The correlations between probable values of the reserves, the invasion constant and the dimensionless time constant are obtained for oil or gas reservoirs with infinite or finite, radial or linear aquifer, by superposing the effects due to a succession of uniform declines of the pressure at the initial gas-water (oil-water) contact.
The behavior of correlations deduced for the considered reservoir-aquifer system at each material balance calculation, is successively analyses and found as giving useful information. In fact, when represented in linear diagrams, they can be the basis to evaluate with a good approximation the geological reserves, the properties of the water influx and, also, to find the pressure values in the past production history which have the worse influence on the results of the material balance.
This is useful in the initial phase of reservoirs exploitation giving information to predict earlier their future behavior, when the instrumentation and evaluation errors in the reservoir pressure can be of the same order of the pressure drop in the corresponding time intervals.
The correlations can also provide a method for the simultaneous determination of the unknown parameters of the aquifer-reservoir systems which can be used in any case in combination with the usually methods, to give more complete results.
We will assume, as usually: an homogeneous and istropic aquifer with constant thickness (linear or radial, finite or infinite); a deplacement front undeformed by fluids different densities; the absence of collateral phenomena as the compaction of the surrounding shales or the oversaturation of the oil; uniform conditions in all zones of the reservoir; the pressure at the initial hydrocarbons-water boundary equal to the average pressure of the reservoir until the last calculating time; always a sufficient number of wells.
Moreover, we prefer to express the water influx by superposing the effects of the pressure variations at the reservoir-aquifer boundary as due to successive linear declines in every production interval. We do this with the formulation 1).