Total Fracture Surface Area Research Articles

Martian Impact Fracturing Pervasively Influences Habitability

AbstractOn Mars, the lack of either plate tectonics or a prominent erosional hydrological cycle since the Noachian means geological changes caused by asteroid and comet impact events have been preserved. On Earth, surviving impact‐induced fractures are localized to the relatively few preserved craters on the planet. We estimate that the shell of impact‐fractured rock on Mars (the “impact‐sphere”) could provide between 9,200 times the surface area of a Mars radius sphere and up to 100 times this value, depending on the assumptions made, as potential microbially accessible space. Although >93% of craters we consider are smaller than 10 km in diameter, they contribute only about 5% of the total fracture surface area generated by all craters, making complex craters the dominant process for potential habitat formation. Microbiological data from terrestrial impact craters suggest that these fractures could have significantly enhanced local habitability by providing pathways for fluid flow, and thus nutrients and energy. However, unlike on Earth, the geological history of Mars means that pervasive impact fractures may also have provided pathways for Hesperian and Amazonian brines to infiltrate the subsurface and locally reduce habitability. Combining the fracture data with previous microbiological observations provides testable hypotheses for Martian drilling missions.

Effect of strain rate on specific fracture energy and micro-fracture surface properties of rock specimen under dynamic uniaxial compression

Effects of strain rate on specific fracture energy and micro-fracture surface properties of rock specimen were investigated at strain rates of ∼ 60–115.0 s-1. To achieve this, rock breakage was conducted under dynamic uniaxial compression using the split Hopkinson’s pressure bar. The fracture surface area of fine fragments (<8*10-3m) were measured using gas absorption method while the fracture surface area of large fragments (>8*10-3m) were measured using close-range photogrammetry. Results reveal that fracture surface area and specific fracture energy generally increase with strain rate during rock breakage under dynamic uniaxial compression. Similarly, the total fracture surface area of broken fragments also increased with dissipated energy. Results from scanning electron microscopy showed that fracture surface roughness and macro-crack abundance also increased with strain rate. Following energy requirement for rock breakage into size specifications for engineering applications, strain rate provides a reliable parameter for estimating specific fracture energy and fracture surface area at the forementioned strain rates. Accordingly, optimizing rock breakage processes using strain rate could reduce ore loss and energy wastage associated with production of unwanted fracture surfaces during rock breakage.

Stage-by-Stage Hydraulic Fracture and Reservoir Characterization through Integration of Post-Fracture Pressure Decay Analysis and the Flowback Diagnostic Fracture Injection Test Method

Summary The post-fracture pressure decay (PFPD) technique is a low-cost method allowing for stage-by-stage hydraulic fracture characterization. The analysis of the PFPD data is complex, with data affected by both hydraulic fracture and reservoir properties. Available analysis methods in the literature are oversimplified; reservoir or fracture properties are often assumed to be constant along the horizontal well, and therefore changes in the trend of pressure decay data are attributed to hydraulic fracture or reservoir properties only. Moreover, methods analogous to those applied to the analysis of conventional diagnostic fracture injection tests (DFITs) are often used and ignore critical mechanisms involved in main-stage hydraulic fracture stimulation. A conceptual numerical simulation study was first conducted herein to understand the key mechanisms involved in main-stage hydraulic fracturing. An analytical model was then developed to account for the dynamic behavior of the hydraulic fracture, leakoff, proppant distribution, multiple fractures, and propped- and unpropped-closure events. The analytical model is cast in the form of a new straightline analysis (SLA) method that provides stage-by-stage estimates of the ratio of unpropped fracture surface area to total fracture surface area. The SLA method was validated against numerical simulation results. Moreover, to account for the variation of reservoir properties along the horizontal well, the PFPD model is integrated with DFIT-flowback (DFIT-FBA) tests, performed at some points along the lateral, to obtain a reliable stage-by-stage hydraulic fracture and reservoir characterization approach. The practical application of the proposed integrated approach was demonstrated using PFPD and DFIT-FBA data from a horizontal well completed in 22 stages in the Montney Formation. The numerical simulation study demonstrated that the use of proppant and injection into multiple clusters (creating multiple fractures) results in multiple closure events. The closure process may start early after the pump-in period at a pressure significantly higher than the minimum in-situ stress. Using DFIT-based analytical models, which ignore the presence of proppant, causes significant errors in hydraulic fracture and reservoir property estimation. The PFPD field data examined herein exhibited a similar pressure trend to the numerical simulation cases. The ratio of unpropped fracture surface area to total fracture surface area was determined stage by stage using the PFPD SLA method, constrained by DFIT-FBA data. Engineers can use this information to optimize the hydraulic fracture stimulation design in real time, optimize the well spacing, and forecast the production. The cost and time advantages of this diagnostic method make this approach very attractive.

