All reservoirs cannot be described by conventional models. These are characterized by constant or piecewise constant rock properties. Sometimes a power law trend may be a better assumption. Power-law trends include but are not restricted to fractal reservoirs. A concept of fractal involves the additional assumption of self-similarity.
Fracture topology, changing flow area, and heterogeneities may also contribute to power-law dependency. We use fractal nomenclature to formulate the mathematical model. The solution methodology, however, is valid for any reservoir that may be characterized by power-law expressions.
We consider boundary dominated flow of pseudo-steady type. This simplifies the partial differential to an ordinary differential equation. An approximate inflow equation pwf vs. q, may be obtained by direct integration. The natural flow rate of a well may be obtained as the intersection of the fractal reservoir inflow performance relationship, IPR, and the vertical lift equation, VLF. The proposed technique is a generalization of a classical technique to plan and design wells in homogeneous reservoirs.
Application of the proposed methodology may improve production forecasting and aid design of wells in drainage areas where the fluid follows a complex flow path towards the well. The current formulation applies to one phase flow of a real gas. The model accommodates rate dependent skin. We investigate the sensitivity of the natural flow rate to changes in reservoir and well parameters. The objective is to shed light on possible benefits of projects to accelerate and improve gas recovery. We investigate the sensitivity to skin removal, infill drilling and change of well head pressures.