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Ogunyomi, Babafemi A. (The University of Texas at Austin) | Patzek, Tadeusz W. (The University of Texas at Austin) | Lake, Larry W. (The University of Texas at Austin) | Kabir, C. Shah (Hess Corporation)
Production data from most fractured horizontal wells in gas and liquid-rich unconventional reservoirs plot as straight lines with a one-half slope on a log-log plot of rate vs. time. This production signature (half-slope) is identical to that expected from a 1D linear flow from reservoir matrix to the fracture face, when production occurs at constant bottomhole pressure. In addition, microseismic data obtained around these fractured wells suggest that an area of enhanced permeability is developed around the horizontal well, and outside this region is an undisturbed part of the reservoir with low permeability. On the basis of these observations, geoscientists have, in general, adopted the conceptual double-porosity model in modeling production from fractured horizontal wells in unconventional reservoirs. The analytical solution to this mathematical model exists in Laplace space, but it cannot be inverted back to real-time space without use of a numerical inversion algorithm. We present a new approximate analytical solution to the double-porosity model in real-time space and its use in modeling and forecasting production from unconventional oil reservoirs.
The first step in developing the approximate solution was to convert the systems of partial-differential equations (PDEs) for the double-porosity model into a system of ordinary-differential equations (ODEs). After which, we developed a function that gives the relationship between the average pressures in the high- and the low-permeability regions. With this relationship, the system of ODEs was solved and used to obtain a rate/time function that one can use to predict oil production from unconventional reservoirs. The approximate solution was validated with numerical reservoir simulation.
We then performed a sensitivity analysis on the model parameters to understand how the model behaves. After the model was validated and tested, we applied it to field-production data by partially history matching and forecasting the expected ultimate recovery (EUR). The rate/time function fits production data and also yields realistic estimates of ultimate oil recovery. We also investigated the existence of any correlation between the model-derived parameters and available reservoir and well-completion parameters.
Diagnostic fracture-injection testing (DFIT) has gained widespread usage in the evaluation of unconventional reservoirs. DFIT entails injection of water above the formation-parting pressure, followed by a long-duration pressure-falloff test. This test is a pragmatic method of gaining critical reservoir information (e.g., the formation-parting pressure, fracture-closure pressure, and initial- reservoir pressure), leading to fracture-completion design and reservoir-engineering calculations. In typical field operations, pressure is measured at the wellhead, not at the bottom of the hole, because of cost considerations. The bottomhole pressure (BHP) is obtained by simply adding a constant hydrostatic head of the water column to the wellhead pressure (WHP) at each timestep. Questions arise whether this practice is sound because of significant changes in temperature that occur in the wellbore, leading to changes in density and compressibility throughout the fluid column. This paper explores this question and offers an analytical model for estimating the transient temperature at a given depth and timestep for computing the BHP. Furthermore, on the basis of the premise of a line-source well, we have shown that the early-time data can be represented by the square-root of time formulation, leading to the new modified Hall relation for the injection period.
Performance prediction of wells producing from tight microdarcy formations is a daunting task. Complexities of geology (the presence/absence of naturally occurring fractures and contribution from different lithological layers), completion and fracture geometry complexities (multiple transverse and/or longitudinal fractures in long horizontal boreholes), and two-phase flow are impediments to simple performance forecasting.
We demonstrate the use of various analytical and numerical tools to learn about both short- and long-term reservoir behaviors. These tools include (a) traditional decline-curve analysis (Arps formulation), (b) Valko's stretched-exponential method, (c) Ilk et al's power-law exponential method, (d) rate-transient and transient-PI analyses to ascertain the stimulated-reservoir volume, and (e) numerical simulation studies to gain insights into observed flow regimes.
The benefits of collective use of analytical modeling tools in history-matching and forecasting both short- and long-term production performance of tight-oil reservoirs are demonstrated with the use of real and simulated data. Diagnosing natural fractures, quantifying stimulated-reservoir volume, and assessing reliability of future performance predictions, all became feasible by using an ensemble of analytical tools.
The extent to which fractures affect fluid pathways is a vital component of understanding and modeling fluid flow in any reservoir. We examined the Wafra Ratawi grainstone for which production extending for 50 years, including recent horizontal drilling, has provided some clues about fractures, but their exact locations, intensity, and overall effect have been elusive. In this study, we find that a limited number of total fractures affect production characteristics of the Ratawi reservoir. Although fractures occur throughout the Wafra field, fracture-influenced reservoir behavior is confined to the periphery of the field where the matrix permeability is low. This work suggests that for the largest part of the field, explicit fractures are not necessary in the next-generation Earth and flow-simulation models.
The geologic fracture assessment included seismic fault mapping and fracture interpretation of image logs and cores. Fracture trends are in the northeast and southwest quadrants, and fractures are mineralized toward the south and west of the field. Pressure-falloff tests on some peripheral injectors indicate partial barriers, and most of these wells lie on seismic-scale faults in the reservoir, suggesting partial sealing. A few wells show fractured-reservoir production characteristics, and rate-transient analysis on a few producers indicates localized dual-porosity behavior. Producers proximal to dual-porosity wells display single-porosity behavior, however, to attest to the notion of localized fracture response. The spatially restricted fracture-flow characteristics appear to correlate with fracture or vug zones in a low-permeability reservoir.
Presence of fracture-flow behavior was tested by constructing the so-called flow-capacity index (FCI), the ratio of kh well (well test-derived value) to kh matrix (core-derived property). Data from 80 wells showed kh matrix to be consistently higher than kh well, a relationship that suggests insignificant fracture production in these wells.
