The differential equations that constitute the mathematical modelfor the GLCC control system are as follows:

.An equation for the rate of change of the liquid volume inthe GLCC.

.An equation for the rate of change of the liquid level inthe GLCC.

.An equation for the rate of change of the pressure in the GLCC.

.An equation for the rate of change of the pneumatic pressureto be sent to the control valve from the pressure controller.

.An equation for the rate of change of the pneumatic pressureto be sent to the control valve from the liquid-level controller.

.An equation for the rate of change of the pneumatic pressureof the control valve at the gas-discharge leg. (This represents thedelay in the pneumatic transmission)ine.)

.An equation for the rate of change of the pneumatic pressureof the control valve at the liquid-discharge leg. (This represents thedelay in the pneumatic transmission line.)

.An equation for the rate of change of the control valve openingat the liquid-discharge leg.

.An equation for the rate of change of the control valve openingat the gas-discharge leg.

The derivation of the equations described above is given below.liquid Volume Rate ofChange. The liquid volume rate of change

is the difference of inlet flow rate and outlet flow rate, namely

where pTmin and PTmax=the minimum and maximum pressuresignal from the transmitter, respectively. For intermediate pressures

(Pmin<P<Pmax),

~dt

= gLin -gLout(3) PT =( 3+12~ ) (psig),

l Pmax Pmin(12)

Liquid Level Rate ofChange. The liquid level rate of change isrelated to the rate of change of the liquid volume by the geometryof the GLCC. and is given as

and the set-point pneumatic pressure is given by

) (psig),PTset =

(13)

(4)

l3+l2~ Prnax PminJ

where (Pmax -PrniJ is the range of the pressure.The error signal, which is the input to the controller, is defined as

e=(pTset-PT) (psi). (14)

Therefore,

4

where d=the inside diameter of the GLCC.Pressure Rate of Change. The equation of state for the gas in

the GLCC is

pVG=ZnGRT. (5) (15)e=KT(Pset-P) (psi), where KT =the transmission gain for the pressure control, and

~JpSI

(6) (16)12

K -T-

Pmax -Prnin

Differentiating Eq. 5 with respect to time yields

VG.2=ZRT!!!!&--p~. dl dl dl

As the volume of the GLCC is constant,

dVG dV:--L ( )dl --~=- qLin -qLout (7)

Substituting e in Eq. 11 yields

Pc =Po +KcKT [ Pset -p+-.!.-f(pset -p)dt

tr

(17)

The gas-mass balance in the GLCC is given by

(8)~=(qGin-qGOut)ff-. G

Substituting Eqs. 7 and 8 in Eq. 6 yields

(9)

Differentiating Eq. 17 with respect to time gives an equation forthe rate of change of the pneumatic pressure to be sent to the gas-control valve from the pressure controller,

~=KK T[ -..2+~ (p t -p )] (18) dl c dl Ir se

The mathematical description of a PD controller for the liquid-level control is given by

238June 2001 SPE Journal

de' determined. At initial condition, X(O)=0, and Pv=3 psig. When pvis suddenly changed to 15 psig (corresponding to a step input), thetime required for the stem position to reach an arbitrarily chosenvalve opening Xtest=ttest and

C" = t

(19)P: = p~ +K~ le' +IDdl J

where ID=the derivative time.Similarly, the pneumatic pressure signal from the liquid-level

transmitter is given by

( \3+12 h-hmin

hmax -hmin

(30)

PT= (20)

( 100

J1nIoo=x:

A similar equation can also be obtained for C~.and the set-point pneumatic pressure is given by

( \ , h -hp = 3+12 set mm

Tseth hmax -min ,

I (psig), (21)

(22)

where (hmax-hmjJ is the range of the liquid level, and

e'=K~(p~set-P~) (psi)

where

12

l~,K~= - (23)

hmax 'mill

Therefore, the controller equation for the liquid-Ievel controllerbecomes

System-Stability Analysis. The stability analysis of the GLCCcontrol system is performed with a linear system model. The blockdiagram of the linear GLCC control system model is given in Fig.3. The details of the derivation are given in the Appendix.

Stability of the total system should be ensured before designingfor transient-response requirements. The root-locus technique isused to perform the stability analysis. If the root locus of the systemis on the left half of the s-plane, the system is always stable for anygain of the controller and vice versa. If the root locus of the systemis partly on the left and partly on the right half of the s-plane, thesystem could be stable, unstable, or oscillatory, based on the totalsystem gain. Root-locus plot can determine the paths of the systempoles using the loop gain.

