**A REVIEW OF APPLICATION OF PRESSURE DERIVATIVE CONCEPT TO MULTIRATE TESTS**

**ABSTRACT**

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.

**CHAPTER ONE**

**INTRODUCTION**

**1.1 Background to the study**

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 reservoir response. 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 conducted if:

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.

**1.2 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”.