CONDITIONS OF SOLUTION

In principle, an infinite number of solutions of equ. (5.1 ) can be obtained depending on the initial and boundary conditions imposed. The most common and useful of these is called the constant terminal rate solution for which the initial condition is that at some fixed time, at which the reservoir is at equilibrium pressure pi , the well is produced at a constant rate q at the wellbore, r = rw. This type of solution will be examined in detail in Chapters 7 and 8 but it is appropriate, at this stage, to describe the three most common, although not exclusive, conditions for which the constant terminal rate solution is sought. These conditions are called transient, semi-steady state and steady state and are each applicable at different times after the start of production and for different, assumed boundary conditions.

a) Transient condition

This condition is only applicable for a relatively short period after some pressure disturbance has been created in the reservoir. In terms of the radial flow model this disturbance would be typically caused by altering the well's production rate at r = rw. In the time for which the transient condition is applicable it is assumed that the pressure response in the reservoir is not affected by the presence of the outer boundary, thus the reservoir appears infinite in extent. The condition is mainly applied to the analysis of well tests in which the well's production rate is deliberately changed and the resulting pressure response in the wellbore is measured and analysed during a brief period of a few hours after the rate change has occurred. Then, unless the reservoir is extremely small, the boundary effects will not be felt and the reservoir is, mathematically, infinite.

This condition is applicable to a reservoir which has been producing for a sufficient period of time so that the effect of the outer boundary has been felt. In terms of the radial flow model, the situation is depicted in fig. 5.2. It is considered that the well is surrounded, at its outer boundary, by a solid "brick wall" which prevents the flow of fluids into the radial cell.