This post grapples with a complicated, nuanced, and important topic: what do hydraulic fractures look like and how should we model them? Should we use planar fracture models or ‘complex’ hydraulic fracture network models? On June 27, I attended the ARMA Hydraulic Fracturing Committee (HFC) workshop in New York. I was inspired by the quality of work presented. I was especially interested in the innovative work being done with direct, in-situ hydraulic fracture observations. This work is perhaps the tip of the iceberg – there is a great deal of work being done in industry that has not been shared publicly. Also, URTeC in Denver later this month will have papers out, such as an important new one from Raterman et al. with ConocoPhillips on the Eagle Ford core-across study.
When hydraulic fracturing is performed, we are separated from the fractures by 1000s of feet of solid rock. The inability to ‘see’ what we’re doing is the central challenge of subsurface engineering. To observe fracturing in-situ, we usually use indirect techniques, such as microseismic or pressure analysis, to infer fracture behavior. However, these techniques require a lot of assumptions and interpretation, and a lot of issues are left unanswered. In contrast, core-across studies and fiber optic distributed acoustic sensors allow us to directly observe what is happening in the formation. We can perform experiments in the lab, but conditions (and length) scale are so different in the laboratory that it is challenging to relate lab results to the field scale.
When I did my PhD from 2009-2012, it seemed to me that complex hydraulic fracture network models were the wave of the future (for both geothermal and oil and gas), and chose to focus in that area. Complex hydraulic fracturing models represent hydraulic fracturing as a branching network of both newly forming and preexisting fractures (Weng et al, 2011; McClure et al., 2015). A model is initialized by stochastically generating a ‘discrete fracture network’ of preexisting fractures. Hydraulic fracture termination against natural fractures is considered to be a key process (Weng et al., 2011). I did a lot of work on the complex hydraulic fracture network approach (for example, McClure and Horne, 2014a, 2014b; McClure et al., 2015). The complex fracture network approach is illustrated schematically as ‘MMS’ in Figure 1. But as I got further from the PhD and interacted more and more with real data, I began to question the usefulness and realism of this modeling approach (for oil and gas; I continue to believe it is important for geothermal applications). Complex hydraulic fracture network models are so computationally demanding that they force tradeoffs, sacrificing physical realism (for example, they are often not fully 3D and/or do not accurately calculate stress shadowing). There is rarely, if ever, data available to populate the ‘discrete fracture network’ needed by the model. Fracture orientations are sometimes available from imaging logs, but the size distribution is almost never known. But most importantly, I became concerned that the complex hydraulic fracture network model is simply not a realistic description of what is happening (in shale). I came to believe that planar fracture models are closer to reality.
So, when I built ResFrac, I chose to focus on the planar fracture modeling approach. Planar fracture modeling is the classical approach, dating back many decades. Hydraulic fractures are modeled as continuous, planar features. Natural fractures are not explicitly represented, though their effect can be considered in a variety of ways using an ‘effective continuum.’ Fractures may turn and have complicated geometry, but they are not modeled as terminating and branching with natural fractures.
Despite great research attention on complex hydraulic fracture network approaches, the planar fracture modeling approach remains the most commonly used technique in industry. The past few years, experience and ongoing developments in the literature have made me even more confident in the decision to focus on planar fracture models. In this blog post, I summarize my thinking. It is a tricky, nuanced topic, and I imagine many readers will find something or another that they don’t completely agree with. Please feel free to send me an email if you’d like to share thoughts on this topic!
