The objective of this paper is to investigate the transient pressure behavior of naturally fractured reservoirs with fractal characteristics. This work is based on the findings of previous studies, which have shown that the networks of fractures in some reservoirs are fractals. Thus, using this assumption, an approximate analytical solution for dual-porosity systems is derived in the Laplace space.The approximate solution presented in this work uses a pseudosteady-state matrix-to-fractal fracture transfer function. This solution is compared with a finite-element solution, and good agreement is found. Short-and long-time approximations are used to obtain procedures in time to determine some fractal parameters. These approximations are compared to the appropriate expressions when an unsteady-state matrix-to-fractal fracture transfer function is used.Synthetic and field examples are presented to illustrate the methodology proposed in this work.This paper also presents an analytical solution for the pseudosteady-state flow period and demonstrates the importance of analyzing both transient and pseudosteady-state flow-pressure data for a single-well situation to fully characterize a naturally fractured reservoir with a fractal geometry. k f ( r) = ͩ aV s ր 2h ͪ mr d mf − d− .

This study presents a new way to model high secondary porosity, mainly vuggy porosity, in naturally fractured reservoirs. New solutions are presented for two cases, where there is no primary flow through the vugs, which is an extension of the Warren and Root model, and where dissolution process of pore throats has created an interconnected system of vugs and caves. In both cases there is an interaction between matrix, vugs, and fracture systems. New insights are provided. Both pressure and production responses during transient and boundary dominated flow periods are explored. In transient well tests, for the case where there is no primary flow through the vugs, a change of slope could be present during the transition period. Thus, this study shows that slope ratios of 2:1 of early or late-time segment versus transition segment do not necessarily imply transient interaction between matrix and fractures. It is also shown that the presence of vugs and caves may have a definitive influence on decline curve and cumulative production behaviors; therefore it is necessary to incorporate vuggy porosity in the process of type curve match. Finally, the use of the methodology obtained in this work is illustrated with synthetic and field examples. Introduction Most of the world's giant fields produce from naturally fractured and vuggy carbonate reservoirs that have complex pore systems, mainly because carbonate rocks are particularly sensitive to post-depositional diagenesis, including dissolution, dolomitization and fracturing processes. Complete leaching of grains by meteoric pore fluids can lead to textural inversion which may enhance reservoir quality through dissolution or occlude reservoir quality through cementation1. Some works have classified carbonates based on fabric selective and non fabric selective pore types. The non-fabric selective are vugs and channels, caverns, and fractures1. For the purpose of this work no distintion is made on vugs, caverns and channels, and they will be denoted by the term vugs. Thus, vugs may vary in size from millimeters to meters in diameter. Vuggs are the result of carbonate and/or sulfate dissolution. From cores observations, the matrix porosity types adjacent to the vuggy zones are moldic, solution-enlarged microfractures, and solution-enlarged intercrystalline. Thus, it is possible to have a permeability enhancement adjacent to the vuggy zones. Three porosity types, matrix, fractures, and vugs, are usually present in naturally fractured, vuggy carbonate reservoirs. The determination of permeability and porosity in vuggy zones from core measurements are likely to be pessimistic because of sampling problems. In areas lacking cores, open-hole wireline logs may be used to help identify vuggy zones; however, vugs are not always recognized by conventional logs because of their limited vertical resolution2. Vuggy porosity is common in many carbonate reservoirs and its importance in the petrophysical and productive characteristics of a carbonate rock have been recognized by several works.

Truncation noise affects the interpretation of transient pressure tests when the total pressure change is very small compared to the total measurement scale of the tool. There are situations, mainly in high permeability reservoirs, where the maximum pressure variation is of the order of one thousandth of the total scale of the probe. Noise greater than one thousandth of the total pressure change hides pressure signals related to the characteristics of the reservoir; even when the accuracy of the tool could achieve one part by million of the total scale. This situation makes almost impossible the interpretation with the logarithmic derivative. It is demonstrated in this paper that the frequency spectrum of noise is in the same frequency band that frequencies associated to the reservoir signal. By using a fitting procedure and wavelets, the signal-noise ratio (SNR) of pressure tests with truncation noise is improved in most of the cases up to 8 dB. This situation is equivalent to measure the maximum pressure change of the reservoir with a tool of one bit of additional effective resolution. Greater improvements can be obtained when only Gaussian white noise is present in the pressure signal. This result offers the possibility to reuse old noisy derivative data logs, especially pressure tests from high permeability reservoirs. This contribution will permit to utilize derivative interpretation techniques in a more appropriate way. The efficiency of the proposed filtering technique is demonstrated with synthetic and field data pressure tests.

TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractThis study presents a new way to model high secondary porosity, mainly vuggy porosity, in naturally fractured reservoirs.New solutions are presented for two cases, where there is no primary flow through the vugs, which is an extension of the Warren and Root model, and where dissolution process of pore throats has created an interconnected system of vugs and caves. In both cases there is an interaction between matrix, vugs, and fracture systems. New insights are provided.Both pressure and production responses during transient and boundary dominated flow periods are explored. In transient well tests, for the case where there is no primary flow through the vugs, a change of slope could be present during the transition period. Thus, this study shows that slope ratios of 2:1 of early or late-time segment versus transition segment do not necessarily imply transient interaction between matrix and fractures. It is also shown that the presence of vugs and caves may have a definitive influence on decline curve and cumulative production behaviors; therefore it is necessary to incorporate vuggy porosity in the process of type curve match.Finally, the use of the methodology obtained in this work is illustrated with synthetic and field examples.

TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractThis work presents results on both pressure and production responses during transient and boundary-dominated flow periods, in naturally fractured reservoirs with vuggy porosity. It is considered that triple-porosity systems may not be treated as dual-porosity reservoirs, mainly because fractures and vugs have different geological origin and therefore their interaction with matrix blocks do not have to be similar. New solutions are presented for the case where there is no primary flow through vugs, an extension of the Warren and Root model, existing an interaction between matrix, vugs, and fracture systems.The new model assumes a single partially penetrating well producing from an undersaturated system considering several boundary conditions. The inner boundary condition at the wellbore can be considered either a fixed flux or constant pressure boundary. The upper, lower, and outer boundaries can be modeled at constant pressure or prescribed flux. These boundaries can be closed, or the influx can be modeled via a step rate or a ramp rate function. The step rate function could represent a waterflood effect and the ramp rate function a natural waterdrive or gas drive cap effect. The transient pressure response is also analyzed by considering an infinite outer boundary. In transient well tests and decline curve analysis, the effects of triple-porosity for different upper and lower boundaries conditions are analyzed, besides considering closed upper and lower boundaries as it has been done in the literature. It is shown that for triple porosity systems the derivative function may exhibit different behavior to that of double-porosity reservoirs. It is demonstrated that the presence of vugs and caves may have a definitive influence on transient well test and decline curve behaviors. Synthetic and field examples are presented to illustrate the methodology proposed in this work.