Well-Test Analysis for Naturally Fractured Reservoirs
Authors: Cinco-Ley Heber 
Published: June 2014

Distinguished Author Series articles are general, descriptive representations that summarize the state of the art in an area of technology by describing recent developments for readers who are not specialists in the topics discussed. Written by individuals recognized as experts in the area, these articles provide key references to more definitive work and present specific details only to illustrate the technology. Purpose: to inform the general readership of recent advances in various areas of petroleum engineering.

Summary
Well testing provides a powerful tool to detect and to evaluate heterogeneities in naturally fractured reservoirs (NFR's). Experience has shown that this type of reservoir may display behavior that consists of a variety of flow models. This paper presents a discussion of the applications and limitations of pressure-transient tests in the evaluation of NFR's.

Introduction
Optimizing the exploitation of a reservoir requires a complete description of the formation. A combination of information from various sources allows a reliable characterization of the system so that data from seismology, geology, well logging, well tests, core and fluid analysis, and well flow rates can be used to estimate reservoir geometry, oil and gas in place, and flow characteristics of the porous medium among other factors. Well testing1–10 provides an ideal tool to find reservoir-flow parameters and to detect and evaluate heterogeneities that affect the flow process in the formation.
NFR's contain a considerable amount of the world hydrocarbon reserves. AsFig. 1 shows, the rock in these types of systems may include several elements (i.e., vugs, fractures, and matrix). Hydrocarbons are contained in both fractures and rock matrix usually, fractures act as channels to yield highwell-flow rates. Reservoir studies must consider these heterogeneities because they can affect oil and gas recovery significantly. Because of the importance of NFR's, many publications haye appeared that provide an understanding of the behavior of these types of reservoirs.11,12 Currently, advances in well-test analysis allow a more reliable characterization of these systems based on new flow models that properly account for heterogeneities of fractured reservoirs. Owing to space limitations, discussing every publication that contributed to the technology used is impossible.
Experience has shown that NFR's may behave according to a variety of reservoir-flow models:homogeneous reservoir,multiple region or composite reservoir,anisotropic medium,single fracture system, anddouble-porosity medium.
Fig. 2 shows the main elements of these models, and Table 1 shows the different sets of parameters that have to be found to describe the flow behavior in the reservoir for each case. Next, we discuss the application and limitations of these models in well-test analysis.

Homogeneous Reservoir Model.
This model considers that reservoir properties are constant and do not vary throughout the reservoir. Fractures and rock matrix act as a single medium so that fluid production is caused by the simultaneous expansion of both elements, and fluid transfer between them, if any, occurs instantaneously without resistance. This behavior is exhibited by either a heavily fractured reservoir with small matrix blocks (Fig. 2a) or by an NFR where fluids are contained mainly in the fracture system (Fig. 2b). The presence of fractures can be detected by the analysis of well logs and cores.
In general, well-test-analysis methods have been developed for homogeneous reservoirs. The pressure behavior in these systems is controlled by the formation flow capacity, kh; porosity f, fluid viscosity µ, and total compressibility, ct. An essential part of well-test-analysis methods is a flow-regime diagnosis achieved through the application of alog-log graph of both pressure and pressure derivative.13 This process allows the detection of flow geometries and the presence of heterogeneities in the reservoir. The parameters of the system are estimated by use of the specialized graphs of pressure, p, vs. time, t (e.g.,p vs. log t, p vs. t1/2, p vs.t1/4, p vs. t-1/2,p vs.1/t, and p vs. :t, correspending to radial,14linear,15 bilinear,16 spherical,17 constant pressure boundary,18 and pseudosteady-state2 flows, respectively.
Fig. 3 illustrates the behavior of a single-well test (drawdown orbuildup) for radial flow in homogeneous systems. The first part of the pressure-derivative graph (unit-slope straight line) shows the presence of wellbore-storage effects followed (after a transition zone) by a horizontal portion representing a radial-flow behavior. The kh of the formation and the skin factor can be determined from the straight line on the semilog graph. The estimated kh for an NFR represents an equivalent value for the fracture/matrix system. As a complement to single-well tests, interference tests are used to estimate the storativity of the formation (fcth); this value is usually high for NFR's because it includes the storativity of both fractures and matrix.
Sometimes a high-productivity well produces from a reservoir with small hydrocarbon reserves; here, the fluids are contained mainly in the fractures and the system behaves as a homogeneous medium. Extended drawdown tests allow the early detection of this case during the appraisal phase of the reservoir.

Multiple Region or Composite Reservoir Model.
Some NFR's are fractured regionally. (Fig. 2c) and can therefore be considered to be composed of two regions: a high- and a low-transmissibility region. In this case, the reservoir behaves as a composite radial system.19 Wells producing from the fractured region exhibit higher productivity than those in the unfractured region. The system is characterized by the flow capacity of both regions (kh)1 and(kh)2.