Effects of fracture filling ratio and confining stress on the equivalent effective stress coefficient of rocks containing a single fracture

Because fractures are ubiquitous in rock masses, the states of stress and fracture filling significantly impact the coupled hydromechanical behaviors of fractured rocks. Based on the effective stress principle of porous media , we developed a method to determine the equivalent effective stress coefficient of rocks containing a single fracture , and analyzed the impacts of fracture filling area ratio, confining stress, and pore pressure . Confining stress and pore pressure were applied sequentially onto rock specimens, and two bulk moduli were calculated based on the measured deformation during the loading process of confining stress and pore pressure. The equivalent effective stress coefficient was then determined as the ratio of the two bulk moduli. Our results show that the equivalent effective stress coefficient increases as the filling area ratio or confining stress decreases, or pore pressure increases. The difference in equivalent effective stress coefficient of specimens with two filling area ratios decreases as the confining stress increases. The effective stress coefficient of a single fracture is inherently considered to be the ratio of the nominal fracture surface occupied by water to the total fracture surface area. When the confining stress and filling ratio increases or the pore pressure decreases, the nominal fracture surface occupied by water decreases, resulting in the corresponding reduction of the equivalent effective stress coefficient. These results provide important insights into the coupled hydromechanical behaviors of fractured rocks.

Mechanisms for the Generation of Complex Fracture Networks: Observations From Slant Core, Analog Models, and Outcrop

We use observations of hydraulic fractures in core, outcrop attributes of natural hydraulic fractures, and analogue models, to address how hydraulic fracture networks evolve. A slant core from the Wolfcamp Formation—an unconventional shale hydrocarbon reservoir in the Permian Basin of West Texas—collected within 18 m and 30 m of two hydraulically stimulated horizontal wells, provided an opportunity to examine hydraulic fractures directly. In approximately 183 m of core, 309 calcite-sealed natural opening-mode fractures and 375 hydraulic fractures were identified. Many hydraulic fractures in the core show complex morphology, including twist-hackle segmentation, diversion, and bifurcation; these structures most commonly develop at lithological bed boundaries and mechanical heterogeneities such as natural fractures and concretions. An outcrop of bed-parallel pavements in the Cretaceous Boquillas Formation in West Texas contains opening-mode fractures that likely formed by natural hydraulic fracturing. Fracture traces provide evidence of twist-hackle segmentation, and are typically associated with bed boundaries and preexisting bed-parallel stylolites. A laboratory study of hydraulic fracturing of 33 synthetic blocks of gypsum and hydrostone revealed fracture steps, diversions, twist hackles, and multiple overlapping fractures together with information on fracture growth directions. These complexities in the fracture network were dominantly nucleated at inclusions used to simulate pre-existing fractures, and as a result of mechanical heterogeneity introduced by the wellbore and perforations. Collectively, our results show that complex fracture networks are produced in hydraulic fracturing of self-sourced reservoir strata. Mechanical stratigraphic boundaries and other heterogeneities are likely to enhance fracture network complexity through the processes of segmentation, diversion, and bifurcation. These processes create multiple fracture strands, resulting in an increased number of hydraulic fractures over those initiated, thereby increasing total fracture surface area. Our study provides insight into hydraulic fracture network propagation, and has applications for evaluation, completion, production, and fracture modeling of unconventional reservoirs.

On the effective stress coefficient of single rough rock fractures

The effective stress coefficient is critical to accurately predict the hydromechanical coupling behavior of single water-bearing rock fractures. The physical meaning of the effective stress coefficient in a rough rock fracture is understood as the ratio of the nominal fracture surface occupied by water to the total fracture surface area. To overcome the difficulty of measuring contact ratio changes in rough rock fractures under normal loading and water pressure, a new effective stress coefficient model for single rough water-bearing fractures is proposed in terms of two mechanical parameters, initial normal stiffness and maximum normal closure. By incorporating the new effective stress coefficient model into the Barton-Bandis constitutive model, a hydromechanical coupling model was built and verified by laboratory and in-situ experimental data. The results indicate that the effective stress coefficient is less than 1 for single rough rock fractures and decreases with increasing difference between normal stress and water pressure. When the normal stress is close to or considerably higher than the fracture water pressure, both the newly built model and Terzaghi's model obtain similar normal displacement. However, for moderate normal stress, the normal displacements predicted by the newly built model and Terzaghi's model differ significantly. The implications of the newly built model in subsurface engineering are discussed.

