Study on Synchronous Propagation Behavior of Hydraulic Fractures and Cementing Interfacial Cracks during Fracturing of Shale Horizontal Wells

Large-scale staged hydraulic fracturing stimulation technology is an effective method to increase shale oil and gas recovery. However, cracks will appear along with the cementing interface and expand under the drive of fluid while hydraulic fracturing, failing wellbore sealing. To solve this problem, the synchronous propagation model of hydraulic fractures and cementing interfacial cracks in hydraulic fracturing is established. The Newton iteration method and displacement discontinuity method are used to solve the propagation length of each fracture, and the effects of cement sheath parameters and fracture parameters on the interface failure range are studied. The results show that when multiple hydraulic fractures expand, the interfacial cracks are also affected by “stress shadow,” offering an asymmetric expansion, and the cementing interfacial cracks in the area between hydraulic fractures are easier to expand. The failure range of interface between the hydraulic fractures expands rapidly if the cement elastic modulus increases from 5 GPa to 10 GPa; while the cement elastic modulus is higher than 10 GPa, the failure area is mainly affected by the number of hydraulic fractures; the failure range is not affected by the number of hydraulic fractures if the hydraulic fracture spacing is less than 10 m or more than 30 m; while the crack spacing is between 10 m and 30 m, the more the number of hydraulic fractures, the easier it is to cause the interface failure range to increase and connect. The research results can provide a theoretical basis for the optimization of cement slurry systems and fracturing parameters.

A New Higher Order Displacement Discontinuity Method Based on the Joint Element for Analysis of Close-Spacing Planar Fractures

Summary The 2D displacement discontinuity method (DDM) has been widely used to characterize the hydraulic fracture geometry and the induced in-situ stresses in the oil and gas industry owing to its simplicity and accuracy. As smaller fracture spacing is used by multistage fracturing, the constant DDM (CDDM) loses its accuracy in predicting the fracture behaviors, especially for the inner fractures in a stage where they are subjected to the strong stress shadowing effect. In this paper, the 2D higher order DDM (HDDM) based on the joint elements was developed to overcome this limitation. The higher order displacement discontinuity intensively increases the accuracy of CDDM but maintains the same amount of computation time by using patched-element pattern. The joint elements are introduced to simultaneously determine the opening, shearing, and closing of each fracture element based on the stress boundary condition, which can avoid the “negative width” of the inner fractures given by CDDM which are mechanically closed under the strong stress shadowing effect. The developed 2D joint element HDDM (JE-HDDM) gives the same results with the CDDM when the fracture spacing is relatively large, but shows its outperformance in both efficiency and accuracy over the CDDM in predicting the displacement discontinuities and induced in-situ stresses in close fracture-spacing case.

Thermal Effects on Far-Field Distributed Acoustic Strain-Rate Sensors

Summary Fiber-optic cables cemented outside of the casing of an unconventional well measure crosswell strain changes during fracturing of neighboring wells with low-frequency distributed acoustic sensing (LF-DAS). As a hydraulic fracture intersects an observation well instrumented with fiber-optic cables, the fracture fluid injected at ambient temperatures can cool a section of the sensing fiber. Often, LF-DAS and distributed temperature sensing (DTS) cables are run in tandem, enabling the detection of such cooling events. The increasing use of LF-DAS for characterizing unconventional hydraulic fracture completions demands an investigation of the effects of temperature on the measured strain response by LF-DAS. Researchers have demonstrated that LF-DAS can be used to extract the temporal derivative of temperature for use as a differential-temperature-gradient sensor. However, differential-temperature-gradient sensing is predicated on the ability to filter strain components out of the optical signal. In this work, beginning with an equation for optical phase shift of LF-DAS signals, a model relating strain, temperature, and optical phase shift is explicitly developed. The formula provides insights into the relative strength of strain and temperature effects on the phase shift. The uncertainty in the strain-rate measurements due to thermal effects is estimated. The relationship can also be used to quantify uncertainties in differential-temperature-gradient sensors due to strain perturbations. Additionally, a workflow is presented to simulate the LF-DAS response accounting for both strain and temperature effects. Hydraulic fracture geometries are generated with a 3D fracture simulator for a multistage unconventional completion. The fracture width distributions are imported by a displacement discontinuity method (DDM) program to compute the strain rates along an observation well. An analytic model is used to approximate the temperature in the fracture. Using the derived formulae for optical phase shift, the model outputs are then used to compute the LF-DAS response at a fiber-optic cable, enabling the generation of waterfall plots including both strain and thermal effects. The model results suggest that before, during, and immediately following a fracture intersecting a well instrumented with fiber, the strain on the fiber drives the LF-DAS signal. However, at later times, as completion fluid cools the observation well, the temperature component of the LF-DAS signal can be equal to or exceed the strain component. The modeled results are compared to a published field case in an attempt to enhance the interpretation of LF-DAS waterfall plots. Finally, we propose a sensing configuration to identify the events when “wet fractures” (fractures with fluids) intersect the observation well.