Liquid-Level Control Loop. The loop gain of the liquid-levelcontrol loop for a PD controller is given from the linear model

(Appendix) by:

(24)G(S)H(S)=K~(t~S+I)

( 1KJ' ( 1 J ' (31) s s+--. s+-.

Co To .

where G(S) and H(s)= the feedforward loop-transfer function andfeedback loop-transfer function, respectively. K~=liquid-legvalve-controller gain. K' is given by

Taking the derivative with respect to time yields the equation forthe rate of change of pneumatic pressure to be sent to the liquidcontrol valve from the liquid-level controller:

,/ d2h '\

(25)dp , , l dh J--2---KK ---1 -

dl -c T dl D dl2

K' = D2G'--;--;- (32)Pneumatic Transmission Line Equations. The pressure signal

is sent through a pneumatic transmission line to the control valvefrom the controller. Therefore, some kind of delay is expected tooccur until the signal reaches the valve. In this study, the delay isapproximated as followsl4:

Co To

and G' is given by

Pv = Pc +(Pv" -pj eX. (26)

Control- Valve Equations. There are two kinds of controlvalves. air-to-open and air-to-close. The type of valve to be used isdetennined by safety considerations. The valves that are used forthe GLCC control system were chosen to be air-to-close valves. Ifthe air pressure fails, the pressure and the liquid level in the GLCCwill not increase significantly.

The first order approximation of the control-valve equationlO isgiven by

~=(l5-Pv-&X )~ (28)

for the pressure-control valve, and

~=(l5-P:-&X')~ (29)

for the liquid-level control valve, where X and x' =the positions ofvalve stem; Co and C~=constants, which can be experimentally

r~,

\,~x ,

100G =D (36)

June 2001 SPE Journal239

~ =x"' Pmax -Pmin

The root -locus plots for small and large values of reset times aregiven in Figs. Sa and Sb, respectively, for specific valve-responsetime and the time constant of the pneumatic transmission line.

Note that for specific values of Co (say, 2 seconds) and To (say,0.4 seconds), two paths of the root locus for a small value of tr (say,0.1 seconds) are located on the right half of the s-plane for anyvalue of gain, which means that the system is always unstable.Considering the root locus for large values of tr (say, 10 seconds),two paths of the root locus will pass through the imaginary axis asgain increases, which means that the system is stable for small valuesof total-system loop gain and unstable for large values of gain(>3.45). For system-loop gains of 3.45 or less, the system isalways stable (or oscillatory) with a step input, as shown in Fig. 6a.Similarly, for loop gains larger than 3.45, the system is unstablewith a step input, as shown in Fig. 6b.

The above analysis of the liquid-level and pressure-controlsystems provides fundamental knowledge of the system behavior.However, for a given GLCC specification and operating condi-tions, it is necessary to design a suitable controller (P, PD, PI, orPill) to satisfy the transient-response requirement. This could beevaluated through simulating the system transient behavior. A

-21-3 -1 O 2

Real Axis

Fig. 4-Root locus for liquid-Ievel control loop.

2 3

tr = 0.2

secondsc~ = 2 secondsT ~ = 0.4 seconds 1.5

0.5

-0.5

cn"x«>-~~c"~~E

~

(1)"x«>.'-~c

.'6>~

E

-1.5

0.4' 0.6-8 -6 -4 -2 0 2 4 -I -0.8 -Q.6 -Q.4 -0.2 0 0.2

Real Axis Real Axis

Fig. 5-Root locus for pressure-controlloop: (a) and (b).

0.8.16 -14 -12 -10

240 June 2001 SPE Journal

KG(s) H(s)=K; (37)+-;-+tDS

trs

~~or

Kr k' G(s) H(s)= kp +-L+sk~

.I'

s ( s+-1-

c;

s+'ro )

,( k' ,

k S2 +-E-+~d k' k'

d d K(38)

/ , , ,

sl s+-k Jl s+~ J

sample design is given later for the GLCC liquid level and pressure-control system that is performed with a software design tool, name-ly MATLAB.15 This is followed by a discussion of the transient-response simulation conducted with Simulink.15

Control-System Design and Transient-Response Simulation

Specifications for control-system design are system stability, tran-sient response (rise time, percentage overshoot, and settling time),and steady-state error. To design a control system, first we need tocheck the stability of the system, and then simulate the transientresponse of the system to satisfy the design specifications. Theroot-locus technique, which is one of the powerful control-systemdesign tools, can be used to evaluate the stability of the system.This technique is used in this study to conduct the system design.The procedure is as follows:

.Plot the root locus using MATLABI6.17 using the open-looptransfer function.

