PETROPHYSICAL FORMULAE

BASIC PETROPHYSICAL FORMULAE Compiled By:- Muhammad Zahidpetrophysicist786@hotmail.com1POROSITYEffective PorosityPHIE = PHIA * (1-Vshl)Density PorosityPHID = (RhoM - RHOB) / (RhoM - RhoF)Average Neutron Density PorosityPHIA = (PHID + PHIN) / 2Gamma Ray Neutron PorosityEnter Values for PorMax, PorMin...PorMax = 0.35PorMin = 0.02Enter Values in Counts Per Second or API...CPS_PorMax = 75CPS_PorMin = 600B = log(PorMax/PorMin) / (CPS_PorMax - CPS_PorMin)A = PorMax / 10 ^ (B*CPS_PorMax)PHIGRN = A * 10 ^ (B * CPS)2Sonic Porosity (Wyllie)PHIS = (DT - DTma) / (DTfld - DTma)Sonic Porosity (Wyllie)Enter Compaction Coefficient below,Cmp = 1.0PHIS = (1/Cmp) * (DT - DTma) / (DTfld - DTma)Sonic Porosity (Empirical)PHIS = 0.67 * (DT - DTma) / DTApparent Sonic MatrixDTma = ( DT - PHIA * DTfld ) / (1 - PHIA)Apparent Density MatrixRHOMa = (RHOB - PHIA * RhoF) / (1 - PHIA)Bulk Volume WaterBVW = PHIA * SwA.Hydrocarbon Pore VolumeHCPV = (1-SwA) * PHIA Hydrocarbon Pore VolumeSoPhiH = (1-SwA) * PHIA 3WATER RESISTIVITYArchie RoRo = a * Rw / (PHIA^m)Apparent Water ResistivityRwa = RT * PHIA^mConductivityCOND = 1000/RTRw from Dual WaterRwDW = Rw * RwBnd / (Rw * Vshl + (1-Vshl) * RwBnd)Ro from Dual WaterRoDW = (1 / (PHIA^m)) * (Rw * RwBnd / (Rw * Vshl + RwBnd * (1 - Vshl)))Modified Simandoux RoIf (Vshl < 1)RoMS = 1/(PHIE^m / (a* Rw*(1-Vshl)) + Vshl/Rshl)4Resistivity Temp CorrectionT1 and T2 in 'FR2 = R1 * (T1 + 6.77) / (T2 + 6.77)Resistivity Temp CorrectionT1 and T2 in 'CR2 = R1 * (T1 + 21.5) / (T2 + 21.5)

WATER SATURATIONArchie Water SaturationSwA = sqrt( Rw / (RT * PHIA^2) )Archie Water SaturationSwA = (a * Rw / ( RT * PHIA^m) )^(1/n)Archie Water Saturation (Humble)SwA = sqrt( .62 * Rw / (RT * PHIA ^2.15) )Archie Water SaturationSwA = sqrt( Rw / (RT * PHID ^m) )Archie Water SaturationSwA = sqrt(Ro / RT)Archie Water SaturationSwA = sqrt(Rw / Rwa)SwA = min( 1, max( 0, SwA ) 6Dual Water SwT & SwECalculate SwT Total PorosityY = Vshl * ( RwBnd - Rw ) / ( 2 * RwBnd )SwT = Y +( (Rw / ( RT * PHIA^2 ) ) + Y^2 )^.5SwT = min( 1, max( Vshl, SwT ) )Calculate SwE Effective PorosityIf ( Vshl < .75 )SwE = ( SwT - Vshl ) / ( 1 - Vshl )Modified Simandoux SwMSIf (Vshl < 1)SwMS = (sqrt( (Vshl/Rshl)^2 + 4*PHIE^m/(a*Rw*(1-Vshl)*RT) ) - Vshl/Rshl)/(2*PHIE^m/(a*Rw*(1-Vshl)) )

7Indonesian SwISwI = sqrt(1/RT) / ( Vshl^(1- 0.5*Vshl) /sqrt(Rshl) + sqrt( PHIE^m / (a*Rw)) )Ratio Method SwRequires normalized SP,Rmf/Rw ratio from SP...K = ~ 61 + 0.1333 * K = -71RmfRwRatio = 10 ^ (SP / K)Sw = Min( 1, ( (ResS/ResD) / (RmfRwRatio) ) ^(5/8) )Vshl = min(1, max(0, (GR-GRcln) / (GRshl-GRcln) ))Vshl = min(1, max(0, (SP-SPcln) / (SPshl-SPcln) ))Vshl = min(1, max(0, (RHOB - RhoM + PHIN * (RhoM - RhoF)) / (RhoShl - RhoM +HIshl * (RhoM - RhoF)) ))

SHALE VOLUMECalculate Vshl from Minimum of GR, SP & N/DVshl_GR = (GR-GRcln) / (GRshl-GRcln) )Vshl_SP = (SP-SPcln) / (SPshl-SPcln) ))Vshl_ND = (RHOB - RhoM + PHIN * (RhoM - RhoF)) / (RhoShl - RhoM +HIshl * (RhoM - RhoF)Vshl = Min(Vshl_GR , Min( Vshl_SP , Vshl_ND ))Clavier Shale CorrectionVshl = 1.7 - (3.38 - (Vshl+0.7)^2)^0.5Steiber Shale CorrectionVshl = 0.5 * Vshl / (1.5 - Vshl)9DT EQUATIONSFaust's Equation for DTDT_F = 1000/(2 * (DEPTH * RT) ^(1 / 6))Gardner's Equation for DTDT_G = ((25 / RHOB) ^4) /140Sonic from Apparent PorosityDT_P = DTma + PHIA * ( DTfld - DTma)Sonic 3pt Average CurveDTAve = (DT [-1] + DT + DT[1])/3Sonic 5pt Average CurveDTAve = (DT[-2] + DT[-1] +DT + DT[1] + DT[2])/5Sonic 7pt Average CurveDTAve = (DT[-3] + DT[-2] + DT[-1] +DT + DT[1] + DT[2]+ DT[3])/710PERMEABILITYTixier PermeabilityK = (250 * PHIE^3/SwIrr)^2Timur PermeabilityK = (100 * PHIE^2.25/SwIrr)^2Coates PermeabilityK = (70 * PHIE^2 * (1- SwIrr)/SwIrr)^2MISCELLANEOUSOil in Barrels; Depth in FeetBBL = 7758 * Acres * PHIA * (1 - SwA)Gas in Mcfd; Depth in FeetMCF = 43.560 * Acres * PHIA * (1 - SwA)Oil in Barrels; Depth in MetersBBL = 25450 * Acres * PHIA * (1 - SwA)Gas in Mcfd; Depth in MetersMCF = 142.9 * Acres * PHIA * (1 - SwA)Oil in Barrels; Depth in MetersBBL = 62890 * Hectares * PHIA * (1 - SwA)Gas in Mcfd; Depth in MetersMCF = 353.1 * Hectares * * PHIA * (1 - SwA)Oil in Barrels with Pay criteriaIf (PAY >0)BBL = 7758 * Acres * PHIA * (1 - SwA)Gas in Mcfd with PAY criteriaIf (PAY >0)MCF = 43.560 * Acres * PHIA * (1 - SwA)Gardner EQ.Gardner proposed a model in 1974 that is widely used to transform acoustic velocity (inverse of travel time or slowness) and vice versa. The relationship is shown graphically at the right (dotted line), and follows the equation: 1: DENS = A * (Vp^B)Where: DENS = density (g/cc) A = 0.31 when Vp is in m/s A = 0.23 when Vp is in ft/s B = 0.25

Gardner EQ.