Deliverability of Wells in Shallow Confined Aquifers of Non-Integer Spatial Dimensions

We propose a generalized methodology to predict the deliverability of wells in fractional drainage areas. A fractional model is characterized by a single term power-law variation of the rock properties. Such a model may provide a more realistic alternative than the traditional homogeneous reservoir model. For example, the traditional models may not be applicable for sparse fracture networks. We assume the validity of the fractional model and find that the homogeneous solution is included in the generalized model as a special case. Simultaneous solution of the reservoir- and vertical lift equation leads to an algebraic equation of second degree. Hence, the prediction of the flow rate delivered into a pipe-line at any pressure is easily available. We investigate the sensitivity of the flow rate to variations in wellbore head, reservoir and flow string properties.