Page 234 - Fundamentals of Reservoir Engineering

OILWELL TESTING 172

c) Multi-rate drawdown testing

In this form of test the well is flowed at a series of different rates for different periods of
time and equ. (7.31) is used directly to analyse the results. The sequence is arbitrary
but usually the test is conducted with either a series of increasing or decreasing rates.
5
Providing that none of the rates is zero, the Odeh-Jones technique can be used to
analyse the results. That is, dividing equ. (7.31) throughout by the final rate q n

p-p
n
2kh ( i wf n ) = ∆ q j p t − t ) + S (7.33)
π
µ q n j = 1 q n D ( D n D − j 1
Values of p wf n are read from the continuos pressure record at the end of each flowing
period and the corresponding values of the summation are computed on each
occasion, so that each value represents a point on the graph. A plot of (p − p wf n )/q n
i

µ
m =
2π kh

p i − p wf n

q n

n ∆q
j p(t − t )
mS = j1 q n D D n D − j 1

Fig. 7.8 Multi-rate flow test analysis

n ∆ q
t
versus j p D ( D − t D ) should be linear as shown in fig. 7.8, with slope
−
j = 1 q n n j 1
m = µ / 2 kh and intercept on the ordinate mS.
π
The test yields the value of kh from the slope and S from the intercept assuming, as in
the case of the single rate drawdown test, that p i is measured prior to flowing the well at
the first rate. Exercise 7.8 provides an example of the traditional Odeh-Jones analysis
technique.

The basic oilwell test equation, (7.31), is fairly simple in form and yet it presents one

major difficulty when applying it to well test analysis. The problem is, how can the p D
functions, which are simply constant terminal rate solutions of the radial diffusivity
equation, be evaluated for any value of the dimensionless time argument t − t ) ?
( D
n D j 1
−
So far in this chapter dimensionless pressure functions have only been evaluated for
transient and semi-steady state flow conditions, equs. (7.23) and (7.27), respectively.
For a well draining from the centre of a circular, bounded drainage area, the full
constant terminal rate solution for any value of the flowing time is