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Calculation of Pressure Rise vs. Distance in Minnelusa Formation: Diffusivity Equation, Lecture notes of Materials Physics

Northumbria UniversityMaterials Physics

The calculation of pressure rise vs. Distance in the minnelusa formation using the diffusivity equation. The equation involves terms such as pressure differential, flowrate, formation volume factor, viscosity, permeability, reservoir thickness, formation effective porosity, total matrix and fluid compressibility, radius, injection time, and skin factor. The document also includes various calculations for different areas and injection rates.

Typology: Lecture notes

2021/2022

Uploaded on 09/12/2022

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Calculated pressure Rise vs. Distance (Diffusivity Equation) - Minnelusa Formation Table A-3 Class V Permit App
dp= -70.6[(qBu)/(kh)][ln(1688.388* por*u*ct*rw^2/kt)-2s] wh ere
dp= pressure differential solve psi
q= flowrate (STB/d) 2,571.43 bbl/d
B= formation volume factor (RB/STB) 1.01 RB/STB
u= viscosity (cp) 0.74 cp
k= permeabilitiy (md) 150 md
h= reservoir thickness (feet) 164 feet
por= formation effective porosity (percent) 0.21 fraction
ct= total matrix and fluid compressibility (1/psi) 6.50E-06
psi-1
rw= radius (feet) variable feet
t= injection time (hours) 87600 10 years
s= skin factor (units) 0
Term 1= -70.6(qBu/kh) Injection Rate (gpm)= 75
Term 2= (por*u*ct*rw^2/kt)
dp= Term 1 * ln(1688.388*Term2)
Radius (rw)
(ft) Term 1 Term 2 [ln(1688.388*Term 2) - 2s]
dp
(psi)
0.26042 -5.51566 5.21336E-15 -25.4557311 140.41
0.5 -5.51566 1.92180E-14 -24.1511063 133.21
1-5.51566 7.68721E-14 -22.76481193 125.56
5-5.51566 1.9218E-12 -19.5459361 107.81
13.2 -5.51566 1.33942E-11 -17.60437827 97.10 Pc Minnelusa to Unkpapa/Sundance Burdock Area
14.45 -5.51566 1.60511E-11 -17.4234231 96.10 Pc Minnelusa to Unkpapa/Sundance Dewey Area
22.6 -5.51566 3.92632E-11 -16.52891211 91.17
25 -5.51566 4.80451E-11 -16.32706028 90.05
35 -5.51566 9.41684E-11 -15.6541158 86.34
48.5 -5.51566 1.80823E-10 -15.00168433 82.74
50.5 -5.51566 1.96043E-10 -14.92086525 82.30
75 -5.51566 4.32406E-10 -14.1298357 77.94
100 -5.51566 7.68721E-10 -13.55447155 74.76
125 -5.51566 1.20113E-09 -13.10818445 72.30
150 -5.51566 1.72962E-09 -12.74354134 70.29
172 -5.51566 2.27419E-09 -12.46982297 68.78
200 -5.51566 3.07489E-09 -12.16817719 67.12
Diffusivity Calculations
pf2

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Download Calculation of Pressure Rise vs. Distance in Minnelusa Formation: Diffusivity Equation and more Lecture notes Materials Physics in PDF only on Docsity!

Calculated pressure Rise vs. Distance (Diffusivity Equation) - Minnelusa Formation Table A-3 Class V Permit App

dp= -70.6[(qBu)/(kh)][ln(1688.388poructrw^2/kt)-2s] where

dp= pressure differential solve psi

q= flowrate (STB/d) 2,571.43 bbl/d

B= formation volume factor (RB/STB) 1.01 RB/STB

u= viscosity (cp) 0.74 cp

k= permeabilitiy (md) 150 md

h= reservoir thickness (feet) 164 feet

por= formation effective porosity (percent) 0.21 fraction

ct= total matrix and fluid compressibility (1/psi) 6.50E-06 psi

rw= radius (feet) variable feet

t= injection time (hours) 87600 10 years

s= skin factor (units) 0

Term 1= -70.6(qBu/kh) Injection Rate (gpm)= 75

Term 2= (poruct*rw^2/kt)

dp= Term 1 * ln(1688.388*Term2)

Radius (rw)

(ft) Term 1 Term 2 [ln(1688.388*Term 2) - 2s]

dp

(psi)

0.26042 -5.51566 5.21336E-15 -25.4557311 140.

0.5 -5.51566 1.92180E-14 -24.1511063 133.

1 -5.51566 7.68721E-14 -22.76481193 125.