Before I dive into the details, here is my overall thesis. Field observations suggest that hydraulic fracturing creates multistranded bands of hydraulic fractures. When zooming out to perform field-scale modeling, it is reasonable to represent each of these bands as a single hydraulic fracture in a planar fracture model. Complexity exists at smaller-scale within these bands of fractures. Constitutive laws can be used to account for the reservoir scale consequences of these smaller-scale forms of complexity within the band. For example, we can modify relations for proppant transport to account for proppant trapping caused by small-scale nonplanarity. Even though planar fracture models describe fractures as planar, they can still have rather complicated geometry, as shown in Kaufman et al. (2019). In contrast, the ‘complex hydraulic fracture network modeling approach emphases flow through natural fractures, creates zig-zagging flow paths through the reservoir, and hypothesizes the formation of a broad ‘stimulated rock volume’. The formation of multiple fractures in a narrow band challenges theory and our physical understanding of hydraulic fracture propagation. Nevertheless, the observations have now been repeated enough times that we cannot ignore them; propagation of multiple fractures in a band is apparently common.
Modeling fluid flow in fractured rock
Before talking about hydraulic fracturing, I need to review two general approaches to describing flow through fractured rock – discrete fracture network (DFN) and dual porosity models. These two approaches were developed to describe fluid flow, not specifically for hydraulic fracturing/stimulation. Nevertheless, to understand methods of modeling hydraulic fracturing, it’s important to review these approaches to modeling flow through fractured rock.
Dual porosity models keep track of ‘average’ fracture properties in a region of rock, rather than trying to represent each individual fracture. Dual porosity models track the overall amount of fluid in fracture pore volume and in matrix pore volume. This approach, pioneered by Warren and Root (1963) has been used ubiquitously in reservoir engineering for many decades.
Discrete fracture networks (DFN) were developed in the 1980s for describing flow in fractured formations (Cacas et al., 1990). In the DFN approach, you explicitly define a large number of fractures (usually assumed planar), and fluid flows through the network of cracks. The DFN makes it possible to capture the complexities and idiosyncrasies of flow through natural fractures.
In deciding between DFN and dual porosity approaches, scale matters. If there are a relatively small number of major flow pathways, DFN modeling is advantageous because it can capture unpredictable, tortuous flow paths through fractured rock. However, if there is a large number of smaller fractures, then dual porosity is a better approach. If there are many well-connected fractures, it is reasonable to ‘zoom out’ and consider the fractures’ average properties. With a larger number of well-connected fractures, the flow becomes more distributed and more like an effective porous medium.
In many areas of engineering and science, modeling choices are made based on the scale of investigation. For example, molecular modeling can be used to study molecular scale processes such as protein folding and catalysis. But when considering macro-scale systems such as a chemical reactor, engineers average out the properties of the molecules and use thermodynamics and chemical kinetics equations to capture the behavior in bulk. As another example, pore-scale modeling can be used to describe multiphase flow through rock. But for reservoir-scale modeling, we find it sufficient to use relative permeability curves. It is impractical to perform pore-scale modeling at reservoir scale. Thus, the level of detail required in a model must be tailored for the application and scale of measurement.
Modeling hydraulic fracturing and stimulation
In hydraulic fracturing/stimulation modeling, there are two common approaches – planar fracture models and ‘complex’ hydraulic fracturing models.
Planar fracture modeling is the classical approach, dating back to at least the 1950s. From a vertical well, it is assumed that a single planar fracture propagates away from the well. In a horizontal well, it is usually assumed that a planar fracture propagates away from each perforation cluster. Planar fracture models have evolved from fairly simple analytical solutions (such as PKN, KGD, and radial) to fully 3D numerical simulators. The majority of hydraulic fracture modeling performed in the industry uses the planar fracture modeling approach – Stimplan, Gohfer, ResFrac, and FracPro.
The ‘complex’ hydraulic fracturing modeling approach is initialized using a DFN representation of the preexisting natural fractures in the formation. Planar fractures form and propagate, but it is assumed that the hydraulic fractures often experience full termination against the natural fractures (‘MMS’ in Figure 1). New hydraulic fractures may initiate off the natural fractures, and the overall result is a network of newly formed and preexisting hydraulic fractures. Kinetix and FLAC3D use this approach. Fracman uses a hybrid approach – planar fracture modeling within a DFN.
