This paper presents a simplified method for drawdown and buildup analysis of naturally fractured reservoirs. This method permits handling of wellbore storage and matrix blocks of different shapes. Although there are excellent techniques in the literature for handling these problems, all of them require the use of specialized software. The technique developed in this paper allows approximate, yet sound solutions to these problems, using a few columns in a spread sheet. The method allows calculation of parameters such as fracture permeability, wellbore storage, skin, storativity ratio ?, interporosity flow coefficient λ, fracture spacing, number of fractures intercepted by the wellbore and amount of secondary mineralization within fractures. The method is illustrated with actual data from fractured reservoirs.


There are excellent commercial software packages in the oil industry for evaluating well testing data from dual porosity models. The idea behind the methods presented in this paper is not to replace sophisticated software packages but to provide step by step simplified methods that still give reasonable results. Some of the basic principles behind well test analysis of naturally fractured reservoirs have been published by Barenblatt and Zheltov,1 Warren and Root2Kazemi, 3de Swann, 4Najurieta, 5 and Streltsova. 6 Aguilera7,8 published functions for handling various matrix block shapes. Several type curves have appeared in the literature (literally hundreds of type curves) including works by Bourdet and Gringarten9and Jalali and Ershagui.10 Still the problem of non-uniqueness will be with us anytime that we analyze transient pressure data, due to the inverse nature of the problem we are dealing with.

Drawdown Test

Flow pressure (pwf) as a function of time (t), capable of matching recorded pressures that include skin and wellbore storage in a dual porosity system, can be calculated from the equation: Equation (1) (Available in full paper) where (ηgc) is a general hydraulic diffusivity that includes wellbore storage; c1, c2 and c3 are constants that apply to either customary or SI units. Other nomenclature are defined at the end of the paper. The general hydraulic diffusivity can operate under conditions of restricted or unrestricted interporosity flow.

Restricted Interporosity Flow

This section presents the equations for generating a synthetic drawdown. The procedure starts with an estimate of the ratio α' between the shape factor of matrix blocks and the shape factor of a stratum model. This is given by: Equation (2) (Available in full paper)

A function, f (t, λ) for the case of restricted interporosity flow is determined from: Equation (3) (Available in full paper)

Next a hydraulic diffusivity (ηg) for the dual porosity system, without wellbore storage, is calculated from: Equation (4) (Available in full paper)

A pressure change (Δp)c that includes wellbore storage, C, is given by: Equation (5) (Available in full paper)

A function of Equation that includes wellbore storage is determined from: Equation (6) (Available in full paper)

The storativity ratio (ω) is calculated from: Equation (7) (Available in full paper)

Eqs. 2 to 7 permit calculating the general hydraulic diffusivity (ηgc) from: Equation (8) (Available in full paper)

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