Fracture Propagation Velocity Research Articles

Crosswell Strain and Production-Interference Testing Integrated in the Permian Basin

_ This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 212336, “How and Where Wells Talk: Integrating Crosswell Strain and Production-Profile-Interference Testing,” by Matthew Lawrence, SPE, Ziebel; Janel Andersen, SPE, PDC Energy; and Yuanshan Zhang, Ziebel. The paper has not been peer reviewed. _ In Permian Basin fracturing operations, azimuths and intensities recorded by single-use distributed fiber optics in two wells are integrated and compared with post-flowback production-allocation and interference testing acquired with intervention fiber optics to identify areas of hydraulically conductive fractures and communication between offset wells. The production-allocation/interference testing method appears to reveal hydraulically connected fractures even in the absence of strain data. Introduction Intervention-based fiber optics have proved a valuable and cost-effective tool in understanding during-fracturing and post-flowback well and section performance. During-fracturing diagnostics, such as crosswell strain measurements from an offset monitor well, describe where fractures intersect the monitor well and reveal details such as azimuth, fracture-propagation velocity, and activation and reactivation statistics. These critical data points help inform cluster, stage, and well-spacing decision-making. While the absence of observed strain activity does not indicate the absence of created fractures, the existence of a strain activity indicating a fracture does not guarantee hydraulic functionality. The hydraulically functional fracture network can be understood with post-flowback production profiling. Particularly when combined with interference testing, fiber-optic production profiling identifies and differentiates productive and unproductive sections of unconventional laterals. Combination of during-fracturing and post-flowback technologies reveals the clearest picture of the functional fracture network. On an eight-well pad in the Permian Basin, the operator acquired fiber-optic crosswell strain data on two wells using single-use fiber, revealing details about the created fracture network. Sixty days after the wells went on production, a combination production-allocation and interference sensing program was executed with intervention fiber optics on two of the wells. Designing a Diagnostic Project in the Delaware Basin The operator completed an eight-well pad in the Delaware Basin on the western slope of the Permian. The wells were landed in three rows across the upper and lower Wolfcamp, which had a formation thickness of approximately 600 ft true vertical depth. Four of the laterals were completed from south to north (Wells 11N, 14N, 21N, and 31N), and five of the laterals were completed north to south (Wells 12S, 13S, 22S, 23S, and 31S). Two of the north-to-south wells, one in the middle (23S) and one in the lower bench (31S), were designated as monitor wells for during-fracturing diagnostic data acquisition (Fig. 1). Zipper operations were conducted in three groups, with the laterals on the outside edges of the pad fractured first (11N, 14N, and 21N) in a south-to-north order, followed by the inner laterals in the second zipper group (12S, 13S, and 22S) in a north-to-south order.

Analysis Model of Crack Arrest for Supercritical CO2 Pipelines Containing Impurities

CO2 transport pipelines, as a critical link in CCUS technology, are more prone to fracture propagation under the effects of environment and high pressure due to the special characteristics of CO2, resulting in ductile fracture incidents. However, the commonly used original Batelle two curves method (BTCM) has large errors applied to CO2 pipelines containing impurities. In this paper, a corrected BTCM based on a hoop stress calibration factor was proposed to evaluate the crack arrest ability of CO2 pipelines. The reliability of the modified model was verified based on the experiments data. The results show that the GERG-2008 equation of state is more suitable in predication of decompression wave velocity, and fracture propagation velocity model with a correction factor of ccf =2.0 was verified in quite good agreement with experiment results. This corrected BTCM that can be directly applied to engineering, provided theoretical basis and suggestions in the design and safe operation of CO2 pipelines containing impurities.