Both of these approaches model discrete, individual hydraulic fractures. However, only the ‘complex’ approach uses a true DFN, initializing the simulation with a large, complicated network of preexisting fractures.
What do things look like in reality?
Which approach should we use? Fracturing and stimulation processes vary between formations. The modeling approach should be chosen on the physics of the particular formation. Having said that, I believe that planar fracture modeling should be used in the great majority of oil and gas applications, in both conventional rock and in shale. Planar fracture models are a simplification of reality, and constitutive equations must be selected in order to account for ‘complexity’ at smaller scale than represented by the model. Nevertheless, I believe that planar fracture models are closer to reality than what is represented in a complex hydraulic fracturing model. Let’s look at direct, in-situ observations reviewed this week at the ARMA HFC workshop.
As covered by Jordan Ciezobka, the recent HFTS project involved directly coring through hydraulic fractures in the Wolfcamp (Ciezobka et al., 2018; Gale et al., 2018). Another recent project cored through hydraulic fractures in the Eagle Ford (Raterman et al., 2017). John Lorenz discussed results from the MDX project, which cored across hydraulic fractures in the Mesaverde in 1990 (Warpinski et al., 1993). Tim Kneafsey discussed very detailed characterization work going on at the SigmaV project, a mesoscale project off the side of a deep mineshaft (Kneafsey et al., 2019). John McLennan discussed ongoing work in preparation for the FORGE project, a DOE-sponsored multistage hydraulic fracturing project in Utah in granitic rock for Enhanced Geothermal Systems.
There are a few key observations from the HFTS and MDX projects that I want to emphasize – these observations were broadly similar in the Mesaverde, Wolfcamp, and Eagle Ford cores.
1. Hydraulic fractures propagated consistently in the direction of the maximum horizontal stress.
2. There was no apparent stimulation of the matrix surrounding the hydraulic fractures.
3. Flow dominantly localized into hydraulic fractures, not natural fractures.
4. There was a very large number of hydraulic fracture strands, many more than the number of perforation clusters, mostly localized into bands, and showing evidence of bifurcation and small-scale (cm) nonplanarity.
Observations #1, #2, and #3 are strongly in favor of the planar fracture model approach. Observation #4 is a curveball not necessarily captured by any of the modeling approaches and not predicted by theory.
I will start with observations #1, #2, and #3. In the complex hydraulic fracturing model approach, flow pathways are rather tortuous, passing through a variety of hydraulic fractures and natural fractures (‘MMS’ in Figure 1). If this represented reality, then core-across studies would show abundant flow in natural fractures, abundant hydraulic fracture termination against natural fractures, and zig-zagging flow pathways. This is not what has been observed. There was small scale branching, offsets, and roughness in the hydraulic fractures. Natural fractures were present in the core, but there was not evidence of widespread transport in these natural fractures, nor proppant placement. While the hydraulic fractures had small-scale complexity, the core also showed that the flow paths consisted of newly formed hydraulic fractures consistently oriented in the direction of SHmax. This is not consistent with the complex hydraulic fracturing model approach, which represents rather zig-zagging flow pathways through newly formed and preexisting fractures.
Also at the ARMA HFC meeting, Gustavo Ugueto presented fiber optic distributed acoustic sensor (DAS) data that was supportive of the planar model approach (the material will be presented in a paper at ATCE this fall). They placed DAS in wellbore offset laterally from wells being hydraulically fractured. This allowed them to directly observe when and where hydraulic fractures intersected the offset well. They observed discrete frac hits in the offset wells that were oriented consistently in the direction of SHmax. This is consistent with the planar fracture model – fracture features oriented in the same direction, propagating in a relatively narrow band of rock. Ugueto described comparison of DAS with microseismic and noted that microseismic clouds were wider than the region of frac hits observed with the DAS. In other words, the microseismic gave the impression of a wider region of fracturing than occurred in reality.
