08_Appendix1

a-1 Pipe Pressure Drop MethodVapour Phase Pressure Drop MethodsPressure drop can be calculated either from the theoretically derived equation for isothermal flow of a compressible fluid in a horizontal pipe:Where:G = Mass flowa = Cross sectional area of pipeP 1 = Upstream pressureP 2 = Downstream pressureR = Universal gas constantf = Moody friction factorφ = Internal diameterL = Equivalent lengthT = TemperatureM = Molecular weightOr from the theoretically derived equation for adiabatic flow of a compressible fluid in a horizontal pipe:Where: G = Mass flowa = Cross sectional area of pipeP 1 = Upstream pressureR = Universal gas constantV 1 = Upstream velocityV 2 = Downstream velocityf = Moody friction factorφ = Internal diameterL = Equivalent lengthγ = Ratio of specific heatsThe Moody friction factor is calculated using an equation appropriate for the flow regime. These equations correlate the friction factor to the pipe diameter, Reynolds number and roughness of the pipe:Turbulent Flow (Re > 4000)Where: f = Moody friction factorRe = Reynolds numberφ = Internal diametere = Absolute pipe roughnessOr from the Chen equation:Where: f = Moody friction factorRe =Reynolds numberφ = Internal diametere = Absolute pipe roughness Transition Flow (2100 < Re < 4000)Where: f = Moody friction factorRe = Reynolds numberφ = Internal diametere = Absolute pipe roughness Laminar Flow (Re < 2100)Where: f = Moody friction factorRe = Reynolds numberThe Darcy friction factor is given by:Where: f = Moody friction factorf d = Darcy friction factor2-Phase Pressure DropBeggs and BrillThe Beggs and Brill9 method is based on work done with an air-water mixture at many different conditions, and is applicable for inclined flow. In the Beggs and Brill correlation, the flow regime is determined using the Froude number and inlet liquid content. The flow map used is based on horizontal flow and has four regimes: segregated, intermittent, distributed and transition. Once the flow regime has been determined, the liquid hold-up for a horizontal pipe is calculated, using the correlation applicable to that regime. A factor is applied to this hold-up to account for pipe inclination. From the hold-up, a two-phase friction factor is calculated and the pressure gradient determined.The boundaries between regions are defined in terms of two constants and the Froude number:Where: x = ln(λ)λ = input liquid content = q liquid /(q liquid +q gas )q = in situ volumetric flowrateAccording to Beggs and Brill:1. If the Froude number is less than L1, the flow pattern is segregated.2. If the Froude number is greater than both L1 and L2, the flow pattern is distributed.3.If the Froude number is greater than L1 and smaller than Lthe flow pattern is intermittent.2Dukler MethodThe Dukler method breaks the pressure drop into three components - Friction, Elevation and Acceleration. The total pressure drop is the sum of the pressure drop due to these components.Where: ∆P Total = Total change in pressure∆P F = Change in pressure due to friction∆P E = Change in pressure due to elevation∆P A = Change in pressure due to accelerationThe pressure drop due to friction is:Where: fTP = Two-phase friction factor (determined empirically)L = Equivalent length of the pipeline (ft)V m = Velocity of the two-phase mixture in pipeline assuming equal velocity (ft/s)ρm = Density of two-phase mixture (lb/ft 3 )g c = Gravitational constant (32.2 lbm-ft/lbf-s 2 )D = Inside diameter of pipe (ft)The pressure drop due the elevation is:Where: Eh = Liquid head factor (determined empirically)ρL = Liquid densityΣH = Sum of elevation changesThe pressure drop due to acceleration is usually very small in oil/gas distribution systems, butbecomes significant in designing flare systems:Where: A = Cross-sectional areaρg = Gas densityQ GPL = Volume of gas flowing at pipeline temperature and pressure (ft 3 /hr)Q LPL = Volume of liquid flowing at pipeline temperature and pressure (ft 3 /hr)R L = Liquid holdup in pipeline as a percentage of pipeline capacityθ = Angle of the pipe bendOrkiszewski MethodThe Orkiszewski method assumes there are four different flow regimes existing in vertical two-phase flow - bubble, slug, annular-slug transition and annular-mist.The bubble flow regime consists mainly of liquid with a small amount of a free-gas phase. The gas phase consists of small, randomly distributed gas bubbles with varying diameters. The gas phase has little effect on the pressure gradient (with the exception of its density).In the slug flow regime, the gas phase is most pronounced. The gas bubbles coalesce and form stable bubbles of approximately the same size and shape. The gas bubbles are separated by slugs of a continuous liquid phase. There is a film of liquid around the gas bubbles. The gas bubbles move faster than the liquid phase. At high flow velocities, the liquid can become entrained in the gas bubbles. The gas and liquid phases may have significant effects on the pressure gradient.Transition flow is the regime where the change from a continuous liquid phase to a continuous gas phase occurs. In this regime, the gas phase becomes more dominant, with a significant amount of liquid becoming entrained in the gas phase. The liquid slug between the gas bubbles virtually disappears in the transition regime.In the annular-mist regime, the gas phase is continuous and is the controlling