In pressure transient analysis, often the geological model is not known, or is ambiguous. Many well tests can be analyzed using a composite reservoir model which assumes that the flow capacity (k*h) near the wellbore is different from that away from the wellbore. There are many naturally occurring reservoirs that can legitimately be modeled this way because the transmissivity is indeed varying laterally. However there are many more reservoirs which have a different flow capacity near the well as compared to the bulk of the formation, not because of lateral permeability changes but because of layering. In these situations, it is the net pay and reserves, not the necessary the permeability, that is changing.
This paper compares the pressure transient behavior of a multi-layer system with that of a composite system, and illustrates the similarities and the differences in their respective Derivative signatures. It also investigates the extension of these two different models to pseudo-steady state forecasting. Even though the behavior of these two systems may be similar during transient flow (this is the time domain of most well tests), the long-term performance is significantly different if the improper model is used (this is the time domain of many engineering and economic decisions). The role of the geological model in well testing and deliverability forecasting is discussed, as it can have a significant effect on some parts of the analysis and an insignificant effect on other parts.
It is commonly known that if two or more layers of a reservoir are open to a wellbore, and are initially at a common pressure and constant drawdown, the general characteristics of the drawdown response is similar to that of a well producing from a single layer reservoir(1,2). Specifically, each layer will contribute production which is proportional to its transmissibility (kh/ µ). Therefore, the semi-log slope (m) calculated from the infinite acting flow 1 data will be nearly proportional to the sum of the individual layers transmissibilities (any modification of this slope would be due to unequal diffusivities or skin factors). For example, if a well is producing commingled at the wellbore from a layer of 2m and a layer of 3 m net pay (both with a permeability of 20 mD), the semi-log analysis of the radial flow data (refer to Figure #1) will show a flow capacity of 100 mD.m
If one layer of a two-layer model is limited in drainage area, a depletion of the limited layer will eventually occur. Upon depletion of this layer, a semilog straight line with a slope "m" that is inversely proportional to the transmissibility of the more extensive layer may be observed. On the derivative nalysis, after the initial radial flow, a unit slope develops followed by a transition to a second radial flow characterized by the typical zero slope. Figure #2 shows the semi-log plot for a two-layer reservoir where the extensive layer has a net pay of 2 m and a permeability of 20 mD (the corresponding dimensionless typecurve is embedded within the figure).