Experimental study of decompression wave characteristics and steel pipe applicability of supercritical CO2 pipeline

High-strength pipeline steel is the optimal choice for continuously transporting large amounts of carbon dioxide (CO2) in the future Carbon capture, utilization and storage (CCUS) industrial chain, and supercritical CO2 (S–CO2) is the ideal phase state from an emitter to an onshore storage site. In CCUS projects, it is very indispensable to carry out the suitability of high steel-grade pipelines to ensure the safe operation of pipelines. It is considered a catastrophic incident for creatures and equipment once pipeline failure when fractures or propagation occurs. In this paper, the fracture propagation velocity of X70, X80, and X90 pipeline materials is calculated base on the high strength line pipe (HLP). Meanwhile, three sets of full-bore fracture (FBR) experiments of S–CO2 pipelines were conducted with similar initial status on an industrial-scale setup, and the decompression wave velocity was obtained with the data acquisition system. The result shows that the initial decompression wave velocity of S–CO2 is about 270 m/s, and the pressure plateau is between 6.8 and 7.3 MPa, corresponding to the decompression wave velocity, which is about in the range of 100–220 m/s. After that, the decompression wave velocity prediction model was established based on the homogeneous equilibrium method (HEM) and the equation of state (Eos), and the prediction results are more conservative than the experimental results. To ensure that the pipeline will not ductilely fracture in the event of a leakage or rupture, X70, X80 and X90 grade steel pipeline design wall thickness and minimum arrest toughness values are determined based on the two-curve method (TCM), respectively. Furthermore, a CO2 pipeline design model is developed based on the experimental data and decompression wave calculation method. The significant experimental data could be used for safety assessment and theoretical model validation in the CO2 transport pipeline and is useful in developing better fracture control models.

Low-frequency distributed acoustic sensing shape factors for fracture front detection

Accurate knowledge of fracture extents generated in multistage unconventional completions remains elusive. Crosswell low-frequency distributed acoustic sensing (LF-DAS) measurements can determine the time and location of a frac hit. Knowing where and when a frac hit occurs constrains the fracture extent but does not estimate it quantitatively. A recent study on crosswell LF-DAS demonstrated a simple method to rapidly determine the instantaneous fracture propagation rate when a frac hit occurs. This method, the zero strain-rate location method (ZSRLM), is based on laboratory experiments and numerical modeling assuming a radial fracture geometry. The method estimates a fracture propagation velocity that is used to extrapolate the final fracture extent. The propagation rate is calculated based on dynamic estimates of the nearest distance from the fiber to the front of a propagating fracture. The ZSRLM is adapted to estimate the distance to the fracture front based on rectangular fracture geometries. A 3D displacement discontinuity method program generates crosswell LF-DAS strain-rate waterfall plots considering a single, rectangular fracture of constant height. Over 150 different simulations were conducted varying formation mechanical properties, fracture height, and the vertical and horizontal offset between the treatment and monitor well. For each simulated case, the ZSRLM is used to estimate the distance to the fracture front based on the simulated waterfall plots. The difference between the estimated and actual distance to the front is corrected by a shape factor. The relationship among the shape factor, fracture height ratio, and vertical offset ratio is determined. Using a shape factor improves the performance of the ZSRLM by up to a factor of two for rectangular fractures. The updated ZSRLM is applied to extrapolate final fracture extents in two field cases: a single cluster stage in the Montney Formation and a multicluster stage of an Austin Chalk completion.

Role of natural fractures with topology structure for hydraulic fracture propagation in continental shale reservoir

Natural fractures tend to further promote fracture network which is initiated by hydraulic fracturing. However, how natural fractures with various topology structures impact hydraulic fracture propagation in continental shale reservoir is still unclear. With Fullbore Microscan Imager (FMI) and geo-statistics of Chang 7 reservoir in Yanchang Formation, typical natural fractures are classified into three topology structures, which are natural fractures with type I, type II and type III nodes respectively, and the average occurrence strikes of natural fractures with type I, type II and type III nodes are SW260°, SW255° and SW255°. Coupling with seepage field and stress field, a model simulating fracture initiation and propagation is established considering the transversely isotropic property of continental shale reservoir. On this basis, the role of typical natural fractures with topology structure for hydraulic fracture propagation is studied qualitatively and quantitatively by Finite Element Method (FEM) with globally embedded cohesive element. Natural fractures with type II nodes have largest effect on inducing hydraulic fracture propagation, hydraulic fractures can communicate most easily with them, and also the length and velocity of hydraulic fracture propagation are the longest and fastest, so fracture network is the most complex after fracturing in naturally fractured continental shale reservoir with type II nodes, which follows by the effect of hydraulic fracture propagation in naturally fractured continental shale reservoir with type III nodes. In comparison, natural fractures with type I nodes have insignificant impacts on hydraulic fracture propagation. The research results are conductive to fracturing design in continental shale reservoir.

