Fractional Dimension Rate Transient Analysis or FD-RTA is explained using fracture swarm models and then applied to the analysis of parent-child well interaction. The expected behavior for unconventional wells is a straight line in the derivative of the log-log diagnostic plot. Parent wells many times show a segmented derivative that is displaced upwards after child wells start production. FD-RTA calibration parameters estimated before the child wells are put on production mismatch history afterwards. We use the theory of FD-RTA to propose that variations in the parent well drainage volume can explain the observed behavior. A method to account for these variations and match the complete history of the parent wells is demonstrated with a simulated case and tested with a field case from the SPE data repository. The method also results is the diagnostic log-log plot recovering its expected shape. Other possible reasons for the observed changes are presented and discussed.
The log-log diagnostic plot extracted during RTA typically shows a pressure derivative with slope greater than 0.5 and less than 1. It is well known that linear flow should give a slope of 0.5 and boundary dominated flow a slope of 1. In a typical case a slope of 0.7, for example, is clearly stablished and lasts months to years. This power-law flow regime is well documented (Chu et al., 2017) and it is often called transitional flow (Apte and Lee, 2016). It has been described as a deviation from expected linear flow and different explanations for it have been offered.
One proposed explanation is anomalous diffusion (Chen and Raghavan, 2015). According to this explanation the contrast in conductivity between fractures and matrix together with petrophysical heterogeneity leads to heterogeneity of the velocity field where fluid particles undergo long jumps (superdiffusion) due to excitations or facilitations, or holdups (subdiffusion) due to entrapments or retardations (Albinali and Ozkan, (2016)). These effects are claimed to invalidate the assumption that properties such as pressure and fluid velocity vary continuously over the permeable flow domain leading to anomalous diffusion.