How To Recognize "Double-Porosity" Systems From Well Tests
Authors: Gringarten Alain C. 
Published: December 2007

Introduction
Well tests are performed to acquire qualitative and quantitative knowledge of the well and the reservoir being, tested. Typically, a well test involves modification of the rate or the pressure at one or more wells in the reservoir and observation of the resultant reservoir response (a change in pressure or rate, respectively) at the perturbed well and/or adjacent wells. The reservoir response is then used to construct a well test interpretation model from which well and reservoir parameters, such as permeability and skin, can be calculated.
The well test interpretation model describes the pressure or rate behavior of the actual well/reservoir system during the test and must be identified from the shape of the reservoir response. This information is different from, but complementary to, the information provided by other interpretation models that can be derived, for example, from log measurements or geologic observations. A well test interpretation model indicates primarily how many media with significantly different permeabilities and porosities are involved in the flow process and how these media interact.
One possible well test interpretation model is the double-porosity model, which describes double-porosity behavior. Double-porosity behavior is obtained when two different media are involved in the flow process: a higher-permeability medium that produces fluid into the well and a lower-permeability medium that recharges the higher-permeability medium. Double-porosity behavior is typical of fissured reservoirs and multilayered reservoirs with high permeability contrast between layers.
Different double-porosity behaviors are possible, depending on the degree of interaction, or interporosity flow, between the two constitutive media. The two extremes are (1) restricted. or "pseudosteady-state," interporosity flow, obtained when there is a significant impediment to flow, or interporosity skin, between the most-permeable and the least-permeable media, and (2) unrestricted, or "transient," interporosity flow, obtained when there is no interporosity skin.
The following describes the various techniques available for identifying double-porosity behavior from well test pressure data.

Conventional Analysis
Conventional analysis involves plotting test pressure data vs. some function of time on a semilog plot (Figs. 1a and 1b).
In theory, double-porosity behavior yields two parallel straight lines on a semilog plot, provided there are no near-wellbore or outer-boundary effects. Such a semilog plot is schematically represented in Fig. la. The first semilog straight line represents the homogeneous behavior of the most-permeable medium before the least-permeable medium starts recharging. As Fig. 1a indicates, this first straight line lasts longer for restricted interporosity flow than for unrestricted interporosity flow. The second semilog straight line represents the homogeneous behavior of both media when recharge from the least-permeable medium is fully established. The two parallel straight lines are separated by a transition zone that corresponds to the onset of interporosity flow. The transition can be a straight line in the case of unrestricted interporosity flow. The slope of such a transition straight line is equal to half that of the two parallel straight lines.
In practice, however, the two parallel straight lines may or may not be present. This depends on the condition of the well, the composition of the reservoir fluid, and the duration of the test. As a result, the same well may yield different responses in different tests. Fig. 1b illustrates a case of double-porosity behavior where only the last semilog straight line exists. This straight line represents the homogeneous behavior of the total system and is not characteristic of double-porosity behavior.
Thus a semilog plot is not an efficient tool for identifying double-porosity behavior. More generally, straight-line analysis techniques are not valid as diagnostic tools, because an apparent straight line through a range of data does not necessarily prove the existence of a specific flow regime.

Log-Log Analysis
Log-log analysis involves a log-log plot of pressure change vs. elapsed time (Fig. 2).
Double-porosity behavior yields an S-shaped log-log pressure curve on a log-log plot, as illustrated in Fig.
2. The initial portion of the curve represents a homogeneous behavior resulting from depletion in only the most-permeable medium. This corresponds to the region labeled "homogeneous behavior (most-permeable system)" in Figs. la and lb. A transition follows, corresponding to interporosity flow, during which pressure in the two media tends to equilibrate. Finally, homogeneous behavior resumes again, as a result of depletion in both constitutive media at the same time.
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