.Optimize the root locus for stability and detennine the controllerand control-valve parameters.

.Determine the controller gain for the required transient-

response specification..Simulate and evaluate the transient response of the system

using the closed-loop transfer function.

Liquid-Level Control-System Design. The controller design isbased on the GLCC geometry, the specifications of the controlvalve and the pneumatic line, operational conditions, and the fluidproperties. These details are given in Table 1.

The open-loop transfer function for the liquid-level controlloop, equipped with a commercial controller (pm), is given fromthe linear model (Appendix) by

4)

]"E.

~

0 15 2010

Time, seconds

Fig. 6-Pressure-control system step response: (a) stable andoscillatory and (b) unstable.

June 2001 SPE Journal 241

where k~, k; and k~=the proportional, integral, and derivative

gains, respectively.The Pill controller design procedure is as follows:1. Design of P Controller. Plot the root locus for the uncom-

pensated system. Design the value of controller gain K~ to satisfythe percent overshoot of 10%. The transfer function for the root-locus plot is

The settling time reduces to 8 seconds, as shown in Fig. 8,marked "PD." This settling time can be further improved in thePID controller stage.

5. Design a Pill controller to reduce the steady-state error andimprove the settling time.

Any ideal integral compensator zero can eliminate the steady-state error for a step input as long as the zero is placed close to theorigin. The ideal integral compensator can be chosen as

(3H)

(44)

where

k=K~K (40)

The root-locus plot is shown in Fig. 7. The total system gain cor-responding to 10% overshoot is 0.35 as given by the design point.

2. Check second-order approximation for transient response.Because the third closed loop pole ( -2.57) is far from the domi-nant second-order poles, the second-order approximation is validfor the system.

The settling time can be calculated as follows:

where GpAs)=the PI controller transfer function.So the total loop gain (k) for the Pill-compensated system is

4.87, from the modified root locus. The Pill compensator gain K~can be calculated if the system gain K' is known.

6. Comparing the Pill compensator transfer function to the Pillcontroller formula (Eqs. 37 and 38), determine the controller set-tings (gain, integral time, and derivative time). The results of thePill controller design are summarized in Table I.

7. Simulate the system response. The system response is shownin Fig. 8 marked "Pill." The settling time has improved to 5 secondsfor 10% overshoot.

A similar procedure as described above has been adopted forthe designing of a suitable control system for the GLCC pressurecontrol. The results of the Pill controller design for pressure controlare provided in Table 2.

(41)

GLCC Control-System Simulator. Based on the design of thelinear model described in the Appendix, a block diagram of theGLCC control system simulator is developed in this investigationfor system performance evaluation for liquid-level control, which isshown in Fig. 9. The transfer functions corresponding to each blockare provided in this figure. This control-system simulator is a usefultool not only for characterizing the liquid- and/or gas-flow behaviorfor different inflow conditions, but also for providing correspondingGLCC liquid-level and pressure-transient responses. However, itshould be noted that a similar, but separate, block diagram is neces-sary for the GLCC pressure-controlloop. The transient response ofthe control system indicated that the overshoot in the GLCC liquidlevel for such a step input of 0.1 ft3/S is only about 0.7 ft and thatthe settling time is around 4 seconds. This software simulator canbe used for evaluating the behavior of each subsystem in the controlloop in terms of its sensitivity and also for different inflow condi-tions such as ramp, parabolic, or sinusoidal inputs.

Similarly, a simulator has been developed for the GLCC pressure-control loop to evaluate the system behavior. In the interest ofbrevity, the block diagram of this simulator is not provided. Thetransient response of the pressure-controlloop indicated that for astep input of 2 ft3/S gas flow, the overshoot of the pressure, withreference to a set point of 15 psig, is about 2 psi. It may also be noted

3. The simulated system response for unit-step input is shownin Fig. 8 marked "P." From the system response, the settling timeis approximately 20 seconds, which matches the above-calculatedvalue. It is necessary to improve the settling time to accommodatehigher frequency of the disturbance (in this case, the frequency ofthe slug flow).

