[机械模具数控自动化专业毕业设计外文文献及翻译]【期刊】石油生产设备中三相重力分离器的建模与控制-外文文献

Modeling and Control of Three-Phase Gravity Separators in OilProduction FacilitiesAtalla F. Sayda and James H. TaylorAbstract Oil production facilities exhibit complex andchallenging dynamic behavior. A dynamic mathematical mod-eling study was done to address the tasks of design, controland optimization of such facilities. The focus of this paper ison the three-phase separator, where each phases dynamicsare modeled. The hydrodynamics of liquid-liquid separationare modeled based on the American Petroleum Institutedesign criteria. Given some simplifying assumptions, the oiland gas phases dynamic behaviors are modeled assumingvapor-liquid phase equilibrium at the oil surface. In order tovalidate the developed mathematical model, an oil productionfacility simulation was designed and implemented based onsuch models. The simulation model consists of a two-phaseseparator followed by a three-phase separator. An upset in theoil component of the incoming oil-well stream is introducedto analyze its effect of the different process variables andproduced oil quality. The simulation results demonstrate thesophistication of the model in spite of its simplicity.I. INTRODUCTIONThe function of an oil production facility is to separate theoil well stream into three components or “phases” (oil, gas,and water), and process these phases into some marketableproducts or dispose of them in an environmentally accept-able manner. In mechanical devices called “separators”, gasis flashed from the liquids and “free water” is separatedfrom the oil. These steps remove enough light hydrocarbonsto produce a stable crude oil with the volatility (i.e., vaporpressure) to meet sales criteria. Separators are classified as“two-phase” if they separate gas from the total liquid streamand “three-phase” if they also separate the liquid stream intoits crude oil and water components. The gas that is separatedis compressed and treated for sales 1. Modeling suchfacilities has become very crucial for controller design, faultdetection and isolation, process optimization, and dynamicsimulation. In this paper, we focus on three-phase gravityseparators as they form the main processes in the upstreampetroleum industry, and have a significant economic impacton produced oil quality.Three-phase separators have rich and complex dynam-ics, which span from hydrodynamics to thermodynamicsand conservation laws. Many modeling techniques andapproaches have been used to model three-phase separators.As far as the thermodynamics aspects of the separator areconcerned (i.e., the oil and gas phases), many modelingapproaches have been suggested in the literature. The phaseequilibrium modeling approach have been used for 50 yearsJames H. Taylor is a professor with the Department of Electrical &Computer Engineering, University of New Brunswick, PO Box 4400,Fredericton, NB CANADA E3B 5A3 jtaylorunb.caAtalla F. Sayda is a PhD candidate with the Department of Electrical& Computer Engineering, University of New Brunswick, PO Box 4400,Fredericton, NB CANADA E3B 5A3 atalla.saydaunb.caand has provided satisfactory results for such equipment asflash tanks and distillation columns 2. The basic equationsin this approach are used to describe the material balances,equilibrium relations, the composition summation equa-tions, and the enthalpy equations. Nonequilibrium modelshave been developed to describe real physical separationprocesses; other modeling approaches were also consideredsuch as the computational model, the collocation model,and the bubble residence contact time model 3.Historically, the hydrodynamics of the separators aque-ous part have been modeled using complex mathematical-numerical models, which describe the coalescence andsettling of oil droplets in oil-water dispersions. Such modelstake into account separator dimensions, flow rates, fluidphysical properties, fluid quality and drop size distribution.The output of these models is the quality of the outputoil 4. Other models, which describe the kinetics of lowReynolds number coalescence of oil droplets in water-oil dispersions, have been developed to give the volumesof separated continuous-phase and coalesced drops 5. Acomputational fluid dynamic (CFD) model was developedto model the hydrodynamics of a three-phase separator,based on the time averaging of Navier-stokes equations forthree phases; it