Fracture Surface Area Estimation from Hydraulic-Fracture Treatment Pressure Falloff Data

Summary It has often been reported that the peak production of a well drilled in tight formations is highly dependent on the fracture-contact area. However, at present, there is no efficient approach to estimate the fracture surface area for each fracture stage. In this paper, we propose a method to calculate the fracture surface area on the basis of the falloff data after each stage of the main hydraulic-fracture treatment. The created hydraulic fracture closes freely before its surfaces hit the proppant pack, and this process can be recognized in the pressure falloff data and its diagnostic plots. The pressure-decline rate during fracture closure is mainly caused by the fluid leakoff from the fracture system into the formation matrix. For a horizontal well drilled in the same formation, with the known leakoff coefficient(s) and fracture-closure stress(es), the total-fracture surface area can be calculated for all stages to meet the requirement of the fluid-leakoff rate. The wellbore-storage effect, friction dissipation, and tip extension dominate the early pressure falloff data. Whereas the transient pressure dominated by friction losses typically lasts approximately 1 minute, the tip extension might end after approximately 15 minutes. Therefore, falloff data should be acquired for at least 30 minutes to observe a fracture-closure trend. The fracture-closure behavior can be identified on the G-function plot as an extrapolated straight line or on the Bourdet derivative in log-log plot as a late-time unit slope. The behavior of the late unit slope depends on the pressure-decline rate, or correspondingly, to the fluid-leakoff rate. Therefore, the total-fracture surface area can be estimated using hydraulic-fracture design input values for the formation-leakoff coefficient and fracture-closure stress. The calculated fracture surface area represents the combined area of primary and secondary fractures—effectively all fracture surfaces contributing to the fluid leakoff. We applied the approach to all stages in a horizontal well that exhibit the fracture-closure behavior. The approach shows some promise as a potential way to estimate fracture surface areas that could allow an early estimate of the expected well performance.

Enhancing total fracture surface area in naturally fractured unconventional reservoirs via model predictive control

In naturally fractured unconventional reservoirs, naturally present fractures will interact with hydraulic fractures, and divert fracture propagation. Because of complex fracture growth, the ultimate goal of hydraulic fracturing operation in naturally fractured unconventional reservoirs should be changed from achieving the desired fracture geometry to maximizing the total fracture surface area (TFSA) for given fracturing resources, as it will allow more drainage area available for oil recovery. Unfortunately, there are no such techniques available to develop pumping schedules to maximize TFSA for given fracturing resources in naturally fractured unconventional reservoirs. Motivated by this, in this work, we will develop a new model-based pumping schedule by utilizing a recently developed unconventional complex fracture propagation model called Mangrove as our virtual experiment describing complex fracture networks by accounting for the interaction between hydraulic fractures and natural fractures. Initially, using the simulation data from Mangrove, a reduced-order model (ROM) is constructed, which is then used to develop a Kalman filter utilizing the available measurement to estimate the unmeasurable ROM states. Then, we propose a model-based feedback control system to determine the fracturing fluid pumping schedule that maximizes TFSA, which will lead to an enhanced oil production rate from naturally fractured unconventional reservoirs. We demonstrate that by using the proposed control scheme, TFSA can be greatly enhanced which will lead to an oil production rate greater than those of existing pumping schedules which were developed without considering natural fractures.

Reservoir and Fracture-Flow Characterization Using Novel Diagnostic Plots

SummaryMultistage hydraulically fractured horizontal wells provide an effective means to exploit unconventional reservoirs. The current industry practice in the interpretation of field response often uses empirical decline-curve analysis or pressure-transient analysis/rate-transient analysis (PTA/RTA) for characterization of these reservoirs and fractures. These analytical tools depend on simplifying assumptions and do not provide a detailed description of the evolving reservoir-drainage volume accessed from a well. Understanding of the transient-drainage volume is essential for unconventional-reservoir and fracture assessment and optimization.In our previous study (Yang et al. 2015), we developed a “data-driven” methodology for the production rate and pressure analysis of shale-gas and shale-oil reservoirs. There are no underlying assumptions of fracture geometry, reservoir homogeneity, and flow regimes in the method proposed in our previous study. This approach depends on the high-frequency asymptotic solution of the diffusivity equation in heterogeneous reservoirs. It allows us to determine the well-drainage volume and the instantaneous recovery ratio (IRR), which is the ratio of the produced volume to the drainage volume, directly from the production data. In addition, a new w(τ) plot has been proposed to provide better insight into the depletion mechanisms and the fracture geometry. w(τ) is the derivative of pore volume with respect to τ.In this paper, we build upon our previous approach to propose a novel diagnostic tool for the interpretation of the characteristics of (potentially) complex fracture systems and drainage volume. We have used the w(τ) and IRR plots for the identification of characteristic signatures that imply complex fracture geometry, formation linear flow, partial reservoir completions, and fracture-interference/compaction effects during production. The w(τ) analysis gives us the fracture surface area and formation diffusivity, while the IRR analysis provides additional information on fracture conductivity. In addition, quantitative analysis is conducted using the novel w(τ) plot to interpret fracture-interference time, formation permeability, total fracture surface area, and stimulated reservoir volume (SRV).The major advantages of this current approach are the model-free analysis without assuming planar fractures, homogeneous formation properties, and specific flow regimes. In addition, the w(τ) plot captures high-resolution flow patterns not observed in traditional PTA/RTA analysis. The analysis leads to a simple and intuitive understanding of the transient-drainage volume and fracture conductivity. The results of the analysis are useful for hydraulic-fracturing-design optimization and matrix- and fracture-parameter estimation.