Simulation and regulation of fractures asynchronous initiation-propagation for deep shale gas horizontal well fracturing

The intensive cluster fracturing technology is widely applied in deep shale reservoirs. However, field data show that the fracture initiation time and propagation length of each cluster are different, which causes significant non-uniformity and affects the fracturing results. In this paper, a hydraulic fracture asynchronous initiation and propagation model for deep shale gas is established based on mechanics theory, which can consider the influence of in-situ stress variation and stress interference effect on the fracture asynchronous initiation and propagation behavior. According to the model design parameters, deep shale hydraulic fractures are regulated and optimized in combination with the non-uniform flow-limiting perforation technology to achieve uniform fracture propagation. The results show that, the non-uniformity of each fracture is obvious using conventional uniform perforation. However, with non-uniform perforation, each cluster perforation number is adjusted, the difference of initiation time and each fracture propagation velocity is significantly reduced, and the length of all fractures tend to be basically the same. And the field monitoring data are in good agreement with the calculation results, which verifies the reliability of the model. This study can reduce design blindness of non-uniform flow-limiting perforation technique, and has an important theoretical guidance for the optimal design of fracturing.

Experimental evaluation of the transient propagation fracture properties of rocks under dynamic mode I loading: An insight from digital image correlation

Accurate measurement of dynamic fracture properties is crucial for the safety and stability of the engineering applications. In this study, the dynamic mode I fracture tests are conducted on the notched semi-circular bend (NSCB) specimens with the split Hopkinson pressure bar (SHPB) loading system. By virtue of digital image correlation (DIC) technique combined with high-speed photography, the velocity fields of specimen are revealed, and thus an improved method is proposed to accurately calculate the transient kinetic energy and transient propagation fracture toughness of NSCB specimens under dynamic mode I loading. Our method has obvious merits in its specimen preparation and calculation accuracy since no specific assumptions are required. In addition, the crack propagation gauge (CPG) system is also applied into the tests to capture the transient crack propagation velocity and verify the testing results obtained by DIC technique. The results show that the transient propagation velocity of rocks continues to decrease with a three-stage evolution during the process of rock fracture, while the transient fracture energy of rock gradually increases. Moreover, the transient propagation fracture toughness is inversely proportional to the transient crack propagation velocity. Furthermore, the initiation fracrture toughness, propagation fracture toughness, propagation velocity and fracture energy all feature significant loading rate dependence.

A New Model for Calculation of Arrest Toughness in the Fracture Process of the Supercritical CO2 Pipeline.

A new model based on a decompression wave prediction model and an improved BTC model has been developed to investigate the arrest toughness in the fracture process of the supercritical CO2 pipeline. The comparison of the decompression wave velocity and the fracture propagation velocity was carried out to identify whether the pipe can prevent fracture propagation relying on its own toughness. If not, the minimum Charpy V-notch energy and the minimum wall thickness of steel pipes required for arrest fracture can be calculated using the improved BTC model. The results show that the working conditions with an initial pressure for the fracture of 11.7 MPa and a temperature of 323.15 K are the most difficult conditions to stop the fracture. The minimum wall thickness calculated only according to the strength design cannot meet the toughness requirements for ductile fracture arrest in the most difficult conditions in some cases. Then, the minimum wall thickness of the supercritical CO2 pipeline required for ductile fracture arrest in these cases will be obtained. For instance, the minimum wall thicknesses of X65, X70, and X80 steel pipes for fracture arrest with a pipe diameter of 610 mm at a design pressure of 13.2 MPa are 17.28, 14.58, and 12.81 mm, respectively, and when the pipe diameter is 1016 mm at a design pressure of 20.4 MPa, the minimum wall thicknesses of X70 and X80 pipes can meet the requirements of arrest toughness. The model established in this study can quickly and accurately calculate the minimum wall thickness and minimum Charpy energy required to stop fracture in the supercritical CO2 pipeline, which is suitable for engineering applications. The findings of this study can help in better understanding of the fracture process of supercritical CO2 pipelines.