phase. The bulk of the liquid is entrained and carried in the gas phase.Orkiszewski defined bubble flow, slug flow, mist flow and gas velocity numbers which are used to determine the appropriate flow regime.If the ratio of superficial gas velocity to the non-slip velocity is less than the bubble flow number, then bubble flow exists, for which the pressure drop is:Where: ∆P = Pressure drop (lb/ft 2 per foot of length)f tp = Two-phase friction factorρL = Liquid density (lb/ft 3 )V sL = Superficial liquid velocity (ft/s)R L = Dimensionless factor dependent on non-slip velocityg c = Gravitational constant (32.2 lbm-ft/lbf-s 2 )D = Hydraulic diameter (ft)If the ratio of superficial gas velocity to the non-slip velocity is greater than the bubble flow number, and the gas velocity number is smaller than the slug flow number, then slug flow exists. The pressure drop in this case is:Where: V ns = Non-slip velocityV r = Bubble rise velocityΓ = ConstantThe pressure drop calculation for mist flow is as follows:Where: V sg = Superficial gas velocity (ft/s)ρg = Gas density (lb/ft 3 )The pressure drop for the transition flow is:Where: ∆Ps = Pressure drop for slug flow∆Pm = Pressure drop for mixed flowχ = Weighting factor, dependent on mist flow, slug flow, and gas velocity numbers.The pressure drop calculated by the previous equations are for a one-foot length of pipe. These are converted to total pressure drop by:Where : ρ = Density of the flowing regime (lb/ft 3)Q total = Mass rate of combined liquid/gas (lb/s)G f = Gas flow rate (ft 3/s)A p = Cross-sectional area of pipe (ft 2)p = Average pressure in segment (psia)∆P = Unit pressure drop (as calculated above)L = Length of line segment (ft)A-2 Fittings Pressure Drop MethodsFitting pressure losses are calculated from a type specific loss coefficient, K, which is defined by:Where: ∆P = Total Pressure LossP = Static Pressureρ = DensityU = VelocityThe static inlet pressure is then calculated from the following equation in which it is assumed that there is no elevation change across the node:Where: P = Total pressure lossP = Static pressureρ = Density U = VelocitySubscripts:1 = Inlet2 = OutletEnlargers/ContractionsThe loss coefficient is calculated from the ratio of the smaller diameter to the larger diameter, which is defined by:Sudden and gradual contractionSudden and gradual enlargementTeesTees can be modelled either using a flow independent loss coefficient for each flow path or using variable loss coefficients that are a function of the volumetric flow and area for each flow path as well as the branch angle. The following numbering scheme is used to reference the flow paths:Constant Loss CoefficientVariable Loss CoefficientsThe loss coefficient is a function of the branch angle, branch area to total flow area ratio and branch volumetric flow to total volumetric flow ratio. These values have been graphically represented by Miller. reference here A typical chart for K23 in combining flow is shown:Orifice PlatesOrifice plates can either be modelled as a sudden contraction from the inlet line size to the hole diameter followed by a sudden expansion from the hole diameter to the outlet line size. This simplistic treatment if often adequate given the uncertainty in the prediction of two phase loss coefficients.Alternatively the equation for a thin orifice plate may be used:= Inlet pipe diameterWhere:d1= Hole diameterd2SeparatorsThe pressure loss for a separator is modelled by treating it as a sudden enlargement of the total flow from the inlet line size to the hydraulic diameter of the body followed by a sudden contraction of the vapour flow from the hydraulic diameter of the body to the to the outlet line size. Friction losses within the separator body are ignored.Vapour-Liquid EquilibriumCompressible GasThe PVT relationship is expressed as:Where: P = pressureV = VolumeZ = Compressibility factorR = Gas constantT = TemperatureThe compressibility factor Z is a function of reduced temperature and pressure. The overall critical temperature and pressure are determined using applicable mixing rules.Vapour PressureThe following equations are used for estimating the vapour pressure, given the component critical properties:Where: p *r = Reduced vapour pressure (p */p c )p * = Vapour pressure (psi abs)p c = Critical pressure (psi abs)ω = Acentric factor T r = Reduced temperature (T/T c )T = Temperature (°R)T c = Critical Temperature (°R)This equation is restricted to reduced temperatures greater than 0.30, and should not be used below the freezing point. Its use was intended for hydrocarbons, but it generally works well with water.Soave Redlich KwongIt was noted by Wilson (1965, 1966) that the main drawback of the Redlich-Kwong equation of state was its inability of accurately reproducing the vapour pressures of pure component constituents of a given mixture. He proposed a modification to the RK equation of state using the acentricity as a correlating parameter, but this approach was widely ignored until 1972, when Soave (1972) proposed a modification of the SRK equation of this form:The a term was fitted in such a way as to reproduce the vapour pressure of hydrocarbons using the acentric factor as a correlating parameter. This led to the following development:The reduced form is:The SRK equation of state can represent with good accuracy the behaviour of hydrocarbon