Not all formations are the same, and it’s impossible to generalize. I do think that in some formations, some of the time, the complex fracture network model is more representative of reality. For example, in McClure and Horne (2014a), we argued that this is the mechanism of stimulation in many Enhanced Geothermal Systems in crystalline rock. But the new studies coming out, and my own experience, are both leading me to believe that in shale, hydraulic fractures form in multistranded bands, and that the planar fracturing approach is the better approach the great majority of the time.
What’s the counter-argument?
Microseismic observations have often been used to argue in favor of the complex hydraulic fracture network approach. Microseismic clouds often show significant width. The problem is: (1) microseismic event location error causes the cloud to appear wider than the true distribution of hypocenters, (2) stresses induced around fracture can create ‘dry’ microseismic events that occur in regions where substantial fluid flow and stimulation have not occurred, and (3) even if fluid does leak off into natural fractures surrounding the hydraulic fractures and cause microseismic events, proppant is unlikely to get into these secondary fractures, and so they may not actually represent the areas where stimulation is primarily localized.
The concept of ‘shear stimulation’ is based on the idea that increased fluid pressure causes slip on fractures, and that slip causes enhanced fracture conductivity. This concept is absolutely valid. However, in McClure and Horne (2014b), we stepped through the conditions that must be in place for shear stimulation to occur and cause a widespread, pervasive stimulation of formation permeability. You need fractures that are correctly oriented to slip, fractures that are sufficiently large and connected to form continuous and pervasive flow pathways (ie, a percolating network), and mineralogy that enables unpropped fractures to retain conductivity as pressure is drawn down.
Comparison with hydraulic stimulation in granitic rock for geothermal energy is instructive. In geothermal energy, it has been shown conclusively that during high rate fluid injection, shear stimulation of natural fractures can cause large enhancement of formation permeability (Genter et al., 2000). However, in these settings, shear stimulation is most successful when causing slip on km-scale faults. These are the kinds of ‘seismic-scale’ faults that we typically try to avoid when performing hydraulic fracturing in shale because they divert fracturing fluid. Faults like this have well-developed structure – with a core surrounded by a complex, fractured, often permeable, and mineralogically modified damage zone (Figure 3). These large faults are nothing like the thin, mineralized cracks that we typically encounter in shale core. Consider the thin, calcite-filled fractures from the Barnett in Figure 4. These fractures are evidently very small because they terminate within the core. If they were much larger than the core, they would be unlikely to terminate within the core.
This comparison makes clear why shear stimulation has been successful in certain geothermal settings, but is not the primary mechanism of stimulation in shale. Effective shear stimulation requires large, well-developed fault zones. Even in geothermal applications in granitic rock, in formations without large-scale, well-developed faults, shear stimulation alone has not been effective, and stimulation has occurred primarily through propagation of hydraulic fractures (McClure and Horne, 2014a,b).
Proponents of the complex hydraulic fracturing model point to laboratory experiments and some field observations indicating that propagating hydraulic fractures can terminate against preexisting planes of weakness (Gu and Weng, 2010). This is possible under certain conditions. Direct in-situ observations suggest that this kind of termination might occur, but generally, causes only a cm-scale offset before the fracture continues. Thus, this process might in some cases create small-scale complexity. A caveat – if a hydraulic fracture does encounter a large, seismic-scale fault, then it could terminate against the feature because the fault is large and permeable and can capture subsequent fluid injection.
