Multiphase Transient Well Testing for Gas Condensate Reservoirs
Authors: Jatmiko W. , Daltaban T.S. , Archer J.S. 
Published: December 2007

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Abstract
One of the most important parameters for analysing wellbore pressure response in gas condensate reservoirs is the pseudopressure function. This function correlates the reservoir pressure and saturation distributions, and hence the non-linear governing equation can be transformed into a linear equation and solved using a standard method.
This paper describes a method of analysing wellbore pressure response of a gas condensate reservoir under transient conditions. In this study the pressure distributions are calculated using iterative line source approximation and superposition principles. Initially, the steady-state saturation is assumed. The reservoir saturation distributions are estimated from the sandface saturation and the two-phase flow radius using a qudratic equation. The pseudopressure function is then calculated based on these distributions. The pressure distribution is then recalculated based on this saturation distribution. The material balance method is used to verify the saturation distributions. The dimensionless wellbore pseudopressure is calculated from the wellbore pressure data and compared with the dimensionless pressure (liquid solution).
In general the proposed method shows a good agreement with the liquid solution during transient conditions and hence it can be used to estimate the transport properties of gas condensate reservoirs.

Introduction
For the black oil system commonly described in the literature the physical properties of oil phase and the gas phase including, density, viscosity, formation volume factor and the solubility are assumed to be function of the pressure variable only. In gas condensate systems considered in this paper, the compositions and properties of the gas phase and the liquid phase is assumed to vary with the pressure, and is considered that it is not a valid approach to treat them as one of a 'liquid' dissolved in a 'gas' (the inverse black oil model). The composition dependence with pressure may need to be treated explicitly.
In this paper the flowing pressure response in a gas-condensate reservoir will be discussed, and the liquid drop out effects on its performance will be examined. For the sake of simplicity, the discussion is confined to a 'homogeneous' reservoir where a uniform absolute permeability is assumed. The primary objective is to apply the iterative line source solution method to analyse the flowing pressure response of a well in a gas-condensate reservoir. Initially any damage in the vicinity of the wellbore is ignored.
When the reservoir pressure drops below its saturation pressure, there are three important factors dominating the reservoir performance, namely the pressure distribution, the saturation distribution and the total compressibility. If these factors can be quantified properly, the flowing pressure response can be used to deduce the actual reservoir properties.
The purpose of this work is to present an analytical expression of reservoir pressure and saturation distributions, and addressing the reservoir characteristics during transient conditions. The well is assumed to produce under a constant molar rate. An appropriate dimensionless pseudopressure function will be used to compare the reservoir performance with the liquid solution.

Mathematical Formulations
The diffusivity equation for the ith component can be stated as follow:
(1)
P. 27^