Solution and Type Curve Analysis of Fluid Flow Model for Fractal Reservoir

Abstract

Conventional pressure-transient models have been developed under the assumption of homogeneous reservoir. However, core, log and outcrop data indicate this assumption is not realistic in most cases. But in many cases, the homogeneous models are still applied to obtain an effective permeability corresponding to fictitious homogeneous reservoirs. This approach seems reasonable if the permeability variation is sufficiently small. In this paper, fractal dimension and fractal index are introduced into the seepage flow mechanism to establish the fluid flow models in fractal reservoir under three outer-boundary conditions. Exact dimensionless solutions are obtained by using the Laplace transformation assuming the well is producing at a constant rate. Combining the Stehfest’s inversion with the Vongvuthipornchai’s method, the new type curves are obtained. The sensitivities of the curve shape to fractal dimension (θ) and fractal index (d) are analyzed; the curves don’t change too much when θ is a constant and d change. For a closed reservoir, the up-curving has little to do with θ when d is a constant; but when θ is a constant, the slope of the up-curving section almost remains the same, only the pressure at the starting point decreases with the increase of d; and when d = 2 and θ = 0, the solutions and curves become those of the conventional reservoirs, the application of this solution has also been introduced at the end of this paper

Analysis of diffusion process in fractured reservoirs using fractional derivative approach

“…The sensitivity of pressure response to fractal dimension is weak [18]. So, it can be assumed that dmf = d. Then Eq.…”

Anomalous diffusion of fluid momentum and Darcy-like law for laminar flow in media with fractal porosity

“…Accordingly, it is widely employed to fit data of field measurements, while the scaling exponent θ m is treated as the fitting parameter (see, for example, Refs. [31][32][33] and references therein).…”

A mathematical model considering complex fractures and fractal flow for pressure transient analysis of fractured horizontal wells in unconventional reservoirs

“…Lopez and Velazquez (2003) studied the transient and pseudosteady-state flow regimes to obtain values for the fracture model in a history matching study. Yulong and Zhang (2011) developed the pressure-transient type curves in reservoirs of fractal structure. The outer-boundary condition is the dominant reservoir parameter affecting the shape of the pressure curve.…”