It is often said that a complex fracture network is needed to account for production rates in low permeability shale. In ResFrac, our experience does not support this premise. We have used ResFrac, a planar fracturing and reservoir simulation model, to history match production data in the Wolfcamp, Eagleford, Bakken, Meramac, Powder River, Utica, and Marcellus. We have not needed a ‘complex network’ to match that data, nor have we needed to create a zone of enhanced permeability around the hydraulic fractures in the model (though ResFrac is capable of doing this with irreversible permeability multipliers and/or a dual porosity model for flow around the main fractures). In a modern gas shale well, there could be a 10,000 ft lateral with 25 ft cluster spacing. If 80% of those break down, that’s 320 hydraulic fractures. If you perform a simple linear flow calculation to estimate the surface area required to match production data with that many hydraulic fractures, you’ll find that you can assume a single planar fracture per cluster, and those fractures don’t need to be very large. Walton and McLennan (2013) performed this exact calculation using production data from the Barnett shale. Similarly, they concluded that production data could be explained solely from the surface area created by modestly-sized planar fractures.
The rate-transient calculation has a nonunique tradeoff between permeability and fracture area. If you assume lower permeability, then the area requirement becomes higher. You could argue that we are getting away with underestimating surface area by overestimating permeability. However, in the ResFrac DFIT study, we estimated permeability in-situ in eight shale plays across the US. The permeability estimates are consistent with values that allow production to be matched with planar fracture models (McClure et al., 2019).
Consider the DFIT interpretation paper we have coming out at URTeC next month from our DFIT study. In that paper, we propose that in gas shale, operators systematically overpredict permeability from DFIT. In an upcoming ATCE paper, we history match a Utica/Point Pleasant dataset with ResFrac (a planar fracture model) using the lower permeability estimate. Many/most operators in Utica/Point Pleasant use a much higher permeability estimate, which implies that surface area is even smaller than we are using in our planar fracture model. If we used the higher permeability value, the fracture surface area was unrealistically small.
I don’t want to give the impression that flow in natural fractures is never important. For example, Warpinski (1990) describes fracturing tests in lenticular tight sandstones where natural fractures greatly increase formation permeability. Because of the natural fractures in these sands, the system permeability is ~ 50,000 nd. There are some modern ‘shale’ plays that have enhanced permeability due to natural fractures, such as in some areas of the Middle Bakken (though ironically, formations with open fractures can sometimes have less hydrocarbon in place because the fracture permeability causes ineffective hydrocarbon trapping). But generally, modern shale plays have system permeability in the range of 10-1000 nd, much lower than the permeability of the fractured formations described by Warpinski (1990). The difference is stark when we consider the changing role of 100 mesh proppant. Warpinski (1990) used sweeps of 100 mesh proppant to reduce leakoff by sealing off natural fractures. In modern shale plays, 100 mesh proppant is used as the primary proppant in the main fracture.
Ciezobka and Salehi (2013) reports results in the Marcellus suggesting a swarm of fractures enhanced production in certain clusters along a lateral. However, these clusters only accounted for 20% of overall production in the wells. The implication is that the majority of production was from clusters that did not intersect a fracture swarm. The importance of natural fractures in a particular pad is surely variable – they may be important in some areas and not others. But without special knowledge to the contrary, it is parsimonious to assume they are not present, and add them to a model if data is available demonstrating otherwise. Within the stages intersecting the fracture swarm in the Ciezobka and Salehi (2013) study, there is not any data to distinguish whether the hydraulic fractures branched into a complex network, or whether they were still predominantly a band of mostly planar hydraulic fractures, with enhanced production from these stages due to the enhanced ‘system permeability’ of the fracture swarm.
It has been argued that slickwater is successful because it encourages leakoff and stimulation of secondary fractures. But an alternative explanation is that slickwater has been successful because it avoids damage to the frac pack conductivity caused by gel residue (for example, note the ubiquitous gel residue observed in core by Warpinski et al., 1993). Also, slickwater is cheaper. High viscosity friction reducers are becoming increasingly popular because they clean out from the proppant pack while delivering higher viscosity than a traditional slickwater fluid. The small-scale complexity seen in core suggests that vertical proppant placement is achieved, even in slickwater, by proppant trapping due to small-scale branching and ledges. This is not dependent on fluid viscosity, and (speculatively) might be enhanced by using lower viscosity fluid. This kind of cm-scale complexity is too small scale to be captured by any kind of reservoir-scale fracturing model and is best handled with constitutive equations.
