We investigate coupled flow and geomechanics in gas production from extremely low permeability reservoirs such as tight and shale gas reservoirs, using coupled dynamically porosity and permeability during simulation. The intrinsic permeability is a step function of the status of material failure, and is updated every time step. We investigate the reservoirs with vertical and horizontal primary fractures, employing the single and double porosity models. We modify the multiple porosity constitutive relations for modeling double porous continua for flow and geomechanics. The numerical results indicate that production of gas causes redistribution of the effective stress fields, increasing the effective shear stress and resulting in plasticity. Shear failure occurs away from the primary fractures as well as near the fracture tips, which indicates generation of secondary fractures. These secondary fractures increase the permeability significantly, and change the flow pattern, which in turn causes a change in distribution of geomechanical variables. When the double porosity flow model is used, we observe a faster evolution of the enhanced permeability area than that obtained from the single porosity model because of the higher permeability of the fractures in the double porosity model. Additionally, we find that the complicated physics for stress sensitive reservoirs cannot properly be captured by uncoupled or decoupled methods, and thus tightly coupled flow and geomechanical models are highly recommended to accurately describe the reservoir behavior during gas production in tight and shale gas reservoirs.
Unconventional natural gas such as tight and shale gas has become an increasingly important source of natural gas in the United States over the past decade and the estimates of the natural gas resource potential for shale gas range from 14.16×1012 m3 to 28.3×1012 m3 (500~1000 Tcf) (Arthur et al. 2008; Jenkins and Boyer 2008). Geological formations of tight and shale gas reservoirs exhibit extremely low permeability within which gas is trapped (Hill and Nelson 2000), and accordingly hydraulic fracturing is performed in order to enhance permeability and increase production rate (Dean and Schmidt 2008; Ji et al. 2009; Nassir et al. 2012). The success of gas production from the Barnett Shale is based on horizontal wells and hydraulic fracturing techniques and has led to gas production of other shale reservoirs such as the Marcellus Shale, one of the largest natural gas resources in the United States (Arthur et al. 2008; Cipolla et al. 2010).
Several studies have been made on production of gas from tight and shale gas reservoirs as well as hydraulic fracturing. Freeman et al. (2011) investigated non-Darcy flow without geomechanics, examining the effects of Knudsen diffusion on gas composition, because flow mechanism of shale gas is significantly different from that of conventional oil and gas reservoirs due to extremely low permeability and small pore throat. Vermylen and Zoback (2011) studied different scenarios for hydraulic fracturing along horizontal wells, and found significant differences in stimulation robustness for different fracturing procedures, for example, two alternatively fractured (zipperfrac) and simultaneously fractured (simulfrac) wells. Ji et al. (2009) developed a numerical model for hydraulic fracturing, accounting for coupled flow and geomechanics, and Nassir et al. (2012) incorporated shear failure to tensile fracturing. Dean and Schmidt (2008) employed the same fracturing algorithm, using different criteria of fracture propagation. Fisher and Warpinski (2011) analyzed the fracture growth induced by hydraulic fracturing with real data, and concluded that the fracture propagation was limited in the vertical direction, compared with the horizontal direction. Yet, coupled flow and geomechanics that can consider dynamic interrelations among pore volume, permeability, and material failure during production are little investigated. Geomechanics with material failure may change permeability and porosity followed by flow patterns significantly, and, in turn, redistribution of pore-pressure can affect geomechanics (e.g., Armero (1999) and Rutqvist and Stephansson (2003)), Thus, rigorous modeling for coupled flow and geomechanics is necessary for gas production in shale and tight gas reservoirs.
Various models featuring horizontal wells with multiple fractures have been proposed to characterize flow behavior over time in tight and shale gas systems. Currently, only very little is known about the effects of nonideal fracture patterns and coupled primary-secondary fracture interactions on reservoir performance in unconventional gas reservoirs.
We developed a 3D Voronoi mesh-maker that provides the flexibility to accurately represent various complex and irregular fracture patterns. A numerical model was developed based on such fracture concepts to assess the potential performance of unconventional gas reservoirs. We conducted simulations using up to a half-million cells and considered production periods that are orders of magnitude longer than the expected life of wells and reservoirs. Our aim is to account for a wide range of flow regimes that can be observed in irregular fracture patterns, and to fully assess even slight nuances in flow behavior.
We investigated coupled primary-secondary fractures, with multiple vertical hydraulic fractures intersecting horizontal secondary "stress-release" fractures. We studied irregular fracture patterns to show the effect of fracture angularity and nonplanar fracture configurations on production. The results indicate that the presence of high-conductivity secondary fractures results in the highest increase in production, while, contrary to expectations, strictly planar and orthogonal fractures yield better production performance than nonplanar and nonorthogonal fractures with equivalent propped fracture lengths.