Geomechanical Template for Distributed Acoustic Sensing Strain Patterns during Hydraulic Fracturing

SummaryRecently more distributed acoustic sensing (DAS) data have been collected during hydraulic fracturing in shale. Low-frequency DAS signals show patterns that are intuitively consistent with the understanding of the strain field around hydraulic fractures. This study uses a fracture simulator combined with a finite element solver to further understand the various patterns of the strain field caused by hydraulic fracturing. The results can serve as a “type-curve” template for the further interpretation of cross-well strain field plots.Incorporating detailed pump schedule and fracturing fluid/proppant properties, we use a hydraulic fracture simulator to generate fracture geometries, which are then passed to a finite element solver as boundary conditions for elastic-static calculation of the strain field. Because the finite element calculated strain is a tensor, it needs to be projected along the monitoring well trajectory to be comparable with the DAS strain, which is uniaxial. Moreover, the calculated strain field is transformed into a time domain using constant fracture propagation velocity. Strain rate is further derived from the simulated strain field using differentiation along the fracture propagation direction.Scenarios including a single planar hydraulic fracture, a single fracture with a discrete fracture network (DFN), and multiple planar hydraulic fractures in both vertical and horizontal directions were studied. The scenarios can be differentiated in the strain patterns on the basis of the finite element simulation results. In general, there is a tensile heart-shaped zone in front of the propagating fracture tip shown along the horizontal strain direction on both strain and strain rate plots. On the sides, there are compressional zones parallel to the fracture. The strain field projects beyond the depth where the hydraulic fracture is present. Patterns from strain rate can be used to distinguish whether the fracture is intersecting the fiber. Along the vertical direction, the transition zone depicts the upper boundary of the fracture. A complex fracture network with DFN shows a much more complex pattern compared with a single planar fracture. Multiple planar fractures show polarity reversals in horizontal fiber because of interactions between fractures. Data from the Hydraulic Fracturing Test Site 2 (HFTS2) experiment were used to validate the simulated results.The application of the study is to provide a template to better interpret hydraulic fracture characteristics using low-frequency DAS strain-monitoring data. To our understanding, there are no comprehensive templates for engineers to understand the strain signals from cross-well fiber monitoring. The results of this study will guide engineers toward better optimization of well spacing and fracturing design to minimize well interference and improve efficiency.

Fracture criterion and control plan on CO2 pipelines: Theory analysis and full-bore rupture (FBR) experimental study

Pressurized pipelines are the most reliable and cost-effective option for the long-distance transportation of CO2 from an emitter to an onshore storage site. Propagating or unstable factures are considered catastrophic pipeline failures, resulting in a massive escape of inventory within a short period of time. The decompression curve for CO2 exhibits a large drop in decompression wave speed at the phase transition pressure, leading to a higher driving force for crack propagation. The study of fracture control plans is very important for assessing the possibility of fracture propagation and preventing unstable fracturing along CO2 pipelines. Three full-bore rupture (FBR) experiments were performed using an industrial-scale (258 m long, 233 mm inner diameter) CO2 pipeline with initial CO2 states of gaseous, dense and supercritical phases, respectively. The relation between the decompression velocity and the pipeline fracture propagation velocity was analyzed during the process of buried CO2 pipeline release. A fracture propagation criterion was established for the buried CO2 pipeline. For the gaseous CO2 leakage, the pressure plateau corresponding to the decompression wave velocity only appeared near the closed end of the pipeline. For the dense CO2 leakage, the pressure plateau corresponding to the decompression wave velocity was observed near the saturation pressure after rapid decompression. For the supercritical CO2 leakage, the pressure plateau corresponding to the decompression wave velocity was observed in the stage when the supercritical CO2 transformed into the two phases of gas and liquid. Compared with the gaseous and dense CO2, for the supercritical CO2, the initial decompression wave velocity was the smallest, and the requirement of the pipeline safety factor was the highest.