4. Design a PD controller to reduce the settling time. If the settlingtime is to be reduced to 2 seconds, the real part of the second-orderdominant poles can be calculated as follows:

4(w"=2=2. (42)

Search along the 10% overshoot line for the compensated closed-loop poles whose real part equals 2.

Note that there is a limitation for the settling-time design of aspecific system. The compensated zero should make the systemstable. For this case, the only choice is to pick a compensator zerobetween the origin and the pole closest to the origin ( -0.5). Let thecompensator zero be -0.3; then,

GPD(s)=s+0.3, (43)

where GPD(s)=the PO controller transfer function.

0 5 10 15 20 25 30 35

Fig. 8-Liquid-Ievel control-system step response.

40

Real Axis

Fig. 7-Liquid-Ievel control-system design using root-locus

technique.

242 June 2001 SPE Journal

TABLE 2-GLCC PRESSURE-CONTROL LOOP DESIGNet at., 19 and Wang.20 Part of the experimental results related to the

liquid-Ievel and pressure-control strategy are discussed in thefollowing two cases.~

Pset GLCC initial pressure

PGout Liquid-discharge pressure

YG Specific gravity of gas

MG Molecular weight of gas

T Temperature

Z Compressibility factor of gas

y Expansion factor

N7 Numerical constant

hglcc Total height of GLCC

hset Set-point liquid level

V G Volume of gas in GLCC

Pmax Maximum pressure

15.00

10.00

0.81

20.00

80.00

0.90

0.80

0.37

10.00

4.00

0.29

17.00

psig

psig Case 1: Liquid-Level and Pressure-Control System Response toLiquid-F1ow Surges. The inflow conditions of the GLCC maychange owing to the change of production rate. The control-systemresponse to inflow surges is critical for control-system design. Fig. lOashows the system responses in terms of dynamic liquid level, GLCCpressure, and control-valve positions for a lab test unit at the U. ofTulsa. As can be seen, when step-like liquid-flow surges, superim-posed upon the slug flow, are introduced into the GLCC instanta-neously, liquid level and the GLCC pressure are very well controlledaround their set points (liquid level: 35 in. water; pressure: 20 psia).The initial norninalliquid rate is ~1=2.2 ftls, and the nominal gasflow rate is ~g=4.0 ftls. Suddenly, the liquid flow rate is increased byL\~1=0.27 ftls. After a while, the nominal liquid rate is decreased byL\ ~l= -0.54 ftls from the highest flow rate, ~1=2.47 ftls, to the low-est flow rate, ~l= 1.93 ftls. Then, the liquid flow rate is increased tothe initial value. During this cycle, the liquid level and pressure arecontrolled very well. It is even difficult to identify, from the liquid-level response, whether there are liquid-flow surges. However, it canbe noted very clearly from the liquid control-valve position. The equi-librium control-valve positions are approximately 80% open at normalflow conditions, 90% open for the highest liquid flow rate, and 75%open for the lowest liquid flow rate. The equilibrium gas-control-valve positions for all the conditions are fairly uniform, as the gasflow rate did not change. This demonstrates that the control systemscan control the liquid level and pressure around their set points at dif -ferent normal slug flow conditions, as the instantaneous liquid flowrate for liquid slug is about three times higher than the norninalliquidflow rate. Moreover, the control systems can handle the liquid flowrate surge of 10 to 20% of the norninalliquid flow rate, which issuperimposed upon the normal slug flow. The is the case when theproduction rate changes by 10 to 20%.

(Ib/lb mol)

of

ft

ft

ft3

psig

13.00

0.25

28.00

0.50

2.00

Pmin Minimum pressure psig

d Diameter of the GLCC ft

Cv Gas control-valve flow coefficient

dCv IX Characteristics of control-valve rate of changeof the flow coefficient over the rate of changeof valve opening at the set point

Co Parameter of the control valve srelated to the time response ofthe control valve

T o Time constant of the actuator s

Gain Calculation

0.40

04

03

G

2.55

0.34

4.21

K

k

13.39

9.05

GLCC pressure calculation

Gas control-valve flow-rate calculation

Constant from valve characteristicsand hmax, hmin

System gain

Total-design gain

Calculation of PID Se~

~

Kc

Zd

Zj

Output

Kp I

t,

td

Design-controller gain

Zero of D compensator

Zero of I compensator

0.676

0.200

0.100

p gain

Reset time

0.203

15.000

3.333Derivative time

or

kp

ki

kd

p gain

I gain

D gain

0.203

0.014

0.676

that the transient response of the GLCC pressure is much slower(settling time of about 30 seconds) as compared to the liquid levelbecause of the compressibility of gas.

