Contents Specific Gravity... 2 Formation Volume Factor... 3 Compressibility Equation... 4 Pseudo-Reduced Variables... 5 Pseudo-Critical Variables... 6 SI Conversions... 6 Output... 6 Input... 6 Viscosity... 7 SI Conversions... 7 Output... 7 Input... 7 Density... 8 Pressure Gradient... 8 Compressibility... 8 Coefficient of Thermal Expansion... 9 Compressional Wave Velocity... 9 Darcy s Law... 10 Pseudo-Pressure... 10 Macros... 11 1
Specific Gravity γγ gg = ρρ ff ρρ ss Equation 1: Gas Specific Gravity (Real).γγ g specific gravity [1/air] [1/air].ρρ ff density of fluid of interest at standard conditions [lb/cuft] [kg/m 3 ].ρρ ss density of reference fluid at standard conditions [lb/cuft] [kg/m 3 ] γγ gg = MM wwww MM wwwwwwww Equation 2: Gas Specific Gravity (Ideal).γγ g specific gravity [1/air] [1/air].M wf apparent molecular mass of fluid of interest [lb/mol] [g/mol].m wair apparent molecular mass of reference fluid (air) [lb/mol] [g/mol] 2
Formation Volume Factor BB gg = VV VV ssss Equation 3: Gas Formation Volume Factor.B g formation volume factor [cuft/scf] [m 3 /sm 3 ].V reservoir volume [cuft] [m 3 ].V sc volume at standard conditions [scf] [sm 3 ] pp = ZZZZZZZZ VV Equation 4: Real Gas Equation.p pressure of interest [psia] [Pa].T temperature of interest [ o R] [K].V volume at pressure and temperature of interest [cuft] [m 3 ].n number of moles contained in volume [lb-mol] [g-mol].r universal gas constant [psia.cuft]/[mol. o R] [J/mol/K].Z compressibility factor [ ] [ ] BB gg = ZZZZ pp pp ssss ZZ ssss TT ssss Equation 5: Gas Formation Volume Factor from Real Gas Equation.p pressure of interest [psia] [kpa].t temperature of interest [ o R] [K].Z compressibility factor at conditions of interest [ ] [ ].p sc standard pressure [psia] [kpa].t sc standard temperature [ o R] [K].Z sc compressibility factor at standard conditions [ ] [ ] 3
Compressibility Equation ZZ = XX 2 ρρ pppp Equation 6: Dranchuk & Abu-Kassem Z-Factor 0 = 1 + XX 1 ρρ pppp + XX 2 + XX ρρ 3 ρρ 2 pppp + XX 4 ρρ 5 pppp + XX 5 1 + aa 11 ρρ pppp pppp XX 1 = aa 01 + aa 02 + aa 03 TT 3 + aa 04 4 + aa 05 5 pppp XX 2 = aa 00 pp pppp XX 3 = aa 06 + aa 07 + aa 08 TT 2 pppp XX 4 = aa 09 aa 07 + aa 08 XX 5 = aa 10 3 TT2 pppp 2 ρρ 2 pppp ee aa 11ρρ 2 pppp Where: Oilfield/SI. Z compressibility factor [ ]. ρ pr reduced density [ ]. p pr reduced pressure [ ]. T pr reduced temperature [ ].. a 00 to a 11 are constants Constant Value Constant Value a01 0.3265 a07-0.7361 a02-1.07 a08 0.1844 a03-0.5339 a09 0.1056 a04 0.01569 a10 0.6134 a05-0.05165 a11 0.721 a06 0.5475 a00 0.27 4
Pseudo-Reduced Variables pp pppp = pp pp pppp Equation 7: Pseudo-reduced pressure = TT Equation 8: Pseudo-reduced Temperature ρρ pppp = ρρ ρρ pppp Equation 9: Pseudo-reduced density.p pr pseudo-reduced pressure [] [].p pressure of interest [psia] [kpa].p pc pseudo-critical pressure [psia] [kpa].t pr pseudo-reduced temperature [] [].T temperature of interest [ o R] [K].p pc pseudo-critical temperature [ o R] [K].ρ pr pseudo-reduced density [] [].ρ fluid density at conditions of interest [lb/cuft] [kg/m 3 ].ρ pc pseudo-critical pressure [lb/cuft] [kg/m 3 ] 5
Pseudo-Critical Variables pp pppp = aa 00 + aa 01 γγ gg + aa 02 γγ gg 2 Equation 10: Standing's pseudo-critical pressure correlation = aa 10 + aa 11 γγ gg + aa 12 γγ gg 2 Equation 11: Standing's pseudo-critical temperature correlation Where: Oilfield.p pc pseudo-critical pressure [psia].t pc pseudo-critical temperature [ o R].γγ g specific gravity [1/air] a 00-a 12 are constants Constant Value Constant Value a00 677 a10 168 a01 15 a11 325 a02-37.5 a12 12.5 SI Conversions Output p pc [kpa] = p pc [psia] 0.145037738 T pc [K] = T pc [ o R] 5 9 Input [None] 6