Thermal Effects on Far-Field Distributed Acoustic Strain-Rate Sensors

Fiber-optic cables cemented outside of the casing of an unconventional well measure cross-well strain changes during fracturing of neighboring wells with low-frequency distributed acoustic sensing (LF-DAS). As a hydraulic fracture intersects an observation well instrumented with fiber-optic cables, fracture fluid injected at ambient temperatures can cool a section of the sensing fiber. Often, LF-DAS and distributed temperature sensing (DTS) cables are run in tandem, enabling the detection of such cooling events. The increasing use of LF-DAS for characterizing unconventional hydraulic fracture completions demands an investigation of the effects of temperature on the measured strain response by LF-DAS. Researchers have demonstrated that LF-DAS can be used to extract the temporal derivative of temperature for use as a differential-temperature-gradient sensor. However, differential-temperature-gradient sensing is predicated on the ability to filter strain components out of the optical signal. In this work, beginning with an equation for optical phase shift of LF-DAS signals, a model relating strain, temperature, and optical phase shift is explicitly developed. The formula provides insights into the relative strength of strain and temperature effects on the phase shift. The uncertainty in the strain-rate measurements due to thermal effects is estimated. The relationship can also be used to quantify uncertainties in differential-temperature-gradient sensors due to strain perturbations. Additionally, a workflow is presented to simulate the LF-DAS response accounting for both strain and temperature effects. Hydraulic fracture geometries are generated with a 3D fracture simulator for a multi-stage unconventional completion. The fracture width distributions are imported by a displacement discontinuity method program to compute the strain-rates along an observation well. An analytic model is used to approximate the temperature in the fracture. Using the derived formulae for optical phase shift, the model outputs are then used to compute the LF-DAS response at a fiber-optic cable, enabling the generation of waterfall plots including both strain and thermal effects. The model results suggest that before, during, and immediately following a fracture intersecting a well instrumented with fiber, the strain on the fiber drives the LF-DAS signal. However, at later times, as completion fluid cools the observation well, the temperature component of the LF-DAS signal can equal or exceed the strain component. The modeled results are compared to a published field case in an attempt to enhance interpretation of LF-DAS waterfall plots. Finally, we propose a sensing configuration in order to identify the events when "wet fractures" (fractures with fluids) intersect the observation well.

Analysis of Flexural Toppling Failure in Rock Slopes Using Discrete Element Method

Flexural toppling failure is a common failure mode of natural and artificial rock slopes, which has caused serious damage to human life and property. In this work, an advanced numerical method called the Universal Distinct Element Code (UDEC) was used to study the mechanism of flexural toppling failure. In total, more than twenty slope models were built and analyzed. Two new parameters (displacement discontinuity and transition coefficient of failure surface) were introduced to present a further understanding of flexural toppling. The results show the failure zone of rock slopes subjected to flexural toppling includes two parts: the first-order instability part (FOIP) and the independent toppling zone (ITZ). The FOIP can be further divided into two subzones: the sliding zone (SZ) and the superimposed toppling zone (STZ). The occurrence of surface deformation discontinuities is the precursor to flexural toppling failure. The first displacement discontinuity occurs on the boundary between the FOIP and the ITZ. The angle, spacing, and angle of the joints, the angle of the slope has a significant influence on the stability of anti-dip bedding rock slopes. However, they do not affect the deformation and failure pattern of the slope.

Efficient Modeling of Proppant Transport During Three-Dimensional Hydraulic Fracture Propagation

We propose an adaptive Eulerian-Lagrangian (E-L) proppant module and couple it with our simplified three-dimensional displacement discontinuity method (S3D DDM) hydraulic fracture model. The integrated model efficiently calculates proppant transport during three-dimensional (3D) hydraulic fracture propagation in multi-layer formations. The results demonstrate that hydraulic fracture height growth mitigates the form of proppant bed, so the proppant placement is more uniform in the hydraulic fracture under a smaller stress contrast. A higher fracturing fluid viscosity improves the suspension of proppant particles and generates a fracture larger in height and width but shorter in length. Lower proppant density and particle size reduce the proppant settling and create more uniform proppant placements, while they do not affect the hydraulic fracture geometry. Moreover, a larger proppant particle size limits the accessibility of the hydraulic fracture to the proppant, so the larger proppant particles do not fill the fracture tip and edge where the fracture width is small.