Pressure build-up data in low permeability reservoirs take too long
and are usually of poor quality. A pressure buildup test is perhaps the
most widely performed transient test. In pressure buildup test, a well
which has been producing for some time at a constant rate is shut-in and
the bottom hole pressure is measured as a function of shut-in time. It
is easier to conduct and interpret than most other transient tests, but
often it is not economically feasible to shut in a well with a high
production rate for a buildup test. Sand producing wells are not good
candidates for long pressure drawdown tests. It is often impracticable
to maintain a constant rate long enough to complete a drawdown test. In
these cases, a multi-rate flow test should be run instead of buildup or
drawdown tests. In most cases, the well is shut-in at the surface and as
a result, some of the early time pressure data may be affected by
wellbore storage. Actually a well-designed multi-rate flow test may
minimize the influence of wellbore storage on pressure data.
A new technique based on the pressure derivative concept is presented
for interpreting a multi-rate flow test. It is shown here that a
Cartesian plot of the pressure derivative data versus a time group is a
straight line from which the reservoir permeability can be estimated. It
is also shown that for the case of two-rate test, Tiab’s Direct
Synthesis technique is applicable for calculating permeability and skin.
A step by step procedure is presented for interpreting a multi-rate
test using pressure and pressure derivative data. This new technique is
illustrated by several numerical examples.
Pressure transient testing techniques are an important part of
reservoir and production engineering. From the analysis of the pressure
tests, the reservoir model can be recognized and the reservoir
properties can be obtained. In order to determine such characteristics,
drawdown and Buildup tests are performed. But to run successful pressure
tests, many requirements have to be satisfied. For instance, pressure
buildup analysis requires that:
(1) The well be shut in for a sufficient period of time ∆t and (2)
The producing time, during the last constant rate prior to shut in, be
four times longer than the total shut in time in order to obtain actual
Because we need to shut the well in, the pressure build up test is
uneconomical both for high production wells and tight formations due to
income loss. Drawdown tests require that: (1) The well be shut in long
enough, before the test is run to reach reservoir static pressure. and
(2) The flowrate be maintained constant during the entire test, which is
quite difficult to achieve in practice. Pressure drawdown tests are not
suitable for sand-producing wells.
Consequently, in order to overcome the drawbacks of the conventional
single rate tests, a Multirate flow test should be run instead. A
Multirate test is a draw down test conducted at several production rates
(fig. 1). A well designed, performed, and analysed multirate test
yields the same results as a single flowrate test, reduces income loss
and removes the effects of flowrate fluctuations on the resulting
pressure transient responses. An additional advantage is the
minimization of phase redistribution effects. Such a test may be
1. An operator cannot afford to shut in a well for a build up test
but wishes to obtain the same type of information that can be obtained
from the build up test.
2. Sand production prevents shutting in the well for a build up test.
3. Phase segregation prevents the use of build up test.
4. Required to do so by a regulatory agency as in the case of gas wells.
5. Test began at a constant rate drawdown test, but the rate varied significantly during the test.
Reservoir parameters such as formation permeability, total skin
factor, average reservoir pressure, and distance to a barrier if
present, can be obtained from a Multirate test. In Multirate test, a
well is flowed at a number of constant rates and the flowing BHP are
recorded as a function of time. The constant rates should either be in
increasing or decreasing order of magnitude. The effect can be modelled
by considering a Multirate well to be several single rate well at same
location, and each time the rate changes , a new well with rate equal to
the total rate change is added to the calculation as shown in fig. 1.
1.2 Literature Review
A multi-rate test may be characterized by a series of constant flow
rates, or uncontrolled variable rate. In fact, pressure build-up testing
is a special type of multi-rate well test. The flow meters can aid in
the design of both kinds of tests, variable or constant flow rates, and
as a direct consequence more accurate analysis and results of their
interpretation can be obtained. The approach presented here is based on
the assumption that the system is infinite-acting and the logarithmic
approximation to the line source solution of the diffusivity equation is
applicable. The pressure behaviour caused by a variable flowrate is
given by the principle of superposition with time.
The principle of superposition with time is used to develop a plot to
determine the reservoir parameters. The principle states that adding
solution to a linear differential equation results in a new solution to
that differential equation but for different boundary condition. The
concept of superposition entails:”Every flow rate change in a well will
result in a pressure response which is independent of the pressure
responses caused by other previous rate changes”.