Dynamic fracture testing of polymethyl-methacrylate (PMMA) single-edge notched beam

Dynamic fracture in single-edge notched polymethyl-methacrylate (PMMA) beams have been investigated by three-point-bending impact testing with a drop-weight machine. A high-speed camera combined with the digital image correlation (DIC) method is used to capture the impact-induced crack initiation and propagation, as well as the beam deformation fields and the open mode strain at the original notch tip. The crack propagation length is recorded and the instantaneous crack velocity is calculated. Furthermore, the dynamic fracture toughness KId is quantified from the loading-displacement relations at different impact velocities. The effects of the impact velocity and impact energy on dynamic fracture toughness, fracture initiation strain, as well as the corresponding influences on the fracture propagation velocity, are discussed.

Модель распространения трещины вдоль гидроизоляции скважины

A model of fracture initiation and propagation along the boundary of a cement plug and a steel casing in a plugged wellbore is proposed. The model allows predicting the conditions of hydraulic isolation failure of a cement plug induced by reservoir pressure. The model describes the stress state of the cement and it’s breakaway from the steel casing caused by the pressure of the pore fluid flowing into the fracture. Numerical experiments show that the fracture propagation velocity and the stability of the hydraulic isolation are sensitive to the reservoir pressure and to the prestressed state of the cement. It is shown also that the quality of cement adhesion to steel and the size of the initial cementing defects have little effect on the initiation conditions and fracture propagation velocity.

Assessment of complex projectiles in the early Late Pleistocene at Aduma, Ethiopia.

Complex projectiles—propulsion via mechanical aid—are considered an important technological innovation, with possible relevance for the successful Out-of-Africa dispersal of our species. Conclusive evidence for the beginning of this technology, however, is lacking from the early Late Pleistocene (ca. 130 to 70 thousand years ago; ka). Given the extremely limited applicability of relatively robust methods for validating stone-tipped projectile use, such as through fracture propagation velocity, converging lines of circumstantial evidence remain the best way to examine early complex projectiles. We assess here suggestions for an early Late Pleistocene origin of complex projectiles in Africa. Results from both previous and present independent approaches suggest a trajectory in which complex projectiles were likely adopted during the early Late Pleistocene in eastern Africa. At Aduma (Middle Awash, Ethiopia), morphometric, hafting, and impact damage patterns in several lithic point assemblages suggest a shift from simple spear technologies (thrusting and/or hand-cast) to complex projectiles. Broadly dated to 80–100 ka, lithic points from later phases of the Aduma succession represent a particularly strong candidate for projectile armatures most comparable to ethnographically known spearthrower darts, lending support for previous suggestions and warranting further investigations.

Characteristics of steady-state propagation of hydraulic fractures in ductile elastic and two-dimensionally confined plate media

This study explores the steady-state propagation of hydraulic fractures in ductile and elastic media, with an emphasis on time-varying fracture geometry. A series of well-controlled experiments was performed, in which the hydraulic fracture propagation behaviors in two-dimensionally confined gelatin plates were monitored while varying the gelatin stiffness, fracturing fluid viscosity, and injection flow rate. In all cases, comet-shaped, bi-wing fractures were initiated, and the fluid pressure responses and fracture geometry, including propagation velocity, length, width, and opening area were analyzed using the acquired time-lapsed images. The fracture propagation initiated before the peak pressure value, and the initiation pressure increased with the gelatin stiffness, injection flow rate, and viscosity, however, mainly governed by the elastic stiffness. Contrary to theoretical models, two states were identified over the course of comet-shaped hydraulic fracture propagation: a transient state in which the fracture propagation velocity and fracture width gradually increased, and thereafter, a steady state where the velocity and width became consistent. As a result, the steady-state propagation velocity was primarily determined by the flow rate, and the fracture width in a steady state was proportional to the fluid pressure normalized by the medium stiffness, owing to the elastic response. Based on experimental observations, simple but robust semi-empirical models were suggested to predict the fracture width and propagation velocity in a steady state.

