A new type-curve is presented for analyzing wells with wellbore storage and skin in double porosity systems. This type-curve applies to damaged, acidized, and fractured wells in fissured reservoirs. In addition to the usual well and reservoir parameters (permeability, skin, wellbore storage constant and length of the fracture intersecting the well), analysis yields characteristic parameters that can provide quantitative information on the volume of fissures and the size of porous blocks in the reservoir. These, in classical methods, could only be obtained if semi-log radial flow were present at both early and late times, (thus yielding two characteristic parallel semi-log straight lines on a Horner plot), a condition that is seldom satisfied in practice.
The analysis method presented in the paper is illustrated with actual field examples from several different fissured reservoirs.
The large number of papers1–16 published in the last twenty years on the behavior of naturally fractured reservoirs reflects the importance to the oil industry of this type of producing formation. Although several, apparently different, theoretical models have been proposed, most practical methods for interpretation of transient tests are based on the existence of two parallel, semi-log straight lines, that is considered a characteristic feature of fissured reservoirs.
Unfortunately, in most actual tests, the first semi-log straight line is usually obscured, and these methods cannot be used. As a result, only parameters characterizing the homogeneous behavior of the total system can be obtained (when conventional analysis methods are applicable), and those specific to the fracturation are usually not accessible.
In this paper, we present new type-curves that can provide all the system parameters, by means of log-log analysis. These curves also permit to detect under which conditions the two parallel, semi-log straight lines are present, and can be used for interpretation. Utilization of the type-curves is illustrated on several actual field data, for which no satisfactory analysis was previously available.
Available solutions for the behavior of fissured reservoirs are discussed in detail in Ref.16. A distinction is made there between models based on a detailed physical description of the fissured system, only suitable in relatively small scale, geotechnical type projects; and models where porous blocks and fissures are assumed uniformly distributed throughout the formation which is then treated as an â??equivalentâ?¿ system, either homogeneous or heterogeneous, as dictated by the general behavior of the actual test data. By â??equivalentâ?¿, it is meant a system whose calculated behavior is similar to the observed behavior of the real system.
In this paper, we have only considered the case of reservoirs whose behavior cannot be matched with homogeneous models, and thus indicates the need to take heterogeneities into account. Among the various heterogeneous models suggested in the literature, the double porosity model is certainly the one that has attracted the most attention in the past. Until recently, however, published solutions were restricted to a â??basicâ?¿ model, (a line source or finite radius well, in a horizontal, constant thickness, reservoir of infinite lateral extent, with impermeable upper and lower boundaries), without any of the inner boundary conditions found in practice (wellbore storage, skin, fractures, etc . . .), although outer boundary conditions have been considered by some authors. As a result, these solutions were only applicable to the analysis of interference tests, or to that of data after the start of the infinite acting period in production tests.