Apparent flow-dimension approach to the study of heterogeneous fracture network systems

The generalized radial flow (GRF) model in well-test analysis employs noninteger flow dimensions to represent the variation in flow area with respect to radial distance from a borehole. However, the flow dimension is influenced not only by changes in flow area, but also by permeability variations in the flow medium. In this report, the flow dimension from the combined effect of flow dimensionality and permeability/conductance variation is interpreted and referred to as apparent flow dimension (AFD). AFD is determined using the second derivative of the drawdown-time plot from pressure transient testing, which may have varied noninteger values with time. A systematic set of investigations is presented, starting from idealized channel networks in one, two and three dimensions (1D, 2D and 3D, respectively), and proceeding to a case study with a complex fracture network based on actual field data. Interestingly, a general relation between the AFD upsurge/dip and the conductance contrast between adjacent flow channels is established. The relation is derived from calculations for 1D networks but is shown to be useful even for data interpretation for more complex 2D and 3D cases. In an application to fracture network data at a real site, the presence of flow channel clusters is identified using the AFD plot. Overall, the AFD analysis is shown to be a useful tool in detecting the conductance/dimensionality changes in the flow system, and may serve as one of the different data types that can be jointly analysed for characterizing a heterogeneous flow system.