5 -5.51566 1.9218E-12 -19.5459361 107.

13.2 -5.51566 1.33942E-11 -17.60437827 97.10 Pc Minnelusa to Unkpapa/Sundance Burdock Area

14.45 -5.51566 1.60511E-11 -17.4234231 96.10 Pc Minnelusa to Unkpapa/Sundance Dewey Area

22.6 -5.51566 3.92632E-11 -16.52891211 91.

25 -5.51566 4.80451E-11 -16.32706028 90.

35 -5.51566 9.41684E-11 -15.6541158 86.

48.5 -5.51566 1.80823E-10 -15.00168433 82.

50.5 -5.51566 1.96043E-10 -14.92086525 82.

75 -5.51566 4.32406E-10 -14.1298357 77.

100 -5.51566 7.68721E-10 -13.55447155 74.

125 -5.51566 1.20113E-09 -13.10818445 72.

150 -5.51566 1.72962E-09 -12.74354134 70.

172 -5.51566 2.27419E-09 -12.46982297 68.

200 -5.51566 3.07489E-09 -12.16817719 67.

Diffusivity Calculations

Calculated Pressure Rise vs. Distance (Diffusivity Equation) - Minnelusa Formation Based on 12 Years of Injection Activity at 75 GPM

dp= -70.6[(qBu)/(kh)][ln(1688.388poructrw^2/kt)-2s] where dp= pressure differential solve psi proposed flow rate max flow rate q= flowrate (STB/d) 3,977.14 bbl/d 116 gpm 170 gpm 5828.571 bbl/d DW No. 1 Burdock Area based on Unkpapa/Sundance B= formation volume factor (RB/STB) 1.01 RB/STB 234 gpm 8022.857 bbl/d DW No.3 Dewey Area based on Unkpapa/Sundance u= viscosity (cp) 0.74 cp 110 gpm 3771.429 bbl/d DW No. 1. Burdock Area based on Madison k= permeabilitiy (md) 150 md 97 gpm 3325.714 bbl/d DW No. 3 Dewey Area based on Madison h= reservoir thickness (feet) 164 feet por= formation effective porosity (percent) 0.1 fraction ct= total matrix and fluid compressibility (1/psi) 6.50E-06 psi - rw= radius (feet) variable feet t= injection time (hours) 105216 12 years (incl 4 leap years) s= skin factor (units) 0

nearest potential pathway through confining zone:

Burdock Area: Earl Darrow # Dewey Area: Dewey Fault Term 1= -70.6(qBu/kh) Injection Rate (gpm)= 75 2571.428571 bbl/d Term 2= (poructrw^2/kt) dp= Term 1 * ln(1688.388Term2) Radius (rw) (ft) Term 1 Term 2 [ln(1688.388*Term 2) - 2s]

dp (psi) 0.26042 -8.53088 2.06691E-15 -26.3809028 225. 50 -8.53088 7.61925E-11 -15.8659376 135. 475 -8.53088 6.87637E-09 -11.36335405 96.94 Pc=97.1 for Minn to Unpapa/Sundance Burdock Area 500 -8.53088 7.61925E-09 -11.26076746 96.06 Pc=96.1 for Minn to Unpapa/Sundance Dewey Area 18480 -8.53088 1.04082E-05 -4.041094963 34.47 Pc=34.8 for Minn to Madison Burdock Area 13200 -8.53088 5.31031E-06 -4.714039436 40.21 Pc=40.3 for Minn to Madison Dewey Area Calculating max injection rate by determining the rate that extends the critical pressure to 1000 feet away from the nearest potential breach in confining zone: 2900 -12.50215 2.56311E-07 -7.745051622 96.83 Pc=97.1 for Minn to Unpapa/Sundance Burdock Area based in distance to Earl Darrow #1 of 3,900 from DW No. 1 8375 -17.20885 2.13767E-06 -5.62397094 96.78 Pc=96.1 for Minn to Unpapa/Sundance Dewey Area based in distance to Dewey Fault of 9,375 from DW No. 3 16250 -8.08963 8.04783E-06 -4.298287278 34.77 Pc=34.8 for Minn to Madison Burdock Area based in distance to Lance Nelson of 17,250 from DW No. 1 8375 -7.13358 2.13767E-06 -5.62397094 40.12 Pc=40.3 for Minn to Madison Dewey Area based in distance to Dewey Fault of 9,375 from DW No. 3

3,900 feet away from the Class V injection wells in the Burdock Area. 9,375 feet from the Class V injection wells in the Dewey Area