Experimental ResultsThe liquid- andpressure-control systems developed in this studyhave been tested in the laboratory and applied in the field.Detailed experimental investigations for different control strate-gies and field applications are described in Marrelli et at., 18 Wang

Case 2: Liquid-Level and Pressure-Control System Responses toSevere Slug. Severe slug is a massive liquid slug larger than normalslug. similar to terrain slug, which is formed in a riser pipe or interrain pipeline. In this case, the impact of the severe slug on thecontrol system responses is discussed. Fig. lOb shows the responsesof liquid-level and liquid-control valve (LCV), and liquid slug,pressure, and gas control-valve (GCV) for three consecutive artifi-cial slugs (severe slugs). The initial liquid flow rate is ~1=0.41 ft/s,and the gas flow rate is ~g=6.61 ft/s. The flow pattern for the initialflow condition is slug flow. The liquid-level set point is 25 in. ofwater, and the pressure set point is 21 psia. The severe slug is gener-ated by an inline slug generator. The artificial slug velocity is around7 ft/s, and the slug length is about 15 ft, as compared to the sluglength of 2 to 3 ft for normal slug flow conditions in a 2- ft pipe. Theinstantaneous liquid flow rate is more than 14 times that of thenominal liquid flow rate during the severe slug flow. The liquid slugsare detected using a conductance probe. The length of the three arti-ficial slugs are indicated (about 15 ft) in the plot (dark lines) by theduration time (2.1 seconds) of the slugs as the slug velocity isapproximately 7 ft/s. As can be seen, the liquid level has an over-shoot of about 50 in. and settles down in 25 seconds when a severeslug hits the GLCC. The large overshoot of the liquid level is causedby the small residence time of the GLCC and the high instantaneousliquid rate in the slug. Also, the feedback control system takes sometime to drive the control valve after the liquid level changes. Thisdemonstrates that the feedback control system has the capability ofhandling severe slugs. But the control-valve response time, GLCCcapacity, slug length, and velocity are important parameters thataffect the performance of the feedback control system. Because ofsmall residence time, GLCC's easily get flooded by a long and fast-moving severe slug if the control-valve response is not fast enough.

ConclusionsI. A dynamic model has been developed based on mass-balance

of the liquid and gas in the GLCC for a configuration charac-terized by separate gas and liquid outlets. This model has been

