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Assignment #1 Solution

The document is an assignment for a well test analysis course. It includes two practice problems: 1) Given reservoir properties, calculate the valid time limit for using the Ei function solution, plot pressure vs. radial distance at two times, and calculate additional pressure drop due to skin. 2) Three wells in a reservoir are producing - calculate pressure at an observation well after five days considering the combined pressure effects of the producing wells.

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Saqib Irshad
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431 views4 pages

Assignment #1 Solution

The document is an assignment for a well test analysis course. It includes two practice problems: 1) Given reservoir properties, calculate the valid time limit for using the Ei function solution, plot pressure vs. radial distance at two times, and calculate additional pressure drop due to skin. 2) Three wells in a reservoir are producing - calculate pressure at an observation well after five days considering the combined pressure effects of the producing wells.

Uploaded by

Saqib Irshad
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Department of Petroleum Engineering

College of Engineering and Applied Science


University of Wyoming
Well Test Analysis
PETE 4225
Fall 2020
Assignment #1

Date Posted: August 31st, 2020 Due Date: September 11th , 2020

Problem #1
Given a reservoir with the following properties:
Oil production rate = 600 STBD,

Total compressibility = 6.2510-6 psi-1,


Oil viscosity = 1.1 cp,
External radius = 4500 ft,
Oil formation volume factor = 1.125 bbl/STB,
Wellbore radius = 0.25 ft,
Reservoir permeability = 30 mD,
Formation thickness = 60 ft,
Initial reservoir pressure = 4500 psia,
Formation porosity = 0.175.
A) Calculate the time limit at which the Ei function solution is valid.
B) Calculate and plot the pressure as a function of position on a semi-log graph at t = 100 and 300
hours using the Ei function solution (or its logarithmic approximation) for r= 0.25, 1, 5, 10, 25,
50, 100, 500, 1000, 2500, 3500, and 4500 ft. Use the log approximation only if it is valid.
C) Calculate the additional pressure drop due to skin factor of S=2.

Solution:

First we need to check two conditions for using Ei function solution. These two solutions are line source
approximation and infinite acting condition. The line source approximation determines the lower limit for
applicability of Ei solution and the infinite acting condition determines the upper limit for applicability of
Ei function solution.

A)
1. Line source approximation:

Page 1 of 4 Well Test Analysis (PETE 4225) Fall 2020 M. Dejam


tDw=t/rw2>100 (Line source approximation)
t
t Dw 
rw2
0.0002637k

ct
0.0002637k 0.000263730
   6575 ft 2 / hr.
ct 
0.1751.1 6.25  106 
t Dw 
t
 100 
6575t   100  t  0.00095hr (Lower limit)
2
r
w 0.252
2. Infinite acting condition: re2/4> t hours

re2

4500   770 hrs. (Upper limit)
2

4 4  6575
B)

qBo  1  1  t 6575 t
p r , t   pi   Ei    where t D  2 
0.00708 kh  2  4t D  r r2

pr , t   4500 
600 1.11.125   1 Ei  
1 

0.00708  30  60  2  4t 
 D 

Page 2 of 4 Well Test Analysis (PETE 4225) Fall 2020 M. Dejam


4460

4360
Pressure (psia)

4260

4160

4060 t=100 hrs


t=300 hrs

3960
0.25 2.5 25 250 2500
Radial distance (ft)

C)
pskin  prw , t , S  0  p(rw , t , S  2)  4005 .41  3888 .89  116 .5 psi

Page 3 of 4 Well Test Analysis (PETE 4225) Fall 2020 M. Dejam


Problem #2
Three exploration wells have been drilled into a newly discovered oil reservoir. The following figure
shows the well location in the reservoir. Well A is an observation well (it has a pressure gauge in the hole
to measure the pressure response due to production wells B and C, but is not itself used for production).
Well B begins producing at 500 STBD at time t=0. Well C begins producing at 250 STBD 48 hours later.
C
Reservoir data:
Total compressibility = 4.510-6 psi-1 ,
Oil viscosity = 1.1 cp,
Oil formation volume factor = 1.12 bbl/STB,
Reservoir permeability = 38 mD, 3500 ft
Formation thickness = 82 ft,
B
Initial reservoir pressure = 3500 psia,
Formation porosity = 0.165.
2500 ft
A
Well data:
Well A Well B Well C
Well radius, rw (ft) 0.225 0.25 0.275
Skin factor 3 2 -1
Assume infinite acting behavior and calculate the pressure at well A after five days.

Solution:

ΔpB: t=120 hrs, r=2500 ft, q=500 STB


ΔpC: t=72 hrs, r=3500 ft, q=250 STB
0.0002637k 0.000263738
   12269 ft 2 / hr.
ct 0.1651.1 4.5  10 
6

t DB 
t

12269 120   0.236  p  9.9  10 - 2
2 2 DB
r 2500

t DC 
t

12269 72   0.072  p  3.61  10 -3
2 DC
r 3500 2
Bo
pr , t   pi  qB pDB  qC pDC  
0.00708 kh
3500 
1.11.12  500  9.9  10 - 2  250  3.61  10 -3  3497 .2 psia
 
0.00708 38 82 

Page 4 of 4 Well Test Analysis (PETE 4225) Fall 2020 M. Dejam

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