Composite model with fractional flow dimensions for well test analysis in fractured rocks

The represented analytical model is addressed to fracture-zone aquifers in which well test responses can be commonly matched with models involving fractional flow dimensions. The model assumes a composite structure representing the fractures opening into the pumping well and the fracture system comprising the actual aquifer. The aim is to assess the hydraulic properties for the near-well zone and the aquifer in terms of concrete parameters even if flow dimensions have fractional values. Dimensionless drawdown in pumping and observation wells was solved by applying Laplace transforms. The early-time approximation for the pumping well can be used to assess the transmissivity ( T 1) if the flow dimension in the inner zone ( n 1) is greater than about 1.7. The long-time solutions indicate that the inner zone induces a pseudo-skin effect that can be estimated by comparing the pumping well and observation well data. If K 1 is known, the extent of the inner zone ( r′) can be estimated from the pseudo-skin factor. The responses tend to form log–log straight lines with slopes of 1− n 2. By plotting drawdown vs. t (1− n 2) on the double-logarithmic scale, the product of the hydraulic conductivity and the through-flow area at the wellbore radius ( KA 2) and the hydraulic diffusivity ( D 2) of the aquifer can be estimated from the slope and the intercept. The hydraulic conductivity of the aquifer ( K 2) is estimated by considering the through-flow area as a projection of an n 2-dimensional sphere with a radius of r wb through three-dimensional space by an amount r′ (3− n 2) . The analyzed field example comprises a pumping test of a fracture zone aquifer in south–central Finland. For the pumping well, simultaneous matching of drawdown and derivative type-curves with observed responses can be used to verify the results of the early-time analysis and the proposed straight-line procedure. In addition, type-curve matching yields estimates of the hydraulic diffusivity ratio and a value of the dimensionless wellbore storage. The analyzed observation wells are considered to be sufficiently far from the inner zone. Consequently, type-curves are produced based on the dimensionless drawdown solution that is identical to generalized radial flow model. Type-curve matching of the observation well responses produces estimates for KA 2, K 2 and D 2. The obtained values are similar to previous studies that included models relying on integer flow dimensions. However, models relying on