Transient Pressure Characteristics of Horizontal Wells in a Three-Dimensional Dual Porosity Reservoir with the Existence of Skin and Wellbore Storage Effects
Authors: Ouyang Liang-Biao 
Published: December 2007

Transient Pressure Characteristics of Horizontal Wells in a Three-Dimensional Dual Porosity Reservoir with the Existence of Skin and Wellbore Storage Effects.

Abstract
The present paper focuses on the study of the fluid flow around a horizontal well in dual-porosity reservoirs with the presence of skin and wellbore storage effects. A three-dimensional model describing wellbore pressure and reservoir pressure changes with time and location is proposed, where both finite and infinite reservoirs are studied, and the outer boundary conditions are considered as either impermeable or with constant pressure. Analytical solutions in the Laplace space for the pressure and its derivative are obtained by using the finite Fourier consine transformation and the Laplace transformation.
Based on the analytical formulae in the Laplace space, the early-time and the long-time approximate solutions in physical space are derived. The transient pressure behaviors in physical space can be easily obtained by means of the Stehfest algorithm to investigate the influence of primary parameters, such as skin, wellbore storage, storativity ratio, transmissivity ratio, reservoir geometry and outer boundary conditions.

Introduction
Horizontal wells have become a well established technology for the recovery of oil and gas over the last decade. They have become increasingly attractive for production from thin reservoirs, naturally fractured reservoirs, reservoirs with gas and water coning problems, offshore environments where various wells are drilled from a central platform, as well as in the enhanced oil recovery practices such as steam injection. Horizontal wells can improve inflow performance by increasing contact area with production layers, and they produce more oil and gas with smaller drawdown per unit length as compared to conventional vertical wells.
A considerable amount of analytical and experimental work has been published on various aspects of horizontal well production, including transient flow models, well test analysis, stabilized inflow models and productivity indices, and coning or cresting behavior. The review papers by Joshi and Norris et al. provide state-of-the-art information for horizontal well and drainhole technology in the following different areas:–analytical solutions;–water and gas coning or cresting;–numerical simulation;–hydraulic fracturing;–well test analysis;–drilling and completion.
Well test analysis and investigation for transient pressure response of horizontal wells began with Goode & Thambynayagam's work in the mid-1980s. They presented an analytical solution for the transient pressure response during drawdown and buildup of a horizontal well in a semi-infinite reservoir. Skin effect was included in their model. Four possible flow regimes in horizontal wells, the early-time radial flow, the intermediate-time linear flow, the late-intermediate-time linear flow and the late-time linear flow, were identified. Equations for pressure drawdown and buildup and times for different flow regimes were provided and can be used for well test analysis to determine vertical permeability, mechanical skin and other parameters of interest. Clonts & Ramey solved the pressure drawdown problem for single or multiple horizontal drainholes in an infinite reservoir by means of the instantaneous Green's and source functions and the Neuman's product method. Nevertheless, the uniform-flux was assumed and no skin effect was considered.
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