Page 281 - Introduction to Petroleum Engineering

268 PRODUCTION PERFORMANCE
13.8.3 Exercises

13.1 Prepare a bubble map for the following cumulative oil production data:

Location Oil
Well I J MMSTB
1 2 2 4.0
2 2 3 2.5
3 3 2 2.0
4 3 3 3.0
5 1 1 1.5
6 4 4 1.0

n 1
n
/
13.2 The equation q n nat q is a solution of dqdt aq where a, q are
i
i
constants. What is the value of q at t = 0?
at
13.3 A. Use the exponential decline equation q qe to plot oil flow rate as a
i
function of time for a well that initially produces 12 000 STB/day and has
a decline factor a = 0.05 per year. Time should be expressed in years and
should range from 0 to 50 years. Use a logarithmic scale that ranges from
100 STB/day to 12 000 STB/day.
B. When does flow rate drop below 1000 STB/day?
13.4 The initial gas rate of a gas well is 1000 MSCF/day. The rate declines to
700 MSCF/day after two years of continuous production. Assume the rate of
at
decline can be approximated by the exponential decline equation q qe .
i
When will the gas rate be 50 MSCF/day? Express your answer in years after
the beginning of production.
13.5 The initial production rate of an oil well is 100 STB/month and has an initial
decline factor of 10% per year. Calculate flow rates using Arps’ decline model
for Arps’ n‐values of 0, 0.5, 1.0, and 2.0 at the following times: 1, 5, 10, 25,
50, and 100 years. Prepare semilog plots of rate versus time for all cases on
the same graph.

13.6 A. Well PI = well productivity index = flow rate divided by pressure draw-
down. Suppose the well originally produces 1000 STBO/day at a pressure
drawdown of 20 psia. What is the well PI?
B. The well PI declined 6% a year for the first 2 years of production. What is
the well PI at the end of year 2?
C. The well PI at the beginning of year 3 is 35 STBO/day/psia. A well test
showed an increase in skin and the skin is positive. Does the well need a
workover (Y or N)?