June 2001 SPE Journal243

Liquid Level

~~~

I~~~i Flow rate Volume to Liquid-Ievel PID

! to volume height transmitter gain Controller

~Flow-rate

calculations

~

StepControl-valve

response

Pneumatic

line delay

Out Flow RateFig. 9-GLCC liquid-Ievel control-system simulator.

-Pressure (psia)

~Level (in. water)

-LCV(%open)

-GCV(%close}

~~

~ It-rw -~I ,.

t--~~~r~.f--, ~

(~t~\411 r~"

ItA.. I\AA I\A.~ I~~ .,.P-V'V1ft"V~ I ! W¥1\;;1 -~ v,t \f¥ r

i 15 -

>GI 10

..J5

0

I

1--'

500 1,000 2,000 2,500

Fig. 10-Liquid-Ievel and pressure-control system responses to (a) liquid-flow surges and (b) severe slugs.

used for the GLCC control system design and simulation. Anexample of the control system design is also provided.

2. Detailed analysis of the dynamic model showed that the sys-tem stability and transient-response requirements could beensured by appropriately designing the controller and control-valve characteristics.

3. The PD controller and the PI controller were found to be mostsuitable for liquid-level control and pressure control, respec-tively, from the system stability point of view. However, a Pillcontroller is suitable fo~ both systems in regard to stability andtransient-response considerations.

4. For liquid-dominated systems, liquid-Ievel control using a gas-control valve is desirable. For gas-dominated systems, liquid-level control using a liquid-control valve is desirable.

5. A GLCC control-system simulator has been developed in thisinvestigation, which is capable of optimizing the subsystemperformance and evaluating different inflow conditions such asramp, parabolic, or sinusoidal.

6. Experimental results show that the developed control systemscan control the liquid level and pressure around their set pointsat different slug flow conditions. Moreover, the control systemscan handle the liquid flow rate surge of 10 to 20% of the nominal

244 June 2001 SPE Journal

100'CGI 95 .0)O 90 -

u~ 85.

> 80 -

(.)~ 75 -

70 +-~

65~

~ 60 -

> 55 -

(.)..I 50 .

.! 45 -0)c. 40 -

~ 35 ~ ~~~ :GI 30 ,

; 25 ,

.,

c 20 -

, set = set-point value

T = transmitter

test = test

v = valve

flow rate, superimposed upon the slug flow. The experimentresults also demonstrate that the feedback control system hasthe capability of handling severe slugs.

7. The novel control-system design approach presented in thispaper forms a framework for the GLCC active-control systemoptimization.

NomenclatureCo = time constant of control valve, t, secondsCv = control-valve flow coefficientd = GLCC diameter, L, ft

Dl = constant transfer function for liquid-flow equationD2 = constant transfer function for GLCC geometryD3 = constant transfer function for gas-flow equationD4 = constant transfer function for gas-mass balance

e = controller error, m/Lt2, psiFp = piping geometry factor

G(s) = feedforward loop-transfer function

h = liquid level, L, ftH(s) = feedback loop-transfer function

K = GLCC system gainkd = derivative controller gain

Kc = controller gaink = total GLCC control system loop gaink; = integral controller gainkp = proportional controller gain

M = molecular weightn = number of moles

N7 = numerical constantp = GLCC pressure, m/Lt2, psig

q = volumetric flow rate, L 3/t, ft3/sR = universal gas constant, 10.7317 (lbf/in.2)-ft3nb mol-Rs = Laplace variablet = time, t, secondsti = integral time, t, seconds

tD = derivative time, t, seconds,

tr = reset time, t, secondsT = temperature, T, oR

v = velocity, Ut, ftls

V= volume, L3, ft3x = ratio of pressure drop to upstream static pressurey = expansion factor for gas flowZ = compressibility factor for gas'1 = specific gravity

p = density, m/L 3, lbm/ft3

t = l\amplng ra'tlown = natural frequency, 1/s, rad/sr:o = time constant, t, seconds~ = incremental deviationX = position of control-valve stem, %

Superscripts, = liquid-level control parameters

= average

AcknowledgmentsThe authors wish to thank Tulsa U. Separation Technology Projects

(TUSTP) member companies and Oklahoma Center for theAdvancement of Science and Technology (OCAST AR982-039)for supporting this project.

References

I. Kouba, G.E., Shoham, 0., and Shirazi, S.: "Design and Perfonnance of

Gas-Liquid Cylindrical Cyclone Separators," Proc.. Seventh IntI. Meetingon Multiphase Flow, Cannes, France (1995) 307-327.

2. Kouba, G.E. and Shoham, 0.: "A Review of Gas-Liquid Cylindrical

Cyclone (GLCC) Technology," presented at the 1996 ProductionSeparation Systems IntI. Conference, Aberdeen, U.K., 23-24 April.