takes into consideration the non-ideal flowdue to inlet /outlets and internal equipment for separationenhancement 6. The “alternative path model approach”,which exploits the residence time distribution (RTD) of bothoil and aqueous phases in three-phase separators, was de-veloped to give a quantitative description of hydrodynamicsand mixing in the aqueous phase 7. Powers 8 extendedthe American Petroleum Institute (API) gravity separatordesign criteria to design free-water knockout vessels forbetter capacity and performance. Powers showed that theAPI design criteria can handle nonideal flow by performingpractical RTD experiments.This paper extends the API static design criteria tomodel the hydrodynamics of three phase separators, whichresults in a simpler modeling approach. Furthermore, asimple phase equilibrium model is developed to model thethermodynamic aspects of the separator. We describe theoperation of gravity three-phase separators in section 2. Adynamic model of the separator is developed for each phasein section 3, where it can be used to estimate the steadystate flows and to study the separator behavior during otheroperating conditions. An oil production facility simulationmodel is designed, implemented and tested to validate anddemonstrate the separator behavior during normal operationand upsets in section 4. Finally, simulation results arediscussed and summarized in section 5.II. THREE-PHASE GRAVITY SEPARATION PROCESSDESCRIPTIONThree-phase separators are designed to separate and re-move the free water from the mixture of crude oil and water.Figure 1 is a schematic of a three phase horizontal separator.The fluid enters the separator and hits an inlet diverter.This sudden change in momentum does the initial grossseparation of liquid and vapor. In most designs, the inletdiverter contains a downcomer that directs the liquid flowbelow the oil /water interface. This forces the inlet mixtureof oil and water to mix with the water continuous phase (i.e.,aqueous phase) in the bottom of the vessel and rise to theoil /water interface. This process is called “water-washing”;it promotes the coalescence of water droplets which areentrained in the oil continuous phase. The inlet diverterassures that little gas is carried with the liquid and assuresthat the liquid is not injected above the gas /oil or oil /waterinterface, which would mix the liquid retained in the vesseland make control of the oil /water interface difficult.Some of the gas flows over the inlet diverter and thenhorizontally through the gravity settling section above theliquid. As the gas flows through this section, small drops ofliquid that were entrained in the gas and not separated bythe inlet diverter are separated out by gravity and fall to thegas-liquid interface. Some of the drops are of such a smalldiameter that they are not easily separated in the gravitysettling section. Before the gas leaves the vessel it passesthrough a coalescing section or mist extractor to coalesceand remove them before the gas leaves the vessel. Fig. 1: Three phase horizontal separator schematic.III. THREE PHASE GRAVITY SEPARATORMATHEMATICAL MODELINGWhen the hydrocarbon fluid stream enters a three-phaseseparator, two distinctive phenomena take place. The firstphenomenon is fluid dynamic, which is characterized bythe gravity separation of oil and water droplets entrainedin the aqueous and the oil phases respectively, the gravityseparation of gas bubbles entrained in the stream, and thegravity separation of liquid droplets which are dispersed inthe gas phase. The second phenomenon is thermodynamic,in the sense that some light hydrocarbons and gas solutionflash out the oil phase and reach a state of equilibrium dueto the pressure drop in the separator. Due to the complexityof such phenomena, we are going to focus on the hydro-dynamic separation of oil droplets entrained in the aqueousphase and the thermodynamic separation of gas and lighthydrocarbons from the oil phase. This decision is justifiedby the fact that the water washing process minimizes thewater entrained in the oil phase. Furthermore, precedinggravity separation processes minimize the amounts of gasentrained in the main stream.Figure 2 illustrates the simplified separation process,where an oil-well fluid with molar flow Fin and gas, oil,and water molar fractions Zg; Zo; Zw respectively entersthe separator. The hydrocarbon component