Percolation characteristics of solvent invasion in rough fractures under miscible conditions

Surface roughness and flow rate effects on the solvent transport under miscible conditions in a single fracture are studied. Surface replicas of seven different rocks (marble, granite, and limestone) are used to represent different surface roughness characteristics each described by different mathematical models including three fractal dimensions. Distribution of dyed solvent is investigated at various flow rate conditions to clarify the effect of roughness on convective and diffusive mixing. After a qualitative analysis using comparative images of different rocks, the area covered by solvent with respect to time is determined to conduct a semi-quantitative analysis. In this exercise, two distinct zones are identified, namely the straight lines obtained for convective (early times) and diffusive (late times) flow. The bending point between these two lines is used to point the transition between the two zones. Finally, the slopes of the straight lines and the bending points are correlated to five different roughness parameters and the rate (Peclet number).It is observed that both surface roughness and flow rate have significant effect on solvent spatial distribution. The largest area covered is obtained at moderate flow rates and hence not only the average surface roughness characteristic is important, but coessentially total fracture surface area needs to be considered when evaluating fluid distribution. It is also noted that the rate effect is critically different for the fracture samples of large grain size (marbles and granite) compared to smaller grain sizes (limestones).Variogram fractal dimension exhibits the strongest correlation with the maximum area covered by solvent, and display increasing trend at the moderate flow rates. Equations with variogram surface fractal dimension in combination with any other surface fractal parameter coupled with Peclet number can be used to predict maximum area covered by solvent in a single fracture, which in turn can be utilized to model oil recovery, waste disposal, and groundwater contamination processes in the presence of fractures.

Effects of fractal surface roughness and lithology on single and multiphase flow in a single fracture: An experimental investigation

This paper presents qualitative and quantitative analysis of single and multiphase flow in a single fracture based on experimental results and demonstrates relationships between the roughness and fluid movement and distribution.Experiments were conducted on seven perfectly-matching and tightly-closed rough model fractures reproduced from the single fractures of lithologically different seven rock blocks that were jointed artificially through laboratory indirect tensile tests. Transparent upper and opaque lower walls of these models facilitated the visualization of the flow experiments. Rough surfaces of the model fractures were first digitized. Then, using the gathered data in variogram analysis, surface roughness was quantified by fractal dimension. Another roughness quantification parameter was also handled as the ratio between total fracture surface area and planar surface area. Experimental measurements of flow were quantitatively correlated to surface roughness under different normal loading (aperture) conditions. Also, constant rate immiscible displacement experiments were performed to assess the roughness effect represented by seven different lithologies and wettability effect controlled by the material used in manufacturing the fracture samples on the residual saturation development.

Conjoint bending torsion fatigue — fractography

The fractography of conjoint bending torsion fatigue (CBTF) has been reported in this paper for a superalloy (Nimonic 75A) material used in gas turbine engines. The fracture surface features were characteristic of bending fatigue (BF), a distinct area of CBTF, and a region between the BF and CBTF, overloading (OL). Striations were documented in the two former regions, whereas ductile dimples were noted in the latter. The CBTF fracture comprised predominately 80% or more of the total fracture surface area. However, between these two cracked areas (BF and CBTF), another region experiences overloading, resulting in the failure of flange bolts. Fatigue striations were counted for the CBTF mode and crack growth rate as a function of crack length, and crack length is presented as a function of cumulative striations.

６０６１アルミニウム合金Ｔ６５１材の靭性値と破面変形量に及ぼす負荷速度の影響

It is believed that there exists a close relationship between the deformation on fracture surface and the fracture toughness. On the ductile fracture surface, it is known that macroscopic deformation called shear lip or plastic hinge is observed. In addition, microscopic deformation reflecting minute variation of geometry like fracture surface area is also associated with toughness. In this paper, measurement of fracture was performed by laser displacement meter and scanning laser microscope. Using these devices, instead of conventional planar measurement method, fracture surface can be measured stereoscopically. The macroscopic deformation, microscopic deformation, volume of shear lip and fracture surface area were determined, respectively. Therefore, it enables the investigation of the relationships between toughness at loading speed from 8.3 × 10−6 m/s to 8 m/s and these fracture surface features on 6061–T651 aluminum alloy. The results demonstrated that there is a good agreement between the variation of loading speed for toughness testing and the total fracture surface area.