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**BASIC PETROPHYSICAL FORMULAE**

Compiled By:- Muhammad Zahid

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**POROSITY Effective Porosity PHIE = PHIA * (1-Vshl) Density Porosity**

PHID = (RhoM - RHOB) / (RhoM - RhoF) Average Neutron Density Porosity PHIA = (PHID + PHIN) / 2 Gamma Ray Neutron Porosity Enter Values for PorMax, PorMin... PorMax = 0.35 PorMin = 0.02 Enter Values in Counts Per Second or API... CPS_PorMax = 75 CPS_PorMin = 600 B = log(PorMax/PorMin) / (CPS_PorMax - CPS_PorMin) A = PorMax / 10 ^ (B*CPS_PorMax) PHIGRN = A * 10 ^ (B * CPS)

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**Sonic Porosity (Wyllie)**

PHIS = (DT - DTma) / (DTfld - DTma) Enter Compaction Coefficient below, Cmp = 1.0 PHIS = (1/Cmp) * (DT - DTma) / (DTfld - DTma) Sonic Porosity (Empirical) PHIS = 0.67 * (DT - DTma) / DT Apparent Sonic Matrix DTma = ( DT - PHIA * DTfld ) / (1 - PHIA) Apparent Density Matrix RHOMa = (RHOB - PHIA * RhoF) / (1 - PHIA) Bulk Volume Water BVW = PHIA * SwA. Hydrocarbon Pore Volume HCPV = (1-SwA) * PHIA SoPhiH = (1-SwA) * PHIA

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**WATER RESISTIVITY Archie Ro Ro = a * Rw / (PHIA^m)**

Apparent Water Resistivity Rwa = RT * PHIA^m Conductivity COND = 1000/RT Rw from Dual Water RwDW = Rw * RwBnd / (Rw * Vshl + (1-Vshl) * RwBnd) Ro from Dual Water RoDW = (1 / (PHIA^m)) * (Rw * RwBnd / (Rw * Vshl + RwBnd * (1 - Vshl))) Modified Simandoux Ro If (Vshl < 1) RoMS = 1/(PHIE^m / (a* Rw*(1-Vshl)) + Vshl/Rshl)

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**Resistivity Temp Correction**

T1 and T2 in 'F R2 = R1 * (T ) / (T ) T1 and T2 in 'C R2 = R1 * (T ) / (T )

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**WATER SATURATION Archie Water Saturation**

SwA = sqrt( Rw / (RT * PHIA^2) ) SwA = (a * Rw / ( RT * PHIA^m) )^(1/n) Archie Water Saturation (Humble) SwA = sqrt( .62 * Rw / (RT * PHIA ^2.15) ) SwA = sqrt( Rw / (RT * PHID ^m) ) SwA = sqrt(Ro / RT) SwA = sqrt(Rw / Rwa) SwA = min( 1, max( 0, SwA )

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Dual Water SwT & SwE Calculate SwT Total Porosity Y = Vshl * ( RwBnd - Rw ) / ( 2 * RwBnd ) SwT = Y +( (Rw / ( RT * PHIA^2 ) ) + Y^2 )^.5 SwT = min( 1, max( Vshl, SwT ) ) Calculate SwE Effective Porosity If ( Vshl < .75 ) SwE = ( SwT - Vshl ) / ( 1 - Vshl ) Modified Simandoux SwMS If (Vshl < 1) SwMS = (sqrt( (Vshl/Rshl)^2 + 4*PHIE^m/(a*Rw*(1-Vshl)*RT) ) - Vshl/Rshl)/(2*PHIE^m/(a*Rw*(1-Vshl)) )

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Indonesian SwI SwI = sqrt(1/RT) / ( Vshl^(1- 0.5*Vshl) /sqrt(Rshl) + sqrt( PHIE^m / (a*Rw)) ) Ratio Method Sw Requires normalized SP, Rmf/Rw ratio from SP... K = ~ * <Temp> K = -71 RmfRwRatio = 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)) ))

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**SHALE VOLUME Calculate Vshl from Minimum of GR, SP & N/D**

Vshl_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 Correction Vshl = ( (Vshl+0.7)^2)^0.5 Steiber Shale Correction Vshl = 0.5 * Vshl / (1.5 - Vshl)

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**DT EQUATIONS Faust's Equation for DT**

DT_F = 1000/(2 * (DEPTH * RT) ^(1 / 6)) Gardner's Equation for DT DT_G = ((25 / RHOB) ^4) /140 Sonic from Apparent Porosity DT_P = DTma + PHIA * ( DTfld - DTma) Sonic 3pt Average Curve DTAve = (DT [-1] + DT + DT[1])/3 Sonic 5pt Average Curve DTAve = (DT[-2] + DT[-1] +DT + DT[1] + DT[2])/5 Sonic 7pt Average Curve DTAve = (DT[-3] + DT[-2] + DT[-1] +DT + DT[1] + DT[2]+ DT[3])/7

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**PERMEABILITY Tixier Permeability K = (250 * PHIE^3/SwIrr)^2**

Timur Permeability K = (100 * PHIE^2.25/SwIrr)^2 Coates Permeability K = (70 * PHIE^2 * (1- SwIrr)/SwIrr)^2

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**MISCELLANEOUS Oil in Barrels; Depth in Feet**

BBL = 7758 * Acres * PHIA * (1 - SwA) Gas in Mcfd; Depth in Feet MCF = * Acres * PHIA * (1 - SwA) Oil in Barrels; Depth in Meters BBL = * Acres * PHIA * (1 - SwA) Gas in Mcfd; Depth in Meters MCF = * Acres * PHIA * (1 - SwA) BBL = * Hectares * PHIA * (1 - SwA) MCF = * Hectares * <Step> * PHIA * (1 - SwA) Oil in Barrels with Pay criteria If (PAY >0) Gas in Mcfd with PAY criteria

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