Robert C. Ransom
What are Archie’s Basic Relationships
What is Meant by the Plot of R_{t} versus S_{wt}ϕ_{t}
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
Within the text, clicking on the bold terms FIGURE (*) and APPENDIX (*) will take you to the specific page of interest. Use your browser's back button to return to your previous page.
SUMMARY OF EQUATIONS
TABLE 1
EQUATION NUMBER |
PURPOSE |
Equation No. (1a) for R_{we} 1 / R_{we} = ( ϕ_{e} / ϕ_{t} ) 1 /R_{w} + (ϕ_{ne} /ϕ_{t} ) 1 / R_{wb} |
Equation for R_{we} for 100% water saturated environment. Involves two waters. Converts single-water to dual-water method. |
Equation No. (1b) for R_{we} 1 / R_{we} = ( ( S_{we}ϕ_{e })_{ }/ (S_{wt}ϕ_{t}_{ }) ) 1 /R_{w} + (ϕ_{ne} / ( S_{wt}ϕ_{t}_{ }) ) 1 / R_{wb} |
Equation for R_{we} for ≤ 100% water saturated environment. Involves two waters. Converts single-water to dual-water method. |
Equation No. (1c) for a a = R_{we} / R_{w} |
For the a coefficient. Shows the conversion from R_{w} to R_{we}. |
Equation No. (2a) for R_{0} R_{0 corrected} = F_{t} R_{we} |
For R_{0} in 100% water saturated rock. |
Equation No. (2b) for R_{t} R_{t calculated }= F_{t}_{ }R_{we} |
For R_{t calculated} in ≤ 100% water saturated environment. |
Equation No. (3a) for F_{t} F_{t }= 1.0 / (S_{wt}ϕ_{t}_{ }) ^{m}2 = 1.0 / (ϕ_{t }^{m}1 ) |
For F_{t} conversion from oil-bearing environment to 100% water saturated environment. |
Equation No. (3b) for F_{t} F_{t }= 1.0 / ( S_{wt}ϕ_{t }_{ }) ^{m}2 |
For universal F_{t} in ≤ 100% water saturated environment. |
Equation No. (3c) ( S_{wt}ϕ_{t}_{ }) ^{m}2_{ }= ( S_{wt}_{ }) ^{n} ( ϕ_{t} ) ^{m}1 |
Exponent equivalence equation. |
Equation No. (3d) r ohms = ( ( L / A ) m / m^{2} ) ( R ohms m^{2} / m ) |
Converts resisitance to resistivity and converse. |
Equation No. (4a) for R_{t} R_{t measured} = ( 1.0 / ( (S_{wt}ϕ_{t}_{ }) ^{m}2 ) ) aR_{w} = ( 1.0/( (S_{wt}ϕ_{t}_{ }) ^{m}2 ) ) R_{we} |
Calculates R_{t} while using single-exponent m_{2} saturation method. |
Equation No. (4b) for S_{wt} S_{wt} ^{n}= ( 1.0 / ( ϕ_{t}_{ } ^{m}1 ) ) ( R_{we} / R_{t measured }) |
Dual-water Archie equation using two exponents, m and n, from the triangle CDG of the model. |
Equation No. (4c) for S_{wt} S_{wt}^{n} = R_{0 corrected} /R_{t} = (F_{t}_{ }R_{wz} )/( F_{t}_{ }R_{wa} ) = R_{wz} / R_{wa} |
Water saturation equation from Figure 4, utilizing graphic determination of R_{z }. |
Equation No. (4d) for S_{wt} S_{wt}^{m}2 = (1.0 / ( ϕ_{t} ^{m}2 ) ) (R_{we} /R_{t}_{ }_{measured} ) |
Dual-water saturation equation using equivalent single exponent method from triangle AEG of the model. |
Equation No. (5a) for m m = ( log R_{0} - log R_{w} ) / (log1 - log ϕ_{e }) |
Evaluation of m from raw data from triangle ABC of the model. |
Equation No. (5b) for m m = (log R_{0 corrected} -log R_{we})/( log1 - log ϕ_{t}) |
Evaluation of m from corrected data. |
Equation No. (6) for S_{we} S_{we} = 1.0 - ( ϕ_{t} / ϕ_{e} ) ( 1.0 - S_{wt} ) |
Calculation of water saturation in effective pore space. |
Equation No. (4b) solved for exponent n n = ( log R_{t } - log R_{0} ) / ( log1 - log S_{wt }) |
Calculation of exponent n in both water-wet and oil-wet environments. |
Equation No. (4d) solved for exponent m_{2} m_{2} = ( log R_{t} - log R_{we} ) / ( log1 - log S_{wt}ϕ_{t} ) |
Calculation of exponent m_{2} in both water-wet and oil-wet environments. |