Over the past five years, the industry has shifted away from openhole completion and towards cased, cemented completion with decreasing cluster spacing. Cemented completions with tight cluster spacing do not rely on natural fractures creating broad regions of stimulation.
The Fisher et al. (2002) paper famously showed a Barnett example where nearby wells were ‘killed’ by frac hits, suggesting that a broad region of stimulation developed. But this phenomenon could have other explanations. If the existing wells were producers, then poroelastic stress response to depletion would tend to attract (planar) hydraulic fractures from the child well, creating offset frac hits. Fisher et al. (2002) do not observe microseismic events around the preexisting wells, even though they took frac hits. In some settings, depletion can bring fractures closer to slipping, but in other settings, depletion brings fractures further from slipping, which creates aseismic response to fluid pressurization. If there were large-scale conductive faults in the area, these faults could have captured the fluid and cause anomalous fluid transport. Or, maybe in that region of the Barnett, fracturing really did create a broad region of stimulation. Even if so, subsequent experience in many other shale plays has not shown that to be the norm. Early wells in shale used very long stages (or vertical wells) and openhole completions, relying on achieving SRV’s through ‘complexity.’ The industry has moved away from this style of completion.
Recently, I heard an RTA argument in favor of the complex hydraulic fracturing approach. In many shale plays, production declines more rapidly than predicted by the simple linear flow RTA equation. One way to match that data is to assume that the fractures create a ‘fractal’ network, and it has been argued that this implies the complex hydraulic fracturing approach needs to be used. But in our experience, curving upward RTA trends can be matched with a planar fracture model by considering the effect of going below the bubble point or dew point, interference between adjacent fractures, and/or the complicated planar fracture geometry that naturally arises due to stress shadowing interaction.
How do we explain these bands of hydraulic fractures?
Closely-spaced bands of hydraulic fractures are not predicted by classical theory and are not measured in the laboratory. So why do we keep seeing them in the field? How and why do they form?
At this point, I don’t think we don’t think we know. Conventionally, arguments regarding stress shadowing between fractures have been shown to argue that a single dominant fracture should crowd out its neighbors. I expect that we will see a burst of research in this area. Currently, there are a few explanations that I find most promising.
1. Nonlinearly rate-dependent non-Darcy pressure drop may distribute flow across multiple fractures, analogous to the way that perforation pressure drop distributes flow across more perforation clusters in ‘limited-entry completion.’ Pressure gradient associated with inertial and turbulent effects scale with the square of flow rate. Because it increases nonlinear with flow rate, overall pressure gradient is minimized when flow is distributed across more flow pathways. Perhaps the small-scale nonplanarity and complexity of hydraulic fractures causes non-Darcy effects to be much more important than has been recognized.
2. Small-scale pinchpoints and nonplanarity may cause obstructions to flow that do not scale with aperture and pressure gradient in ways that have been recognized by classical theory.
3. Perhaps each ‘band’ of fractures is actually dominated by a single primary hydraulic fracture that takes most of the proppant. The secondary fractures in the ‘band’ may be created by process-zone fractures formed ahead of the crack tip, bifurcation, or by initiation of fractures from a longitudinal fracture along the well.
4. Hydraulic fractures form at the well, between the perforation clusters, from a longitudinal fracture running along the well, as has been proposed by Raterman et al. (2017). This mechanism is not mutually exclusive with #1-#3.
Mechanism #3 has been observed in geologic outcrop. Delaney and Pollard (1986) show process-zone joints forming ahead of a volcanic dike. If you cored a well through, you’d find a band of hydraulic fractures, even though there is only one primary hydraulic fracture – the dike. Scholz (2010) proposes that this mechanism can explain ‘scale-dependent toughness,’ which is consistent with observations from hydraulic fracturing pressure data. Aside from volcanic dikes, multistranded arrays of natural hydraulic fractures were observed in sandstone formations by Lorenz (2013).