Energy Partitioning During Subcritical Mode I Crack Propagation Through a Heterogeneous Interface

AbstractThe energy budget during the propagation of tensile fractures typically includes two major energy dissipation modes: the fracture energy to create a new interface and the radiated energy. Since seismic hazard is related to the amount of seismic energy released, it is important to evaluate precisely the energy budget during fracture propagation and see in particular if it is constant or not. However, two aspects are typically limiting a precise estimate of the energy budget: first, the measurement of the nonseismic energy release and second, the rock heterogeneity‐like asperities or barriers. We conducted here laboratory experiments, using an analog material (Polymethyl methacrylate (PMMA)), of a stable mode I interfacial crack propagation close to brittle‐creep transition through a heterogeneous interface for different macroscopic rupture velocities to evaluate carefully their energy budget. Both acoustic and optical advances of the crack front were measured simultaneously, providing precise estimates of both types of dissipated energy. We computed the radiation efficiency ηR (ratio of the radiated energy to the available energy for driving the fracture) and observed a nonlinear increase of ηR with the average fracture propagation velocity v over 2 orders of magnitude independently of the initial quenched disorder. The experimental observations are supported by a model based on the fluctuations of the local rupture velocity induced by the crack front pinning on local asperities which leads to ηR ∝ v0.55. We discuss implications for slow shear rupture modes, seismicity rate evolution, and induced seismicity.

Numerical simulation of slurry fracturing during shield tunnelling

The slurry type shield method is an important tunnelling method, especially for underwater tunnels in soft soil. If the slurry pressure is too high, it may lead to slurry fracturing of the stratum in front of the excavation face and cause water inrush accidents. Controlling the face stability of shallow shield tunnels is difficult owing to the inadequate understanding of the slurry induced fracturing mechanism. Most importantly, understanding the details of the slurry fracturing propagation process is not enough, as the process is especially complicated. However, the propagation process cannot be directly observed in the field or in small-scale laboratory tests because it occurs in bodies of soil. Thus far, an effective approach to investigate the slurry fracturing mechanism in the surrounding stratum of a slurry shield tunnel has not been reported. In this paper, a numerical simulation method for evaluating tunnelling-induced slurry fracturing is presented. The developed numerical model considered the couplings of stress distribution, fluid flows, and fracturing. The fracture initiation, branching, and propagation in the stratum could be reproduced numerically. A series of simulations for different ratios of cover depth to tunnel diameter were carried out to investigate the propagation process of slurry fracturing. The effects of slurry pressure at the tunnelling face and the cover depth above the tunnel were investigated. The results of the fracturing process induced by slurry, such as the fracture propagation velocity, slurry pressure distribution along the fracture, fracture initiation pressure, fracture extending pressure, and stratum deformations, were analyzed.

Coupled hydro-thermo-mechanical modeling of hydraulic fracturing in quasi-brittle rocks using BPM-DEM

This paper presents an improved understanding of coupled hydro-thermo-mechanical (HTM) hydraulic fracturing of quasi-brittle rock using the bonded particle model (BPM) within the discrete element method (DEM). BPM has been recently extended by the authors to account for coupled convective–conductive heat flow and transport, and to enable full hydro-thermal fluid–solid coupled modeling. The application of the work is on enhanced geothermal systems (EGSs), and hydraulic fracturing of hot dry rock (HDR) is studied in terms of the impact of temperature difference between rock and a flowing fracturing fluid. Micro-mechanical investigation of temperature and fracturing fluid effects on hydraulic fracturing damage in rocks is presented. It was found that fracture is shorter with pronounced secondary microcracking along the main fracture for the case when the convective–conductive thermal heat exchange is considered. First, the convection heat exchange during low-viscosity fluid infiltration in permeable rock around the wellbore causes significant rock cooling, where a finger-like fluid infiltration was observed. Second, fluid infiltration inhibits pressure rise during pumping and delays fracture initiation and propagation. Additionally, thermal damage occurs in the whole area around the wellbore due to rock cooling and cold fluid infiltration. The size of a damaged area around the wellbore increases with decreasing fluid dynamic viscosity. Fluid and rock compressibility ratio was found to have significant effect on the fracture propagation velocity.

