石油生产工程Petroleum Production Engineering, Elsevier (2007).pdf

ISBN 0750682701 Publisher Elsevier Science that is, Rs Vgas Voil ,21 where Rssolution GOR in scf/stb Vgasgas volume in standard condition scf Voiloil volume in stock tank condition stb The ‘‘standard condition’’ is defined as 14.7 psia and 608FinmoststatesintheUnitedStates.Atagivenreservoir temperature, solution GOR remains constant at pressures above bubble-point pressure. It dropsas pressure decreases in the pressure range below the bubble-point pressure. SolutionGORismeasuredinPTVlaboratories. Empirical correlations are also available based on data from PVT labs. One of the correlations is, Rs gg p 18 1000125 API 10000091t 12048 22 where ggand 8API are defined in the latter sections, and p and t are pressure and temperature in psia and 8F, respectively. Solution GOR factor is often used for volumetric oil and gas calculations in reservoir engineering. It is also used as a base parameter for estimating other fluid properties such as density of oil. 2.2.2Density of Oil ‘‘Density of oil’’ is defined as the mass of oil per unit volume, or lbmft3in U.S. Field unit. It is widely used in hydraulics calculations e.g., wellbore and pipeline per- ance calculations [see Chapters 4 and 11]. Because of gas content, density of oil is pressure depen- dent. The density of oil at standard condition stock tank oil is uated by API gravity. The relationship between the density of stock tank oil and API gravity is given through the following relations API 1415 go 131523 and go ro,st rw ,24 where 8API API gravity of stock tank oil gospecificgravityofstocktankoil, 1forfreshwater ro,st density of stock tank oil, lbmft3 rw density of freshwater, 624lbmft3 The density of oil at elevated pressures and temperatures can be estimated on empirical correlations developed by a number of investigators. Ahmed 1989 gives a summary of correlations. Engineers should select and validate the correlations carefully with measurements before adopting any correlations. Standing 1981 proposed a correlation for estimating the oil ation volume factor as a function of solution GOR, specific gravity of stock tank oil, specific gravity of solution gas, and temperature. By coupling the mathemat- ical definition of the oil ation volume factor with Standing’s correlation, Ahmed 1989 presented the fol- lowing expression for the density of oil ro 624go 00136Rsgg 0972 0000147 Rs ffi ffi ffi ffiffi gg go r 125t 1175, 25 where t temperature, 8F ggspecific gravity of gas, 1 for air. 2.2.3ation Volume Factor of Oil ‘‘ation volume factor of oil’’ is defined as the volume occupied in the reservoir at the prevailing pressure and temperature by volume of oil in stock tank, plus its dis- solved gas; that is, Bo Vres Vst ,26 where Boation volume factor of oil rb/stb Vresoil volume in reservoir condition rb Vstoil volume in stock tank condition stb ation volume factor of oil is always greater than unity because oil dissolves more gas in reservoir condition than in stock tank condition. At a given reservoir tempera- ture, oil ation volume factor remains nearly constant at pressures above bubble-point pressure. It drops as pres- sure decreases in the pressure range below the bubble- point pressure. ation volume factor of oil is measured in PTV labs. Numerous empirical correlations are available based on data from PVT labs. One of the correlations is Bo 09759 000012 Rs ffi ffi ffi ffi ffi gg go r 125t 12 27 ationvolumefactorofoilisoftenusedforoilvolumet- riccalculationsandwell-inflowcalculations.Itisalsousedas abaseparameterforestimatingotherfluidproperties. 2.2.4Viscosity of Oil ‘‘Viscosity’’ is an empirical parameter used for describing the resistance to flow of fluid. The viscosity of oil is of interest in well-inflow and hydraulics calculations in oil production engineering. While the viscosity of oil can be measured in PVT labs, it is often estimated using empirical correlations developed by a number of investigators including Beal 1946, Beggs and Robinson 1975, Stand- ing 1981, Glaso 1985, Khan 1987, and Ahmed 1989. A summary of these correlations is given by Ahmed 1989. Engineers should select and validate a correlation with measurements before it is used. Standing’s 1981 correlation for dead oil is expressed as mod032 18 107 API453 360 t 200 A ,28 Guo, Boyun / Computer Assited Petroleum Production Engg0750682701_chap02Final Proofpage 2022.12.2006708pm 2/20PETROLEUM PRODUCTION ENGINEERING FUNDAMENTALS where A 10 043833 API 29 and mod viscosity of dead oil cp. Standing’s 1981 correlation for saturated crude oil is expressed as mob 10amb od, 210 where mob viscosity of saturated crude oil in cp and a Rs22 107Rs 74 104,211 b 068 10c 025 10d 