of the fluidseparates into two parts; the first stream Fh1 separates bygravity and enters the oil phase, and the second stream Fh2stays in the aqueous phase due to incomplete separation.The liquid discharge from the aqueous phase FWout isa combination of the dumped water stream FW plus theunseparated hydrocarbon stream Fh2. The gas componentin the separated hydrocarbon stream, which enters the oilphase, separates into two parts; the first gas stream Fg1flashes out of the oil phase due to the pressure drop in theseparator, and the second gas stream Fg2 stays dissolved inthe oil phase. The oil discharge Foout from the separatorcontains the oil component of the separated hydrocarbonFo and the dissolved gas component Fg2. The flashed gasFgout flows out of the separator for further processing.Fig. 2: Main separated component streams in three-phasegravity separatorWe model the dynamics of each phase of the separa-tor in the subsequent sections, to simplify the modelingprocess. Additionally, some simplifying assumptions haveto be made. The separation processes are assumed to beisothermal in all phases of the separator at 100oF. We alsoassume that the flow pattern in the liquid phases is plugflow, especially in the aqueous phase. Furthermore, the oildroplets in the aqueous phase have a uniform droplet sizedistribution with a diameter of dm = 500 micron. The oildroplets rising velocities are assumed to obey Stokes law.We model the equilibrium thermodynamics phenomenonunder the assumption that Raoults law is valid. We assumethat only one light hydrocarbon gas flashes out the oil phaseinto the gas phase, namely methane. Methane in the vaporphase is also assumed to be an ideal gas (i.e., the ideal gaslaw applies). Finally, there is liquid-vapor equilibrium atthe oil surface and liquid-liquid equilibrium at the water-oilinterface.A. The aqueous phaseIn order to model the aqueous phase of the separator, wewill follow the API static design criteria under the usualsimplifying assumptions. The API specification permitshydrocarbon droplets (i.e., oil and dissolved light gas) ofdesign diameter to rise from the bottom of the separator tothe surface during the water retention period, as illustratedin figure 3. A hydrocarbon droplet located on the cylinderbottom has the greatest distance to traverse to the oil-waterinterface. Therefore, modeling the oil separation hydrody-namics based on removal of this droplet would ensure re-moval of all others of the same or larger diameter. Given thesimplifying assumptions, the traversing hydrocarbon dropleton its path to the oil-water interface is subjected to a verticalrising velocity component vv governed by Stokes law, anda horizontal velocity component vh governed by the plugflow pattern of the aqueous phase. The vertical velocitycomponent is estimated from Stokes law by equation (1):vv = 1:7886106(SGh SGw)d2mw (1)where SGh;SGw are the specific gravities of the hydro-carbon droplets and water, respectively, dm is the dropletdiameter in microns, and w is the water viscosity in CPat 100oF. The horizontal velocity component is estimatedfrom the aqueous phase retention as vh = L=, where Lis the length of the separator and = Vwat =Fwat is theretention time of the aqueous phase; Vwat is the volume ofthe aqueous phase, and Fwat is the water outflow. The levelof the oil-water interface h is determined from equations(2):Ac = Vwat=L= R2 0:5R2 sin(2 )h = R(1cos( ) (2)where Ac is the cross-sectional area of the aqueous phase,R is the separator radius and is the angle which definesthe circle sector of the cross sectional area Ac. The angle of the longest droplet path to the oil-water interface canbe estimated from equation (3): = tan1 vvvh(3) Fig. 3: Oil separation hydrodynamics under normaloperation conditionsThe design parameters fAc; h; ; g of the aqueousphase will take their nominal values under normal operatingconditions of the three-phase separator, i.e., for the nominalvalue of Fwat which leads to complete separation, as shownin figure 3. However, our model must also be valid for off-nominal values. This is complicated at higher flow values,since we can no longer achieve complete separation. Letus assume that the water outflow Fwat has increased by avalue of Fwat due to a corresponding increase in inflow.This will result in an increase in vh to vh + vh and anangle change of the longest path of a traversing