Fractal techniques are used to create networks with fracture swarm geometry that resembles that of exploratory cores recently reported in the literature. The networks have desired total pore volume, maximum and minimum fracture spacing and fractional dimension. These properties together with fracture conductivity control their hydraulic behavior. Numerical simulation of individual fragments and the addition of production to obtain total production is shown to be consistent with simulations of the entire network when fracture conductivity is high. In this case, the network exhibits sub-linear flow (pressure derivative slope between 0.5 and 1). When fracture conductivity is low, it exhibits sub-radial flow (pressure derivative slope between 0 and 0.5) at early times with transition to sub-linear or boundary dominated flow (BDF) at later times. Longer duration of sub-radial flow is achieved by reducing fracture conductivity. These types of flow behavior cover the entire range seen in unconventional wells. They show how the power-law behavior, frequently observed in diagnostic plots, can be produced by the combined effect of matrix fragments that individually can only show linear, bi-linear or BDF flow. The relatively simple geometry of fracture swarms allows calculation of properties for sub-radial flow that complement those already known for sub-linear flow. New insights into production mechanisms of unconventional wells are discussed.
The very low matrix permeability of unconventional wells causes the pressure transient response to last a long time, typically years. This makes pressure transient analysis (PTA), that relies on analysis of shut-in periods, limited in its ability to characterize flow behavior. Rate transient analysis (RTA), on the other hand, is especially suited to deal with long flowing periods. But there have been two different problems with the application of RTA to unconventional wells. The first is that the theoretical framework for RTA is not as developed as that of PTA. The second problem is that RTA responses of unconventional wells do not exhibit the familiar flow regimes (bi-linear, linear and radial) but rather power-law behavior with log-log derivative slopes different from the expected values for those flow regimes. To tackle the first problem, we developed a new theoretical framework by rewriting and solving the diffusivity equation in terms of cumulative production (Acuna, 2017). This new solution for constant pressure complies with theoretical expectations with respect to the constant flow rate solution as shown in Appendix B. It also handles all flow regimes seen in unconventional wells including the familiar ones mentioned before. To address the second problem, we proposed the simple idea that the flow behavior of an unconventional well is the result of many matrix fragments of different size acting together (Acuna, 2018a b), a concept further developed in this paper.