0062 10e ,212 c 862 105Rs,213 d 110 103Rs,214 and e 374 103Rs,215 Standing’s 1981 correlation for unsaturated crude oil is expressed as mo mob 0001p pb0024m16 ob 038m056 ob 216 2.2.5Oil Compressibility ‘‘Oil compressibility’’ is defined as co 1 V V p T ,217 where T and V are temperature and volume, respectively. Oil compressibility is measured from PVT labs. It is often used in modeling well-inflow perance and reservoir simulation. Example Problem 2.1The solution GOR of a crude oil is 600 scf/stb at 4,475 psia and 140 8F. Given the following PVT data, estimate density and viscosity of the crude oil at the pressure and temperature Bubble-point pressure2,745 psia Oil gravity35 8API Gas-specific gravity0.77 air 1 SolutionExample Problem 2.1 can be quickly solved using the spreadsheet program OilProperties.xls where Standing’s correlation for oil viscosity was coded. The and output of the program is shown in Table 2.1. 2.3 Properties of Natural Gas Gas properties include gas-specific gravity, gas pseudo- critical pressure and temperature, gas viscosity, gas Table 2.1Result Given by the Spreadsheet Program OilProperties.xls OilProperties.xls Description This spreadsheet calculates density and viscosity of a crude oil. Instruction 1 Click a unit-box to choose a unit system; 2 update parameter values in the data section; 3 view result in the Solution section and charts. data U.S. Field unitsSI units Pressure p4,475 psia Temperature t140 8F Bubble point pressure pb2,745 psia Stock tank oil gravity35 8API Solution gas oil ratio Rs600 scf/stb Gas specific gravity gg0.77 air 1 Solution go 1415 API 1315 0.8498 H2O 1 ro 624go 00136Rsgg 0972 0000147 Rs ffi ffi ffiffi gg go q 125t hi1175 44.90 lbmft3 A 10043833API 4.6559 mod032 18 107 API453 360 t 200 A 2.7956 cp a Rs22 107Rs 74 104 0.3648 c 862 105Rs 0.0517 d 110 103Rs 0.6600 e 374 103Rs 2.2440 b 068 10c 025 10d 0062 10e 0.6587 mob 10amb od 0.8498 cp0.0008 Pa-s mo mob 0001p pb0024m16 ob 038m056 ob 1.4819 cp0.0015 Pa-s Guo, Boyun / Computer Assited Petroleum Production Engg0750682701_chap02Final Proofpage 2122.12.2006708pm PROPERTIES OF OIL AND NATURAL GAS2/21 compressibility factor, gas density, gas ation volume factor, and gas compressibility. The first two are com- position dependent.The latter four are pressure dependent. 2.3.1Specific Gravity of Gas ‘‘Specific gravity gas’’ is defined as the ratio of the appar- ent molecular weight of the gas to that of air. The molecu- lar weight of air is usually taken as equal to 28.97 79 nitrogen and 21 oxygen. Therefore, the gas-specific gravity is gg MWa 2897 ,218 where MWais the apparent molecular weight of gas, which can be calculated on the basis of gas composition. Gas composition is usually determined in a laboratory and reported in mole fractions of components in the gas. Let yibe the mole fraction of component i, and the apparent molecular weight of the gas can be ulated using a mixing rule such as MWa X Nc i1 yiMWi,219 where MWiis the molecular weight of component i, and Ncis number of components. The molecular weights of compounds MWi can be found in textbooks on organic chemistry or petroleum fluids such as that by Ahmed 1989. Gas-specific gravity varies between 0.55 and 0.9. 2.3.2Gas Pseudo-Critical Pressure and Temperature Similar to gas apparent molecular weight, the critical properties of a gas can be determined on the basis of the critical properties of compounds in the gas using the mix- ing rule. The gas critical properties determined in such a way are called ‘‘pseudo-critical properties.’’ Gas pseudo- critical pressure ppc and pseudo-critical temperature Tpc are, respectively, expressed as ppc X Nc i1 yipci220 and Tpc X Nc i1 yiTci,221 where pciand Tciare critical pressure and critical tempera- ture of component i, respectively. Example Problem 2.2For the gas composition given in the following text, determine apparent molecular weight, specific gravity, pseudo-critical pressure, and pseudo- critical temperature of the gas. SolutionExampleProblem2.2issolvedwiththe spreadsheet program MixingRule.xls. Results are shown in Table 2.2. If the gas composition is not known but gas-specific gravity is given, the pseudo-critical pressure and tempera- ture can be determined from various charts or correlations developed based on the charts. One set of simple cor- relations is ppc 709604 58718gg222 Tpc 170491 307344gg,223 which are valid for H2S 3, N2 5, and total content of inorganic compounds less than 7. Corrections for impurities in sour gases are always necessary. The corrections can be made using either charts or correlations such as the Wichert and Aziz 1972 correction expressed as follows A yH2S yCO2224 B yH2S225 Table 2.2Results Given by the Spreadsheet