3. Gomez, L.E.: "A State-of-the Art Simulator and Field Application

Design of Gas-Liquid Cylindrical Cyclone Separators," MS thesis, U.of Tulsa, Tulsa, Oklahoma (1998).

4. Wang, S.: "Control System Analysis of Gas-Liquid Cylindrical Cyclone

Separators," MS thesis, U. of Tulsa, Tulsa, Oklahoma (1997).5. Mohan, R. et al.; "Design and Performance of Passive Control System

for Gas/Liquid Cylindrical Cyclone Separators," ASME J. EnergyResour. Technology (1998) 120, No. 1,49-55.

6. Arpandi, I.A. et al. ; "Hydrodynamics of Two-Phase Flow in Gas/Liquid

Cylindrical Cyclone Separators," SPEJ (December 1996) 427.7. Marti, S. et al.; "Analysis of Gas Carry-Under in Gas-Liquid

Cylindrical Cyclones," Proc., 1996 Hydrocyclones IntI. Meeting,Cambridge, England, 2-4 April.

8. Motta, B.R.F. et al.; "Simulation of Single-Phase and Two-Phase Flowin Gas-Liquid Cylindrical Cyclone Separators," Proc.. 1997 ASME

Summer Meeting, Fluid Eng. Division, Vancouver, Canada, 22-26 June.9. Kolpak, M.M.: "Passive Level Control in Two-Phase Separator,"

internal communication, Arco Exploration and Production

Technology (1994).10. Genceli, H. et al.; "Dynamic Simulation of Slug Catcher Behavior,"

paper SPE 18235 presented at the 1988 SPE Annual TechnicalConference and Exhibition, Houston, 2-5 October.

11. Roy, S. and Smith, C.: "Better Than Averaging Level Control," U. of

South Florida, In Tech (1995) 50.12. Galichet, S. et al.; "Fuzzy Logic Control of a Floating Level in a

Refinery Tank," Proc.. 1994 IEEE IntI. Conference on Fuzzy Systems,1538-1542.

\3. r\",\\~l C\)\\\!\)\"', lIl\)\\\\~\ ~'d\'d\\)%, \J .':-.to.. \\~~).14. Weber, R.W.: An Introduction to Process Dynamics and Control, Wiley

InterScience, New York City (1973).15. Mathworks Inc., MATLAB, Version 5.1,9, June (1997).16. Nise, N.S.: Control Systems Engineering, second edition,

Benjamin/Cummings, Redwood City, California (1997).17. Leonard, N.E. and Levine, W.S.: Using MATlAB to Analyze and

.DeJ;gn C&nl'r&l J'y.rl'emJ; second edition, BelljamillICummI:ngs,Redwood City, California (1995).

18. Marrelli, J.D. et al.; "Methods for Optimal Matching of Separation and

Metering Facilities for Performance, Cost, and Size: PracticalExamples from Duri Area 10 Expansion," paper ETCE ETCEOO-ER-10165 presented at the 2000 ETCE Conference of the ASME Petroleum

Division, New Orleans, 14-17 February.19. Wang, S. et al.; "Performance Improvement of Gas Liquid Cylindrical

Cyclone Separators Using Integrated Liquid Level and PressureControl Systems," paper ETCE ETCEOO-ER-035 presented at the 2000ETCE Conference of the ASME Petroleum Division, New Orleans,14-17 February .

20. Wang, S.: "Dynamic Simulation, Experimental Investigation and

Control System Design of Gas-Liquid Cylindrical Cyclone Separators,"PhD dissertation, U. of Tulsa, Tulsa, Oklahoma (2000).

SubscriptS'C = controller

D = derivative controller

G = gas

I = integral controller

in = in to GLCC

L = liquid

max = maximum

min = minimum

net = net flow

o = initial value

out = out of GLCC

p = proportional controller

June 2001 SPE Journal~45

Appendix-Linearized ModelThe linear model block diagram is shown in Fig. 3. The lineartransfer functions of the system are a stepwise mathematicaldescription of the system behavior and are always stated in theLaplace domain. The transfer functions relate deviation variablesinstead of the real variables. The deviation variable is the deviationof a variable from its steady-state or set-point value and is denotedby a preceding A.

The derivation of the transfer function is in the order of blocknumbers given in the diagram.

Block I. This is the transfer function for the liquid-level PDcontroller. The mathematical description of a generic PD controllerwas given in Eq. 19. Considering Eq. 19 for liquid-level controlparameters and differentiating, it yields

~IdP: K' ( de'~= c &+tD dr

Summing Junction. At the summing junction, a disturbance isintroduced to the system. The disturbance is the irregularity in theliquid flow into the GLCC and is given as:

Deviation variables are

(A-2)f1p~ = p~ -p~t

and

d,ie' de'---

dt dt(A-3)f1e' = e ess =e

(A-17)s[ ~VL(S)J=~qLin(S)-~qLOUt(S)(A-4)~=K' ( l+t s), , , c D

Therefore,

~~(s)

8els) Block 6. This block is simply the integration block. From the

previous equation,

C1VL(s) (A-l8)

Taking the Laplace transfonnation yields

6p~ ( s ) ,( )--;---( ) =Kc l+fDs de s (A-S) (,1qLin -,1qLout) --:;;