I shared this blog post with John Lorenz, and he sent me a section from a book that he and Scott Cooper have coming out next year, “Applied Concepts in Fractured Reservoirs.” In that section, they lay out this ‘process-zone’ explanation for the multiple stranded fractures in core-across studies – keep an eye out for the book when it comes out!
I recommend keeping an eye out for the paper by Raterman et al. coming out at URTeC later this month. This paper is a follow up on the Eagle Ford core-across study, and has important new findings, generally supporting mechanism #3 above.
The complex hydraulic fracturing approach is intellectually compelling, has basis in certain laboratory and field experiments, and creates visually impressive numerical simulations. But looking at the totality of observations and data, I have been surprised to find that it does not appear to represent the reality of hydraulic fracturing in most shale plays.
Direct observations indicate that hydraulic fracturing in most shale plays creates bands of hydraulic fractures (<10 ft wide), not broad regions of complex fracturing. Stimulation of natural fractures does not appear to be the dominant mechanism of stimulation in most shale plays. Interaction with natural fractures and bedding planes contribute to hydraulic fracture ‘complexity,’ but only in the sense that interaction causes small-scale nonplanarity, branching, and offset. The hydraulic fracture bands propagate mostly linearly and towards SHmax (with the possible exception of severe rotation caused by poroelastic stress response around a depleted parent well).
When you zoom out to reservoir scale, a complicated band of hydraulic fractures looks an awful lot like a linear, planar fracture. With ResFrac, we perform reservoir-scale modeling, and we apply models to help companies make practical engineering decisions about how to design and complete their wells. We use a planar fracture model and account for multistranded fracturing band complexity with constitutive relations (such as relations for proppant trapping that affect proppant settling). This approach has been very effective, matches field data nicely, and is more consistent with direct, in-situ observations. Because we don’t carry the computational burden of the DFN, we are able to integrate key physics such as full three-dimensionality, fracture closure, poroelastic stress changes from depletion, and full integration with a reservoir simulator. If needed, we can consider natural fractures with a DFN, a few discrete fractures, dual porosity, and/or pressure dependent permeability. But generally, this hasn’t been necessary.
Cacas, M. C, E. Ledoux, G. de Marsily, B. Tillie, A. Barbreau, E. Durand, B. Feuga , and P. Peaudecerf. 1990. Modeling fracture flow with a stochastic discrete fracture network: Calibration and validation 1. The flow model. Water Resources Research.
Ciezobka, Jordan, James Courtier, and Joe Wicker. 2018. Hydraulic Fracturing Test Site (HFTS) – Project overview and summary of results. Paper presented at the Unconventional Resources Technology Conference, Houston, TX.
Delaney, Paul T., David D. Pollard, Joseph I. Ziony, and Edwin H. McKee. 1986. Field relations between dikes and joints: emplacement processes and paleostress analysis. Journal of Geophysical Research.
Fisher, M. K., C. A. Wright, B. M. Davidson, A. K. Goodwin, E. O. Fielder, W. S. Buckler, and N. P. Steinsberger. 2002. Integrating fracture mapping technologies to optimize stimulation in the Barnett Shale. Paper presented at the SPE Annual Technology Conference and Exhibition, San Antonio, TX.
Gale, Julia F. W., Sara J. Elliott, and Stephen E. Laubach. 2018. Hydraulic fractures in core from stimulated reservoirs: Core fracture description of the HFTS slant core, Midland Basin, West Texas. Paper presented at the Unconventional Resources Technology Conference, Houston, TX.
Genter, Albert, Herve Traineau, Beatrice Ledesert, Bernard Bourgine, and Sylvie Gentier. 2000. Over 10 years of geological investigations within the HDR Soultz Project, France. Proceedings World Geothermal Congress, Kyushu – Tohoku, Japan.
