Kansas Geological Survey, Open-file Rept. 95-1a
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Appendix A

Equations and Computer Program

Calculations and Equations

1) Calculating formation temperature:

Temperature Gradient Method: TF = 55 + (E x (A-55)/B)
Where:
TF = formation temp
E = formation depth
A = bottom hole temperature
B = bottom hole temperature depth

Average Temperature Gradient Method: TF = 55 + (E/100) x 1.5)
Where: TF = formation temp
E = formation depth
1.5 = average temperature increase per 100-foot depth increase

For Both: 55 = average surface temperature

2) Resistivity Corrections for Temperature Changes:

Use Arp's Formula (Schlumberger 1987)
F = C x (Temp + 6.77)/(T + 6.77)
Where F = resistivity at new temp
C = resistivity at a temperature other than formation temperature
Temp = temperature at which resistivity (C) was measured
T = new temperature

3) Calculating K:

K = 60 + (.133 + x TF)
Where TF = Formation Temperature

4) Correcting Rmf to Rmfe:

Use empirical corrections for predominately NaCl muds (Schlumberger 1987).
a. Rmf at 75° ≥ .1 ohm-m: Rmfe = .85 Rmf
b. Rmf at 75° < .1 ohm-m: Rmfe = (146 x Z)-5/(337 x Z)+77 Where Z = Rmf at 75°

5) Calculating Rmfe/Rwe Ratio

SSP = - K log Rmfe/Rwe
Therefore:
log Rmfe/Rwe = SSP/-K
and
Rmfe = 10^(SSP/-K)

6) Calculating Rwe

Rmfe/Rwe = Rmfe/Rwe
Therefore:
Rwe = Rmfe/(Rmfe/Rwe)

7) Calculating Rw at 77°F

log R_w = .138 + (1.5 log R_we) + .378 (log R_we)²

8) Where no Rmf value is given but a Rm value is given

Rule of Thumb Rmf = .75 x Rm (Frank 1986)

Basic Computer Program

Rw from SP
Dakota Project

1 INPUT "BHT = ?";A
2 INPUT "BHT DEPTH = ?";B 
3 INPUT "RMF = ?";C
4 INPUT "RMF TEMP = ?";D
5 INPUT "FORMATION DEPTH = ?";E 
6 INPUT "SSP = ?";S
7 IF A = 0 GOTO 10
8 TF = 55 + (E*((A-55)/B))                      FORM TEMP (TEMP GRAD. METHOD USING BHT)
9 GO TO 11
10 TF = 55 + ((E/100)*1.5)                      FORM TEMP (AVE. TEMP GRADIENT)
11 F = C * ((D+6.77)/81.77)                     F=RMF @ 75° (ARPS EQUATION)
12 K = 60 + (.133 * TF)                         K VALUE AT FORM TEMP 
13 Z = 10^^(S/-k)                               Z=Rmfe/Rwe
14 IF F < .1 GOTO 16 
15 IF F > .1 GO TO 18
16 G = ((146*F)-5)/((337*F)+77)                 Rmf to Rmfe (G=Rmfe) (SALT MUDS)
17 GOTO 19
18 G = .85 * F                                  Rmf to Rmfe(G=Rmfe) (FRESH MUDS)
19 H = G/Z                                      H=Rwe @ 75°
20 J = H * (81.77/83.77)                        Rwe @ 77° FROM 75° Rw @ 77°
21 L = 10(.138+(1.5logJ)+(.378*(logJ)2)
22 AA = L * (83.77/(TF+6.77))                   Rw @ FROM TEMP FROM 77°
23 SC = 10000/L                                 SPECIFIC CONDUCTIVITY @ 77°
24 TDS = SC * .6                                TOTAL DISSOLVED SOLIDS
25 IF TDS < 1350 GOTO 27 
26 IF TDS ≤ 1350 GOTO 29 
27 CL = (.3815*TDS) - 163                       CHLORIDE CONCENTRATION
28 GOTO 30
29 CL = (.5441*TDS) - 381 
30 USING "####.####"
31 PRINT "Rwe AT 77° = ";J 
32 PRINT "Rw AT 77° =";L
33 PRINT "Rw AT Form Temp =";AA 
34 USING "######"
35 PRINT "SC AT 77° ="; SC 
36 PRINT "TDS = ";TDS
37 PRINT "CL = ";CL
38 GOTO 1
39 END

Note: Steps 1-20 used to calculate Rwe for empirical database
Steps 21-39 used to correct Rwe to Rw, calculate TDS and chloride concentrations

Appendix B

Empirical Database

Appendix C

SP Water Quality Database

County: Cheyenne

% = Rmf estimated from Rm using Rmf = .75 Rm, @ = Thin Bed Corrected

County: Decatur

% = Rmf estimated from Rm using Rmf = .75 Rm, @ = Thin Bed Corrected

County: Gove

% = Rmf estimated from Rm using Rmf = .75 Rm, @ = Thin Bed Corrected

County: Graham

% = Rmf estimated from Rm using Rmf = .75 Rm, @ = Thin Bed Corrected

County: Logan

% = Rmf estimated from Rm using Rmf = .75 Rm, @ = Thin Bed Corrected

County: Norton

% = Rmf estimated from Rm using Rmf = .75 Rm, @ = Thin Bed Corrected

County: Rawlins

% = Rmf estimated from Rm using Rmf = .75 Rm, @ = Thin Bed Corrected