This paper presents the parametric behavior of a constant pressure well in the center of a two-composite reservoir with wellbore pressure well in the center of a two-composite reservoir with wellbore skin. For infinite composite reservoirs, the effects of mobility ratio, storativity ratio, wellbore skin, and the discontinuity distance on rate decline and cumulative influx are described. For bounded reservoirs, the effects of the outer boundary distance are presented. Type curves for the dimensionless wellbore flow rate in both infinite and bounded composite reservoirs are provided. These type curves are to be used for log-log type curve matching. An analysis method that comprises conventional semi-log analysis and log-log type curve matching to determine the dimensionless variables is proposed, and is tested and demonstrated with simulated data. Rate decline and rate decline derivatives of a constant pressure well are presented for infinite, constant pressure outer boundary, and closed outer boundary homogeneous reservoirs. A rate derivative type curve is provided for these cases as well. This type curve complements the rate decline curves presented by Fetkovich. The effects of the dimensionless reservoir exterior radius are discussed. Rate decline and rate decline derivatives of a constant pressure well in an infinite composite reservoir are also presented. For composite reservoirs, the effects of mobility ratios and discontinuity distance on both rate decline and rate decline derivatives are presented. Type curves for dimensionless wellbore flowrate derivatives for infinite composite reservoirs are provided. A new correlating group for the derivative type curve is provided, and is different than the correlating group for the rate type curve presented in the past. Finally, an analysis method that comprises type curve and derivative type curve matching to determine the dimensionless variables is proposed and demonstrated with a simulated example.
A substantial amount of literature has been devoted to the study of transient pressure analysis in composite reservoirs. Only the most important studies are hereby summarized. Some of the literature about transient rate decline analysis in homogeneous reservoirs are also presented. presented. Hurst analyzed pressure interference between two oil fields of different permeabilities sharing a common aquifer. He provided a limited analytical solution to the problem. A more general study was presented by Loucks and Guerro. They also considered a permeability presented by Loucks and Guerro. They also considered a permeability difference between the adjacent concentric regions. However, they provided general analytical solutions for the pressure distributions provided general analytical solutions for the pressure distributions in the composite reservoir by using the Laplace transformation. Larkin used Green's functions to solve the same problem with the well located anywhere inside the inner region. Bixel and van Poolen used a finite difference technique to solve the composite reservoir problem. They suggested semi-log type curve matching to locate the distance to the radial discontinuity. All the above studies considered the outer region to be infinite. Carter and Odeh treated the case of a closed outer boundary composite reservoir. Carter presented an analytical solution and some numerical results. He only considered a permeability difference between the two reservoir regions. Odeh developed an approximate solution and advanced a trial and error method to compute the distance to the radial discontinuity. Ramey provided approximate solutions for the wellbore flow rate in both infinite and bounded composite reservoirs. He also presented an approximate solution for the case of a moving interface between the two regions. Kazemi et al. investigated the effect of the storativity ratio on the pressure response in both regions of the composite system. They also studied the effects of wellbore storage and skin. Merril et al. investigated the influence of storativity and mobility ratios on locating the distance to the radial discontinuity. They provided correction factors to be used when computing the discontinuity radius from semi-log type curve matching. Eggenschwiler et al. attempted to fully interpret the pressure response from a composite reservoir. They introduced the concept of pseudo-steady state for the transient zone observed between the two pseudo-steady state for the transient zone observed between the two straight semi-log lines. They showed that from the material balance equation and the slope of the pseudo-steady state straight line the volume of the inner region can be computed. In a second study, Eggenschwiler et al. extended the original work to encompass both infinite and bounded composite reservoirs. They also presented deviation factors to be used when computing the discontinuity radius. At the same time, Horne et al. provided the same solution for geothermal composite systems. Horne et al., however, did not consider wellbore storage and skin.