Gu, H., and X. Weng. 2010. Criterion for fractures crossing frictional interfaces at non-orthogonal angles. Paper presented at the 44th US Rock Mechanisms Symposium, Salt Lake City, UT.
Kneafsey, Timothy J., Doug Blankenship, Hunter A. Knox, Timothy C. Johnson, Jonathan B. Ajo-Franklin, Paul C. Schwering, Patrick F. Dobson, Joseph P. Morris, Mark D. White, Robert Podgorney, William Roggenthen, Thomas Doe, Earl Mattson, Carol Valladao, and The EGS Collab Team. 2019. EGS Collab Project: Status and Progress. Paper presented at the Stanford Geothermal Workshop, Stanford, CA.
Kohl, T., T. Megel. 2005. Coupled hydro-mechanical modelling of the GPK3 reservoir stimulation at the European EGS site Soultz-sous-Forets. Paper presented at the Stanford Geothermal Workshop, Stanford, University.
Lorenz, John C. 2013. Fractures, hydraulic injections, and strain accommodation in the Tensleep Formation at Flat Top Anticline, Carbon County, Wyoming. Geology.
McClure, M. W. 2012. Modeling and characterization of hydraulic stimulation and induced seismicity in geothermal and shale gas reservoirs. PhD Thesis, Stanford University, Stanford, California.
McClure, Mark, and Roland Horne. 2014a. Characterizing hydraulic fracturing with a tendency-for-shear-stimulation test. SPE Reservoir Engineering & Evaluation.
McClure, Mark W., and Roland N. Horne. 2014b. An investigation of stimulation mechanisms in Enhanced Geothermal Systems. International Journal of Rock Mechanics and Mining Sciences.
McClure, Mark W., Mohsen Babazadeh, Sogo Shiozawa, and Jian Huang. 2015. Fully coupled hydromechanical simulation of hydraulic fracturing in 3D discrete-fracture networks. SPE Journal.
McClure, Mark, Vidya Bammidi, Craig Cipolla, Dave Cramer, Lucas Martin, Alexei A Savitski, Dave Sobernheim, and Kate Voller. 2019. A Collaborative Study on DFIT Interpretation: Integrating Modeling, Field Data, and Analytical Techniques. Paper presented at the Unconventional Resources Technology Conference (URTeC), Denver, CO.
McClure, Mark, and Charles Kang. 2019. ResFrac Technical Writeup. arXiv:1804.02092.
Raterman, Kevin T., Helen E. Farrell, Oscar S. Mora, Aaron L. Janssen, Gustavo A. Gomez, Seth Busetti, Jamie McEwen, Michael Davidson, Kyle Friehauf, James Rutherford, Ray Reid, Ge Jin, Baishali Roy, and Mark Warren. 2017. Sampling a Stimulated Rock Volume: An Eagle Ford Example. Paper presented at the Unconventional Resources Technology Conference, Austin, TX.
Scholz, Christopher H. 2010. A note on the scaling relations for opening mode fractures in rock. Journal of Structural Geology.
Walton, Ian, and John McLennan. 2013. The role of natural fractures in shale gas production. InTechOpen.
Warpinski, Norman R. 1990. Dual leakoff behavior in hydraulic fracturing of tight, lenticular gas sands. SPE Production Engineering.
Warpinski, N. R., J. C. Lorenz, P. T. Branagan, F. R. Myal, and B. L. Gall. 1993. Examination of a cored hydraulic fracture in a deep gas well. SPE Production & Facilities.
Warren, J. E., and P. J. Root. 1963. The behavior of naturally fractured reservoirs. Society of Petroleum Engineers Journal.
Weng, X., O. Kresse, C. Cohen, R. Wu, and H. Gu. 2011. Modeling of hydraulic fracture network propagation in fractured formation. Paper presented at the SPE Hydraulic Fracturing Technology Conference and Exhibition, The Woodlands, TX.