The Wafra field is in the Partitioned Neutral Zone (PNZ) between Kuwait and Saudi Arabia, as shown in Fig. 1. The field has been producing since the 1950s and has seen renewed drilling activity since the late 1990s, including horizontal drilling and implementation of peripheral water injection (Davis and Habib 1999).
The Lower Cretaceous Ratawi formation contains the most reserves of the producing intervals at Wafra. The Ratawi oolite (a misnomer--it is a grainstone) reservoir has variable porosity (5 to 35%) and permeability that ranges from tens to hundreds of md (Longacre and Ginger 1988). The main Wafra structure is a gentle (i.e., interlimb angle >170°), doubly plunging anticline trending north-northwest to south-southeast, which culminates near its northern end. The East Wafra spur is a north-trending branch that extends from the center of the main Wafra structure. As seen in Fig. 1, relief on the Main Wafra structure exceeds that on East Wafra.
The Ratawi oolite in the Wafra field has been studied at length, and various authors have reported geologic and engineering elements, leading to reservoir characterization and understanding of reservoir performance. Geologic studies are those of Waite et al. (2000) and Sibley et al. (1997). In contrast, Davis and Habib (1999) presented implementation of peripheral water injection, whereas Chawathé et al. (2006) discussed realignment of injection pattern owing to lack of pressure support in the reservoir interior.
Previous studies considered the reservoir to behave like a single-porosity system. But recent image-log fracture interpretations indicate high fracture densities, suggesting that the implementation of a dual-porosity model may be necessary because the high impact of fractures during field development has been recognized in some Middle East reservoirs for more than 50 years (Daniel 1954). Static and dynamic data are required to characterize fracture reservoir behavior accurately (Narr et al. 2006). Geologic description of the fracture system, by use of cores, borehole images, seismic data, and well logs, does not in itself determine whether fractures affect reservoir behavior. While seismic and some image logs were available to locate fractures in the Wafra Ratawi reservoir, no dynamic testing with the specific objective of understanding fracture impact has occurred. So, to determine whether fractures influence oil productivity significantly, we used diagnostic analyses of production data and well tests of available injectors. The assessment of fracture effects in the Ratawi reservoir will be used to guide the next generation of geologic and flow-simulation models.
Dynamic data involving pressure and rate have the potential to reveal the influence of open fractures in production performance. Unfortunately, pressure-transient testing on single wells does not always provide conclusive evidence about the presence of fractures with the characteristic dual-porosity dip on the pressure-derivative signature (Bourdet et al. 1989). That is because a correct mixture of matrix/fracture storativity must be present for the characteristic signature to appear (Serra et al. 1983). In practice, interference testing (Beliveau 1989) between wells appears to provide more-definitive clues about interwell connectivity, leading to inference about fractures.
In contrast to pressure-transient testing, rate-transient analysis offers the potential to provide the same information without dedicated testing. In this field, all wells are currently on submersible pumps. Consequently, the pump-intake pressure and measured rate provided the necessary data for pressure/rate convolution or rate-transient analysis.
We provide the Ratawi-reservoir case study primarily as an example of the integration of diverse geologic and engineering data to develop an assessment of fracture influence on reservoir behavior. It illustrates the use of production-data diagnostic tests to determine fracture influence in the absence of targeted fracture-analysis testing. The workflow can be applied to similar static/dynamic problems, such as fault-transmissivity determination. Secondly, this analysis illustrates the process of deciding that fractures, although present throughout the reservoir, may not lead to widespread fractured-reservoir characteristics (e.g., Allan and Sun 2003).
The extent to which fractures affect fluid pathways is a vital component of understanding and modeling fluid flow in any reservoir. We examined a Lower Cretaceous grainstone for which production extending over 50 years, including recent horizontal drilling, has provided some clues about fractures, but their exact locations, intensity and overall effect have been elusive. This study attempts to discern open fractures, if any, and their locations to facilitate building next generation earth and flow-simulation models.
The geological assessment involved mapping fault orientations from seismic and analyzing image logs and cores for fractures. Fracture trends are in the NE and SW quadrants and fractures are mineralized toward the south and west of the field. Pressure falloff tests on some peripheral injectors indicate partially sealing faults. Most of these wells lie on seismic-scale faults mapped in the reservoir. Some wells show fractured-reservoir production characteristics and rate-transient analysis on a few producers indicates localized dual-porosity behavior. Producers proximal to dual-porosity wells display single-porosity behavior, attesting to the notion of localized fracture response. The spatially-restricted fracture signature may be owing to fracture or vug zones, or to low-permeability reservoir.
Presence of fractures was discerned by constructing the so-called flow-capacity index (FCI), which is the ratio of khwell (welltest-derived value) to khmatrix (core-derived property). Data from 80 wells showed khmatrix to be consistently higher than khwell, with the p-50 reciprocal-FCI being 13, a relationship that suggests insignificant fracture production in these wells.
The Wafra Field is located in the Partitioned Neutral Zone (PNZ) between Kuwait and Saudi Arabia, as shown in Fig. 1. The field has been producing since the 1950's and renewed drilling activity since the late 1990's includes horizontal drilling and implementing peripheral water injection (Davis and Habib 1999).
The Lower Cretaceous Ratawi Formation contains the most reserves of the producing intervals at Wafra and its Ratawi Oolite (a misnomer; it is a grainstone) reservoir has high porosity and permeability (Waite et al. 2000). The main Wafra structure is a gentle (i.e., interlimb angle >170°), doubly-plunging anticline trending NNW-SSE whose culmination is near its northern end. The East Wafra spur is a north-trending fork off the center of the main Wafra structure. As seen in Fig. 1, relief on the Main Wafra structure exceeds that on East Wafra.