systems for separation operations, and since it is readily converted into computer code, its usage has been extensive in the last twenty years. Other derived thermodynamic properties, like enthalpies and entropies, are reasonably accurate for engineering work, and the SRK equation enjoys wide acceptance in the engineering community today.Peng RobinsonPeng and Robinson (1976) noted that although the SRK was an improvement over the RK equation for VLE calculations, the densities for the liquid phase were still in considerable disagreement with experimental values due to a universal critical compressibility factor of 0.3333, which was still too high. They proposed a modification to the RK equation which reduced the critical compressibility to about 0.307, and which would also represent the VLE of natural gas systems accurately. This improved equation is represented by:They used the same functional dependency for the α term as Soave:The accuracy of the SRK and PR equations of state are roughly the same (except for density calculations).Physical PropertiesVapour DensityVapour density is calculated using the compressibility factor calculated from the Berthalot equation. This equation correlates the compressibility factor to the pseudo reduced pressure and pseudo reduced temperature:The density is then calculated from the real gas equation:Liquid DensitySaturated liquid volumes are obtained using a corresponding states equation developed by R. W. Hankinson and G. H. Thompson which explicitly relates the liquid volume of a pure component to its reduced temperature and a second parameter termed the characteristic volume. This method has been adopted as an API standard. The pure compound parameters needed in the corresponding states liquid density (COSTALD) calculations are taken from the original tables published by Hankinson and Thompson, and the API data book for components contained in FLARENET’s library. The parameters for hypothetical components are based on the API gravity and the generalised Lu equation. Although the COSTALD method was developed for saturated liquid densities, it can be applied to sub-cooled liquid densities, i.e., at pressures greater than the vapour pressure, using the Chueh and Prausnitz correction factor for compressed fluids. The COSTALD model was modified to improve its accuracy to predict the density for all systems whose pseudo-reduced temperature is below 1.0. Above this temperature, the equation of state compressibility factor is used to calculate the liquid density.Vapour ViscosityVapour viscosity is calculated from the Golubev method. These equations correlate the vapour viscosity to molecular weight, temperature and the pseudo critical properties.Liquid ViscosityFLARENET will automatically select the model best suited for predicting the phase viscosities of the system under study. The model selected will be from one of the three available in FLARENET: a modification of the NBS method (Ely and Hanley), Twu’s model, and a modification of the Letsou-Stiel correlation. FLARENET will select the appropriate model using the following criteria:Chemical System Liquid Phase MethodologyLight Hydrocarbons (NBP < 155 F)Mod. Ely and HandleyHeavy Hydrocarbons (NBP > 155F)TwuNon-Ideal Chemicals Mod Letsou-StielAll the models are based on corresponding states principles and have been modified for more reliable application. These models were selected since they were found from internal validation to yield the most reliable results for the chemical systems shown. Viscosity predictions for light hydrocarbon liquid phases and vapour phases were found to be handled more reliably by an in-house modification of the original Ely and Hanley model, heavier hydrocarbon liquids were more effectively handled by Twu’s model, and chemical systems were more accurately handled by an in-house modification of the original Letsou-Stiel model.A complete description of the original corresponding states (NBS) model used for viscosity predictions is presented by Ely and Hanley in their NBS publication. The original model has been modified to eliminate the iterative procedure for calculating the system shape factors. The generalised Leech-Leland shape factor models have been replaced by component specific models. FLARENET constructs a PVT map for each component and regresses the shape factor constants such that the PVT map can be reproduced using the reference fluid. It is important to note that the PVT map is constructed using the COSTALD for the liquid region. The shape factorconstants for all the library components have already been regressed and are stored with the pure component properties.Pseudo component shape factor constants are regressed when the physical properties are supplied. Kinematic or dynamic viscosity versus temperature curves may be supplied to replace FLARENET’s internal pure component viscosity correlations. FLARENET uses the viscosity curves, whether supplied or internally calculated, with the physical properties to generate a PVT map and regress the shape factor constants. Pure component data is not required, but if it is available it will increase the accuracy of the calculation.The general model employs methane as a reference fluid and is applicable to the entire range of non-polar fluid mixtures in the hydrocarbon industry. Accuracy for highly aromatic or naphthenic oil will be