A multiscale Implicit Level Set Algorithm (ILSA) to model hydraulic fracture propagation incorporating combined viscous, toughness, and leak-off asymptotics

This study uses an Implicit Level Set Algorithm (ILSA) to model the propagation of planar hydraulic fractures in situations when their progress is determined by an interplay of fluid viscosity, rock fracture toughness, and fluid leak-off into the formation. One of the key features of our approach is the use of the three-process tip asymptotic solution both as a propagation condition and to capture the multiscale behavior in a weak sense. Using this special tip asymptote is necessary because the validity region of the classical square root fracture opening solution (stemming from linear elastic fracture mechanics) is often limited to a small zone near the fracture tip, which can only be captured by a very fine mesh. In addition, this validity zone depends on the velocity of fracture propagation, so that slow and fast portions of the fracture front may experience different near-tip behavior. The multiscale tip asymptotic solution, on the other hand, has an increased validity region, which makes it possible to capture the near-tip multiscale behavior on a coarse mesh and yields a computationally efficient algorithm. The presence of leak-off also complicates the model considerably as it involves a delay term containing the trigger time history, which depends on the earlier fracture front positions. Moreover, the leak-off from tip elements in which the fracture front speed changes significantly requires special treatment. This three-process asymptotic solution is used to solve the fully coupled integro-delay-PDE model for a propagating planar hydraulic fracture by using a level set algorithm in conjunction with the tip asymptotic solution to locate the moving fracture front and to capture multiscale behavior. Firstly, the developed algorithm is validated against a reference solution for an axisymmetric hydraulic fracture. Secondly, a set of numerical examples involving three stress layers is presented to illustrate the variation of the multiscale near-tip behavior along the fracture perimeter and the need to use the multiscale asymptotic solution in a hydraulic fracturing simulator.

Fracture propagation control in CO2 pipelines: Validation of a coupled fluid–structure model

Existing engineering methods to ensure fracture propagation control in natural-gas transmission pipelines have been shown to be non-applicable when dense-phase CO2 is transported. To overcome this, a coupled fluid–structure interaction model has been developed. It consists of a homogeneous equilibrium flow model, coupled with the Span–Wagner equation of state and including solid-phase formation, and a finite-element model of the pipe taking into account large deformations and fracture propagation through a local fracture criterion.Model predictions are compared with data from two medium-scale crack-arrest experiments with dense-phase CO2. Good agreement is observed in fracture length, fracture-propagation velocity and pressure. Simulations show that, compared to natural-gas pipelines, the pressure level at the opening fracture flaps is sustained at a much higher level and at a much longer distance behind the moving fracture tip. This may be one important reason why the existing engineering methods do not work for dense-phase CO2.

Primary oil migration through buoyancy‐driven multiple fracture propagation: Oil velocity and flux

We present a fracture‐mechanics‐based formulation to investigate primary oil migration through the propagation of an array of periodic, parallel fractures in a sedimentary rock with elevated pore fluid pressure. The rock is assumed to be a linearly elastic medium. The fracture propagation and hence oil migration velocity are determined using a fracture mechanics criterion together with the lubrication theory of fluid mechanics. We find that fracture interactions have profound effects on the primary oil migration behavior. For a given fracture length, the mass flux of oil migration decreases dramatically with an increase in fracture density. The reduced oil flux is due to the decreased fracture propagation velocity as well as the narrowed fracture opening that result from the fracture interactions.