Program MixingRule.xls MixingRule.xls Description This spreadsheet calculates gas apparent molecular weight, specific gravity, pseudo-critical pressure, and pseudo-critical temperature. Instruction 1 Update gas composition data yi; 2 read result. CompoundyiMWiyiMWipcipsiayipcipsiaTci, 8RyiTci8R C10.77516.0412.43673521.58344266.60 C20.08330.072.5070958.8555045.65 C30.02144.100.9361812.9866613.99 i-C40.00658.120.355303.187334.40 n-C40.00258.120.125511.107661.53 i-C50.00372.150.224821.458302.49 n-C50.00872.150.584853.888476.78 C60.00186.180.094340.439150.92 C70.001114.230.113610.3610241.02 N20.05028.021.4022711.3549224.60 CO20.03044.011.321,07332.1954816.44 H2S0.02034.080.6867213.45130626.12 1.000MWa20.71ppc661Tpc411 gg0.71 ComponentMole Fraction C10.775 C20.083 C30.021 i-C40.006 n-C40.002 i-C50.003 n-C50.008 C60.001 C70.001 N20.050 CO20.030 H2S0.020 Guo, Boyun / Computer Assited Petroleum Production Engg0750682701_chap02Final Proofpage 2222.12.2006708pm 2/22PETROLEUM PRODUCTION ENGINEERING FUNDAMENTALS 3 120A09 A16 15B05 B40226 Tpc0 Tpc 3corrected Tpc227 Ppc0 PpcTpc0 Tpc B1 B3 corrected ppc228 Correlationswithimpuritycorrectionsixture pseudo-criticals are also available Ahmed, 1989 ppc 678 50gg 05 2067yN2 440yCO2 6067yHsS229 Tpc 326 3157gg 05 240yN2 833yCO2 1333yH2S230 Applicationsofthepseudo-criticalpressureand temperature are normally found in petroleum engineer- ing through pseudo-reduced pressure and temperature defined as ppr p ppc 231 Tpr T Tpc 232 2.3.3Viscosity of Gas Dynamic viscosity mg in centipoises cp is usually used in petroleum engineering. Kinematic viscosity ng is related to the dynamic viscosity through density rg, ng mg rg 233 Kinematic viscosity is not typically used in natural gas engineering. Direct measurements of gas viscosity are preferred for a new gas. If gas composition and viscosities of gas com- ponents are known, the mixing rule can be used to deter- mine the viscosity of the gas mixture mg P mgiyi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi MWi p P yi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi MWi p 234 Viscosity of gas is very often estimated with charts or correlations developed based on the charts. Gas viscosity correlation of Carr et al. 1954 involves a two-step pro- cedure The gas viscosity at temperature and atmospheric pressure is estimated first from gas-specific gravity and inorganic compound content. The atmospheric value is then adjusted to pressure conditions by means of a correc- tion factor on the basis of reduced temperature and pres- sure state of the gas. The atmospheric pressure viscosity m1 can be expressed as m1 m1HC m1N2 m1CO2 m1H2S,235 where m1HC 8188 103 615 103loggg 1709 105 2062 106ggT,236 m1N2 [959 103 848 103loggg]yN2,237 m1CO2 [624 103 908 103loggg]yCO2,238 m1H2S [373 103 849 103loggg]yH2S,239 Dempsey 1965 developed the following relation mr ln mg m1 Tpr a0 a1ppr a2p2 pr a3p 3 pr Tpra4 a5ppr a6p2 pr a7p 3 pr T 2 pra8 a9ppr a10p 2 pr a11p3 pr T 3 pra12 a13ppr a14p 2 pr a15p3 pr, 240 where a0 246211820 a1 297054714 a2 028626405 a3 000805420 a4 280860949 a5 349803305 a6 036037302 a7 001044324 a8 079338568 a9 139643306 a10 014914493 a11 000441016 a12 008393872 a13 018640885 a14 002033679 a15 000060958 Thus, once the value of mris determined from the right- hand side of this equation, gas viscosity at elevated pres- sure can be readily calculated using the following relation mg m1 Tpr emr241 Other correlations for gas viscosity include that of Dean and Stiel 1958 and Lee et al. 1966. Example Problem 2.3 A 0.65 specific–gravity natural gas contains 10 nitrogen, 8 carbon dioxide, and 2 hydrogensulfide.Estimateviscosityofthegasat 10,000 psia and 1808F. SolutionExample Problem 2.3 is solved with the spread- sheet Carr-Kobayashi-Burrows-GasViscosity.xls, which is attached to this book. The result is shown in Table 2.3. 2.3.4Gas Compressibility Factor Gas compressibility factor is also called ‘‘deviation factor’’ or ‘‘z-factor.’’ Its value reflects how much the real gas deviates from the ideal gas at a given pressure and tem- perature. Definition of the compressibility factor is expressed as z Vactual Videal gas 242 Introducing the z-factor to the gas law for ideal gas results in the gas law for real gas as pV nzRT,243 where n is the number of moles of gas. When pressure p is entered in psia, volume V in ft3, and temperature in 8R, the gas constant R is equal to10.73 psia ft3 mole R . Gascompressibilityfactorcanbedeterminedonthebasis of measurements in PVT laboratories. For a given amount of gas, if temperature is kept constant and volume is mea- sured at 14.7 psia and an elevated pressure p1, z-factor can then be determined with the following ula z p1 147 V1 V0 ,244 G