Robert C. Ransom
What are Archie’s Basic Relationships
What is Meant by the Plot of Rt versus Swtϕt
Parallel Resistivity Equations Used in Resistivity Interpretation
What is the Formation Resistivity Factor
How is Exponent n Related to Exponent m
Observations and Conclusions from Figure 10 about Exponent n
Are There Limitations to Archie's Relationships Developed in this Model?
Table of Retrievable Contents:
A CLARIFYING CONCEPT OF ARCHIE'S RESISTIVITY RELATIONSHIPS AND PARAMETERS.
A MODEL AND DISCUSSION
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SUMMARY OF EQUATIONS
TABLE 1
EQUATION NUMBER |
PURPOSE |
Equation No. (1a) for Rwe 1 / Rwe = ( ϕe / ϕt ) 1 /Rw + (ϕne /ϕt ) 1 / Rwb |
Equation for Rwe for 100% water saturated environment. Involves two waters. Converts single-water to dual-water method. |
Equation No. (1b) for Rwe 1 / Rwe = ( ( Sweϕe ) / (Swtϕt ) ) 1 /Rw + (ϕne / ( Swtϕt ) ) 1 / Rwb |
Equation for Rwe for ≤ 100% water saturated environment. Involves two waters. Converts single-water to dual-water method. |
Equation No. (1c) for a a = Rwe / Rw |
For the a coefficient. Shows the conversion from Rw to Rwe. |
Equation No. (2a) for R0 R0 corrected = Ft Rwe |
For R0 in 100% water saturated rock. |
Equation No. (2b) for Rt Rt calculated = Ft Rwe |
For Rt calculated in ≤ 100% water saturated environment. |
Equation No. (3a) for Ft Ft = 1.0 / (Swtϕt ) m2 = 1.0 / (ϕt m1 ) |
For Ft conversion from oil-bearing environment to 100% water saturated environment. |
Equation No. (3b) for Ft Ft = 1.0 / ( Swtϕt ) m2 |
For universal Ft in ≤ 100% water saturated environment. |
Equation No. (3c) ( Swtϕt ) m2 = ( Swt ) n ( ϕt ) m1 |
Exponent equivalence equation. |
Equation No. (3d) r ohms = ( ( L / A ) m / m2 ) ( R ohms m2 / m ) |
Converts resisitance to resistivity and converse. |
Equation No. (4a) for Rt Rt measured = ( 1.0 / ( (Swtϕt ) m2 ) ) aRw = ( 1.0/( (Swtϕt ) m2 ) ) Rwe |
Calculates Rt while using single-exponent m2 saturation method. |
Equation No. (4b) for Swt Swt n= ( 1.0 / ( ϕt m1 ) ) ( Rwe / Rt measured ) |
Dual-water Archie equation using two exponents, m and n, from the triangle CDG of the model. |
Equation No. (4c) for Swt Swtn = R0 corrected /Rt = (Ft Rwz )/( Ft Rwa ) = Rwz / Rwa |
Water saturation equation from Figure 4, utilizing graphic determination of Rz . |
Equation No. (4d) for Swt Swtm2 = (1.0 / ( ϕt m2 ) ) (Rwe /Rt measured ) |
Dual-water saturation equation using equivalent single exponent method from triangle AEG of the model. |
Equation No. (5a) for m m = ( log R0 - log Rw ) / (log1 - log ϕe ) |
Evaluation of m from raw data from triangle ABC of the model. |
Equation No. (5b) for m m = (log R0 corrected -log Rwe)/( log1 - log ϕt) |
Evaluation of m from corrected data. |
Equation No. (6) for Swe Swe = 1.0 - ( ϕt / ϕe ) ( 1.0 - Swt ) |
Calculation of water saturation in effective pore space. |
Equation No. (4b) solved for exponent n n = ( log Rt - log R0 ) / ( log1 - log Swt ) |
Calculation of exponent n in both water-wet and oil-wet environments. |
Equation No. (4d) solved for exponent m2 m2 = ( log Rt - log Rwe ) / ( log1 - log Swtϕt ) |
Calculation of exponent m2 in both water-wet and oil-wet environments. |