increased by supplying viscosity curves when available, since the pure component property generators were developed for average crude oils. The model also handles water and acid gases as well as quantum gases.Although the modified NBS model handles these systems very well, the Twu method was found to do a better job of predicting the viscosities of heavier hydrocarbon liquids. The Twu model1 is also based on corresponding states principles, but has implemented a viscosity correlation for n-alkanes as its reference fluid instead of methane. A complete description of this model is given in the paper titled "Internally Consistent Correlation for Predicting Liquid Viscosities of Petroleum Fractions".For chemical systems the modified NBS model of Ely and Hanley is used for predicting vapour phase viscosities, whereas a modified form of the Letsou-Stiel model is used for predicting the liquid viscosities. This method is also based on corresponding states principles and was found to perform satisfactorily for the components tested.The parameters supplied for all FLARENET pure library components have been fit to match existing viscosity data over a broad operating range. Although this will yield good viscosity predictions as an average over the entire range, improved accuracy over a more narrow operating range can be achieved by supplying viscosity curves for any given component. This may be achieved either by modifying an existing library component through FLARENET’s component librarian or by entering the desired component as a hypothetical and supplying its viscosity curve.Liquid Phase Mixing Rules for ViscosityThe estimates of the apparent liquid phase viscosity of immiscible Hydrocarbon Liquid - Aqueous mixtures are calculated using the following "mixing rules":•If the volume fraction of the hydrocarbon phase is greater than or equal to 0.33, the following equation is used:Where: µ= apparent viscosityeffµ= viscosity of Hydrocarbon phaseoilν= volume fraction Hydrocarbon phaseoil•If the volume fraction of the hydrocarbon phase is less than 0.33, the following equation is used:Where: µ= apparent viscosityeffµ= viscosity of Hydrocarbon phaseoilµ= viscosity of Aqueous phaseH2Oν= volume fraction Hydrocarbon phaseoilThe remaining properties of the pseudo phase are calculated as follows:Thermal ConductivityAs in viscosity predictions, a number of different models and component specific correlations are implemented for prediction of liquid and vapour phase thermal conductivities. The text by Reid, Prausnitz and Poling was used as a general guideline in determining which model was best suited for each class of components. For hydrocarbon systems the corresponding states method proposed by Ely and Hanley is generally used. The method requires molecular weight, acentric factor and ideal heat capacity for each component. These parameters are tabulated for all library components and may either be input or calculated for hypothetical components. It is recommended that all of these parameters be supplied for non-hydrocarbon hypotheticals to ensure reliable thermal conductivity coefficients and enthalpy departures.The modifications to the method are identical to those for the viscosity calculations. Shape factors calculated in the viscosity routines are used directly in the thermal conductivity equations. The accuracy of the method will depend on the consistency of the original PVT map.The Sato-Reidel method is used for liquid phase thermal conductivity predictions of glycols and acids, the Latini et al. Method is used for esters, alcohols and light hydrocarbons in the range of C3 - C7, and the Missenard and Reidel method is used for the remaining components.For vapour phase thermal conductivity predictions, the Misic and Thodos, and Chung et al. methods are used. The effect of higher pressure on thermal conductivities is taken into account by the Chung et al. method.As in viscosity, the thermal conductivity for two liquid phases is approximated by using empirical mixing rules for generating a single pseudo liquid phase property.EnthalpyIdeal GasThe ideal gas enthalpy is calculated from the following equation:Where: H = Ideal enthalpyT = TemperatureA, B, C, D, E = Ideal Gas heat capacity termsLee-KeslerThe Lee-Kesler enthalpy method corrects the ideal gas enthalpy for temperature and pressure.= Critical temperatureWhere: TcH = Specific enthalpyω = Acentric factorr = Reference fluids = Simple fluidH ideal = Ideal enthalpyb, c, d, β, γ = Lee-Kesler termsH dep = Ideal Gas departure enthalpyEquations of StateThe Enthalpy and Entropy calculations are performed rigorously using the following exact thermodynamic relations:For the Peng Robinson Equation of State, we have:For the SRK Equation of State, we have:A andB are defined in the table below:Where:ID = Ideal Gas° = Reference stateR = Ideal gas constantH = EnthalpyS = EntropyNoiseThe sound pressure level at a given distance from the pipe is calculated from the following equations. In these equations the noise producing mechanism is assumed to be solely due to the pressure drop due to friction:Where: L = Equivalent lengthSPL = Sound pressure levelr = Distance from pipeφ = Internal diameter pressureη = Acoustic efficiency∆P = Change in PressureThe acoustical efficiency is calculated from the following graph:Where:The transmission loss due to the pipe wall is calculated from:。