Block 7. The relationship between the liquid level and theGLCC liquid volume was given in Eq. 4. Taking the Laplacetransformation yields

D2=~h(s) 4 (A-19)

Block 2. This is the transfer function of the pneumatic trans-mission line. From Eq. 27, the deviation variables for liquid-Ievelcontrol are

(A-6)11p~ = p~ -p~etl1p~ = p~ -p~et , --

IlVL(s) -1rd2

and

Block 8. This is the gain of the liquid-level transmitter; the

transfer function is

Ap~(s)- 12 (A-20)

d!lp; ~ (A-7)

M(s) h, -hoaround the set point

Block 9. This is the transfer function of the GLCC pressure PIcontroller. Starting from Eq. II and following a similar proceduredescribed for Block I, the following is obtained:

~Pc(s)=K, ( .\

(A-S)

(A-21)

Taking the Laplace transfonnation yields

1lp~(s) ~e'(s)

+-tr s

--;-;-::-I1pcts) Tos+l

Block 3. The differential equation for the control valve is givenin Eq. 29. The deviation variable is

ddX' ~, ,f1x = x -X,et (A-I0)

Eq. 29 becomes

~=- ( ~An'+~, L-'jJv ,dl 12Cn Cn

(A-ll)

Summing junction. The summing junction detennines the net flowin the GLCC. Therefore. the output from the summing junction isTaking the Laplace transformation yields

June 2001 SPE Journal246

~qLin=qLin-qL. (A-15)

The summing junction detennines the rate of change of the liquidvolume as follows:

Blocks 10 through 12. These transfer functions are obtained inthe same way as Blocks 2 through 4 respectively.

Block 13. The gas discharge rate is related to the flow coeffi-cient as given in Eq. 2. For a linear relationship, GLCC pressurewill be replaced by set-point pressure. Then, the transfer function

(A-23)qnet = (/:1qLin + L\qGin) -(/:1qLout + L\qGout)

SI Metric Conversion Factors

ft x 3.048* E -01 = mff X 9.290 304* E -02 = m2ft3 X 2.831685 E -02 = m3

in. X 2.54* E + 00 =(:mpsi X 6.894757 E + 00 = kPa

.Conversion factor is exact.

ddVLdqLin -dqLont =~ (A-24)

and

-MG dl1nG~qGin -~qGont --~.

PG

Therefore, in Laplace domain,

(A-25)

SPEJ

shoubo Wang is a postdoctoral research associate at the U. ofTulsa. e-mail: shoubo-wang@utulsa.edu. Wang conductsresearch in the areas of multi phase flow in pipes, multiphasecompact separators, process control, and control-systemdesign. He holds a BS degree in mechanical engineering fromthe U. of Petroleum, China, and MS and PhD degrees in petro-leum engineering from the U. of Tulsa. Ram s. Mohan is a pro-fessor of mechanical engineering and the associate directorof the Separation Technology Projects (TUSTP) at the U. ofTulsa. e-mail: ram-mohan@utulsa.edu. Mohan teaches andconducts research in the areas of control-system design, com-pact separators, and manufacturing processes. Mohan holds aBS degree in mechanical engineering from the U. of Kerala,India, and MS and PhD degrees in mechanical engineering fromthe U. of Kentucky. Ovadia shoham is a professor of petroleumengineering and the director of the Separation TechnologyProjects (TUSTP) at the U. of Tulsa. e-mail: os@utulsa.edu.Shoham teaches and conducts research in the area ofmodeling two-phase flow and its application in oil and gasproduction, transportation, and separation. He holds a BSdegree in chemical engineering from the Technion, Israel,an MS degree in chemical engineering from the U. ofHouston, and a PhD degree in mechanical engineeringfrom Tel Aviv U., Israel. He served as a member of theProduction Operations Technical Committee from 1989-92and from 1998-2000. Gene E. Kouba is a staff research sci-entist at the Subsea Concepts Team at Chevron PetroleumTechnology Co. email: gkou@chevron.com. His researchinterests include compact separation, multiphase metering,and multiphase-flow simulation. Kouba holds BS and MSdegrees in mechanical engineering from Oklahoma StateU., and a PhD degree in petroleum engineering from the U.of Tulsa.

(A-27)

Block 15. This transfer function relates the net flow into theGLCC to the rate of change of GLCC pressure. The differentialequation was given in Eq. 6. To obtain a linear relationship, p isreplaced by pset, and VG is replaced by VGseto Taking the Laplacetransformation yields

D4 = ~ -~ (A-28)

L\VG(s) VGset

Block 16. This is the gain of the pressure transmitter, whosetransfer function is

L\pT(S) -12

~--(Pmax-Pmin) The input to the system is made up of the set-point deviations.

Because no deviation is desired from the set points, the inputs arezero. Therefore, the summation points determine the errors as

L\e=-L\pT ; L\e'=-L\p~. (A-30)

(A-29)

June 2001 SPE Journal 247

(A-26)

Block 14. This block is simply the integration block. From the

previous equation,