Viscosity μμ gggg = (aa 0 + aa 1 MM ww )TT aa 2 aa 3 + aa 4 MM ww + TT Equation 12: Lee et al. dead gas viscosity correlation μμ gg = μμ gggg μμ pp Equation 13: Lee et al. live gas viscosity correlation μμ pp = ee XX 0ρρ [XX 1 ] Equation 14: Lee et al. pressure correction XX 0 = aa 5 + aa 6 TT + aa 7MM ww XX 1 = aa 8 + aa 9 XX 0 Where: Oilfield.μ g dynamic gas viscosity at pressure and temperature of interest [cp].μ gd dynamic atmospheric gas viscosity at temperature of interest [cp].μ p pressure correction factor [ ].ρ gas density [g/cc].m w gas molecular mass [lb/mol].t temperature of interest [ o F] X 0-X 1 are intermediate variables a 0-a 9 are constants. Constant Value Constant Value a0 9.4 a5 3.5 a1 0.02 a6 986 a2 1.5 a7 0.01 a3 209 a8 2.4 a4 19 a9-0.2 SI Conversions Output μ g [mpa.s] = μ g [cp] 1 Input T [ o F] = T [K] 9 5-459.68.ρ [g/cc] =.ρ [kg/m 3 ] 1000 M w [lb/mol] = M w [g/mol] 1 7
Density ρρ gg = MM wwpp ZZZZZZ Equation 15: Gas Density from the real gas law. ρ g gas density [lb/cuft] [kg/m 3 ].M w apparent molecular mass of the gas [lb/mol] [g/mol].p pressure of interest [psia] [Pa].T temperature of interest [degr] [K].Z compressibility factor [ ] [ ].R universal gas constant [[psia.cuft]/[mol. o R]] [J/mol/K] Pressure Gradient = MM wwpp 144ZZZZZZ Equation 16: Gas Gradient (oilfield units) = MM wwpp gg ZZZZZZ Equation 17: Gas Gradient (SI units). p/ z gas gradient [psi/ft] [Pa/m].M w apparent molecular mass of the gas [lb/mol] [g/mol].p pressure of interest [psia] [Pa].T temperature of interest [degr] [K].Z compressibility factor [ ] [ ].R universal gas constant [[psia.cuft]/[mol. o R]] [J/mol/K] 144 Square inches in a square foot [in 2 /ft 2 ] - g Acceleration due to gravity - [m/s 2 ] Compressibility cc gg = 1 pp 1 ZZ dddd dddd TT Equation 18: gas compressibility from the real gas law.c g compressibility of the gas [1/psi] [1/Pa].p pressure of interest [psia] [Pa].T temperature of interest [degr] [K].Z compressibility factor [ ] [ ] 8
Coefficient of Thermal Expansion αα gg = 1 TT + 1 ZZ dddd dddd pp Equation 19: Coefficient of thermal expansion from the real gas law.α g coefficient of thermal expansion of the gas [1/degF] [1/K].p pressure of interest [psia] [Pa].T temperature of interest [degr] [K].Z compressibility factor [ ] [ ] Compressional Wave Velocity γγ xx vv gg = ρρ gg cc gg Equation 20: Speed of sound in gas 2 1 = 1 TTVV mmαα gg γγ xx CC pp cc gg.v g compressional wave velocity [ft/s] [m/s].c p specific heat capacity at constant pressure [psi.cuft/mol/degf] [J/K].V m molar volume of the gas at temperature and pressure [cuft/lb-mol] [m 3 /g-mol] of interest.ρ g gas density at pressure and temperature of interest [lb/cuft] [kg/m 3 ].c g compressibility of the gas at temperature and [1/psi] [1/Pa] pressure of interest.α g coefficient of thermal expansion at temperature and [1/degF] [1/K] pressure of interest.t temperature of interest [degr] [K] 9
Darcy s Law qq gg = aa 00kk gg h pp ee pp wwww μμ gg BB gg ln rr ee rr 1 ww 2 + ss Equation 21: Darcy's Law for the radial flow of a gas.q g gas flow rate [scf/d] [m 3 /d].k g effective permeability to gas [md] [md].h Thickness [ft] [m].p e pressure at the edge of the reservoir [psia] [kpa].p wf pressure at the wellbore [psia] [kpa].μ g gas viscosity [cp] [mpa.s].b g gas formation volume factor [cuft/scf] [m 3 /sm 3 ].r e radius of edge of reservoir [ft] [m].r w radius of wellbore [ft] [m].s skin factor [ ] [ ].a 00 Unit conversion constant 5.61458/141.2 Pseudo-Pressure mm(pp) = 2 pp pp rrrrrr PP μμμμ dddd Equation 22 Pseudo-Pressure (Al-Hussainy).m(p) pseudo-pressure [psi 2 /cp] [ Pa/s].p ref reference pressure [psia] [kpa].μ gas viscosity [cp] [mpa.s].z gas compressibility factor [ ] [ ] mm(pp) = pp ii pp rrrrrr pp ρρ ii pp μμμμ dddd rrrrrr pp pp rrrrrr ρρ μμμμ dddd + pp rrrrrr Equation 23: Pseudo-Pressure (Walsh & Lake).m(p) pseudo-pressure [psia] [kpa].p i initial (high) reference pressure [psia] [kpa].p ref abandonment (low) reference pressure [psia] [kpa].ρ In-situ gas density [lb/cuft] [kg/m 3 ].μ gas viscosity [cp] [mpa.s].z gas compressibility factor [ ] [ ] 10
Macros Name Purpose Qualifier Units Source Date Module stan_pc Critical Pressure Gas [psia] Brown & Standing 1948 Z stan_tc Critical Temperature Gas [degf] Brown & Standing 1948 Z abou_z Z-Factor Gas [ ] Dranchuk & Abou- 1975 Z Kassem Lee1_Ugb Viscosity Gas, Live [cp] Lee, Gonzalez & Eakin 1966 Viscous Lee1_Ugd Viscosity Gas, Dead [cp] Lee Gonzalez & Eakin 1966 Viscous 11