Few attempts have been made to model shale gas reservoirs on a compositional basis. Multiple distinct micro-scale physical phenomena influence the transport and storage of reservoir fluids in shale, including differential desorption, preferential Knudsen diffusion, and capillary critical effects. Concerted, these phenomena cause a measureable compositional change in the produced gas over time.
We developed a compositional numerical model capable of describing the coupled processes of diffusion and desorption in ultra-tight rocks as a function of pore size. The model captures the various fracture configurations believed to be induced by shale gas fracture stimulations. By combining the macro-scale (reservoir-scale fractures) and micro-scale (diffusion through nanopores) physics, we show how gas composition changes spatially and temporally during production.
We compare our numerical model against measured gas composition data obtained at regular intervals from shale gas wells. We utilize the characteristic behavior illustrated in the model results to identify and to define features in the measured data. We present a workflow for the integration of measured gas composition data into production data analysis tools in order to develop a more complete well performance diagnostic process.
The onset of fracture interference in horizontal wells with multiple transverse hydraulic fractures is shown to be uniquely identified by distinct fluctuations in the flowing gas composition. Using these measured composition data, the timescale and durations of the transitional flow regimes in shales are quantified, even for high levels of noise in the rate and pressure data. Reservoir properties are inferred from the integration of the compositional shift analysis of this work with modern production analysis.
This work expands the current understanding of well performance for shale gas to include physical phenomena that lead to compositional change. This may be used to optimize fracture and completion design, improve well performance analysis and provide more accurate reserves estimation.
This work demonstrates a numerical model which captures multicomponent desorption, diffusion, and phase behavior in ultra-tight rocks. We identify and validate diagnostic trends via high-resolution composition, saturation and pressure maps. We provide a workflow for incorporating measured gas composition data into modern production analysis.
The exploitation of unconventional reservoirs goes hand in hand with the practice of hydraulic fracturing and, with an ever increasing demand in energy, this practice is set to experience significant growth in the coming years. Sophisticated analytic models are needed to accurately describe fluid flow in a hydraulic fracture and the problem has been approached from different directions in the past 3 decades, starting with the work of Gringarten et al. (1974) for an infinite conductivity case, followed by contributions from Cinco et al. (1978), Lee and Brockenbrough (1986), Ozkan and Raghavan (1991) and Blasingame and Poe (1993) for a finite-conductivity case. This topic is still an active area of research and, for the more complicated physical scenarios such as multiple transverse fractures in ultra-tight reservoirs, answers are presently being sought.
Starting with the seminal work of Chang and Yortsos (1990), fractal theory has been successfully applied to pressure transient testing, albeit with an emphasis on the effects of natural fractures in pressure-rate behavior. In this paper, we begin by performing a rigorous analytical and numerical study of the Fractal Diffusivity Equation and show that it is more fundamental than the classic linear and radial diffusivity equations. Subsequently, we combine the Fractal Diffusivity Equation with the trilinear flow model (Lee and Brockenbrough 1986), culminating in a new semi-analytic solution for flow in a finite-conductivity vertical fracture which we name the "Fractal Fracture Solution??. This new solution is instantaneous and overall is more accurate than the Blasingame and Poe solution (1993). Ultimately, this project is a demonstration of the untapped potential of fractal theory; our approach is very flexible and the same methodology can be easily extended to develop new solutions for pressing problems that the industry currently faces.
The objective of this work is to develop a fast and accurate semi-analytical solution for flow in a single vertical fracture fully penetrating a homogeneous infinite-acting reservoir. This would be the first time that fractal theory is used to study a problem that is not related to naturally fractured reservoirs or reservoir heterogeneity. Additionally, as part of the development process, we re-visit the fundamentals of fractals in reservoir engineering and show that the underlying Fractal Diffusivity Equation possesses interesting qualities that have so far not been addressed in the literature.
Overview of Fractals in Reservoir Engineering
While research in the area of pressure transient analysis of naturally fractured systems has made important advances, it became apparent that the models did not always give satisfactory results (Acuña et al. 1995). Standard models have their underpinnings on the classical notion that naturally fractured systems are characterized by several distinct scales that delineate the fracture network and the embedded matrix. Variations on this approach, including randomly generated fracture networks (Chang and Yortsos 1993), triple-porosity systems (Abdassah and Ershaghi 1986), etc., although adding complexity, still obey the general premise that the network of fractures is dense and space filling; namely, that it is of Euclidean geometry (Acuña et al. 1995). Instead, it is perhaps more reasonable to expect that what feeds the well is a network of fractures, which is, however, not necessarily space-filling or perfectly connected. Such networks are best characterized by fractal geometry (Acuña et al. 1995). The advantage of a fractal geometry description is that it generalizes the underlying geometry in a non-trivial manner and allows for a direct and novel interpretation of responses (Acuña et al. 1995).