hydrocarbondroplet from to 1 L0 else (8) Fig. 5: Unseparated hydrocarbon fluid volume under highwater outflow conditionHaving estimated the unseparated hydrocarbon fluid vol-ume fraction , we can calculate the separated and unsepa-rated volumetric flow components of the hydrocarbon fluidFh1v; Fh2v respectively. Finally we can write the dynamicmaterial balance of the aqueous phase by using equations(9), after we convert the molar flows to volumetric flows:Fh1v = (Zg +Zo)FinMwh62:43SGhFh2v = (1)(Zg +Zo)FinMwh62:43SGhFWout = ZwFinMww62:43SGw+Fh2vdVwatdt =FinMwin62:43SGin FWout Fh1v (9)where fMwh; Mww; Mwing are the hydrocarbon,water, and incoming mixture molecular weights;fSGh; SGw; SGing are the hydrocarbon, water, andincoming mixture specific gravities; Vwat is the aqueousphase volume; and FWout is the water discharge volumetricoutflow.B. The oil phaseIn order to model the thermodynamic phenomenon in theoil phase, we first do the flash calculations to estimate theamounts of gas which will flash out of solution. Since weassumed that ideal phase equilibrium state is valid, then byapplying Raoults law we can tell how much methane willstay entrained in the oil phase. Raoults law relates the vaporpressure of components to the composition of the solution.This can be formulated mathematically as yiP = xiPviwhere yi is the mole fraction of the component i in the vaporphase, xi is the mole fraction of component i in the liquidphase, P is the total pressure of the vapor phase (i.e., theseparator working pressure), and Pvi is the vapor pressureof component i 9, 10.Since we have only one flashing light hydrocarbon (i.e.,methane), this implies that the mole fraction of methanein the vapor phase is y = 1, and that the mole fractionof methane entrained in the liquid phase is x = P=Pv.Given the composition fZg1; Zo1g of the separated hy-drocarbon stream Fh1, we can estimate the amounts offlashing methane Fg1 and dissolved methane in the oil phaseFg2. The oil discharge flow Foout can also be estimatedalong with its average molecular weight Mwo1 and itsspecific gravity SGo1. The complete dynamic model of theoil phase, which is given by equations (10), can be thenformulated by taking the material balance:Fg1 = (1x)Zg1Fh1Fg2 = xZg1Fh1Foout = Fo +Fg2dNoildt = Fh1 Fg1 FooutMwo1 = xMwg +(1x)MwoSGo1 = xMwgNoil +(1x)MwoNoilxMwgNoilSGg +(1x)MwoNoilSGo(10)where Noil is the number of liquid moles in the oil phase;Fo is the molar oil component in the oil discharge flowFoout; fMwg; Mwog are the gas and oil molecular weights;and fSGg; SGog are the gas and oil specific gravities.C. The gas phaseGiven the ideal gas law assumption, the gas phase of theseparator is modeled by taking the material balance. We canestimate the gas pressure P by applying the ideal gas law,as described by equations (11):dNgasdt = Fg1 FgoutVoil = Mwo1Noil62:43SGo1Vgas = Vsep Vwat VoilP = NgasRTVgas(11)where Ngas is the number of gas moles in the gasphase; Fgout is the gas molar outflow from the separator;fVoil; Vgas; Vsepg are the volumes of the oil phase, gasphase, and separator respectively; R is the universal gasconstant; and T is the absolute separator temperature.IV. SEPARATOR MODEL VALIDATIONHaving obtained the dynamic model of the three-phasegravity separator, we design a simulation model whichemulates an oil production facility to validate the modelbehavior under several scenarios. The simulation modelbasically consists of three processes, as depicted in figure6. The first is a two-phase separator in which hydrocarbonfluids from oil wells are separated into two phases (gas,oil + water) to remove as much light hydrocarbon gases aspossible. The separator is 15 ft long and has a diameter of 5ft. The two-phase separator model was developed based onthe models of the oil and gas phases of the three-phase sep-arator. That is, we have modeled only the thermodynamicphenomenon of gas flashing out the liquid phase. The liquidproduced is then pumped to the three-phase separator (i.e.,the second process), where water and solids are separatedfrom oil. The oil produced is then pumped out and sold torefineries and petrochemical plants if it meets the requiredspecifications. The three-phase separator has length of 8.6ft and a diameter of 4.8 ft. Flashed light and medium gasesfrom the separation processes are sent to a gas scrubberwhere medium hydrocarbon and other liquid remnants areseparated from gas and sen