Deliverability of Ground Water Wells in Confined Aquifers of Fractional (Non-integer) Spatial Dimensions

Flow in a sparsely fractured reservoir is analyzed by a simplified conceptual model of a single space variable. The fracture network does not fill Euclidian space. The non-filling property shows up as fractional (non-integer) spatial dimensions. The fractal model applies for self-similar geometries. Fractional reservoirs can be described by power law trends. These may have a variety of origins. Fracture architecture, changing flow area and variable rock properties may contribute to power-law dependency. We use fractal nomenclature to formulate the mathematical model. The resulting analytical solutions are valid for any reservoir that may be characterized by power law expressions. Many realizations may give rise to the same power law expressions. Hence the resulting analytical expression is the expected or an average solution. A generalized inflow performance relationship based on single term power law functions has been proposed. The simplicity of the functions facilitates integration of Darcy’s law. The productivity of wells during steady and pseudo steady state flow is investigated. Production rates are proportional to PI. Possible improvements of the productivity index are of obvious importance. We study the effect of a variation in the power law exponent and external radius.