Linear superposition method (LSM) for solving stress tensor fields and displacement vector fields: Application to multiple pressure-loaded circular holes in an elastic plate with far-field stress

Wang

2021

Energies

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Prior studies have noted that the principal stress orientations near the hydraulic fractures of well systems used for energy extraction may wander over time. Typically, the minimum and maximum principal stresses—in the horizontal map view—swap their respective initial directions, due to (1) fracture treatment interventions, and (2) pressure depletion resulting from production. The present analysis shows with stress trajectory visualizations, using a recently developed linear superposition method (LSM), that at least two generations of stress reversals around hydraulic fractures occur. The first generation occurs during the fracture treatment; the second occurs immediately after the onset of so-called flow-back. During each of these stress swaps in the vicinity of the hydraulic fractures, reservoir directions that were previously in compression subsequently exhibit extension, and directions previously stretching subsequently exhibit shortening. The pressure change in the hydraulic fractures—from over-pressured to under-pressured (only held open by proppant packs)—caused the neutral points that separate domains with different stress states to migrate from locations transverse to the fracture to locations beyond the fracture tips. Understanding such detailed geo-mechanical dynamics, related to the pressure evolution in energy reservoirs, is extremely important for improving both the fracture treatment and the well operation, as future hydrocarbon and geothermal energy extraction projects emerge.

Section: Linear Superposition Methods (Lsm)mentioning

confidence: 99%

Section: Computing Impact Of Fracture Treatment On Stress State and Reservoir Pressurementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Stress Reversals near Hydraulically Fractured Wells Explained with Linear Superposition Method (LSM)

Wang

2021

Energies

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“…The static Linear Superposition Method (LSM) and dynamic Time-Stepped Linear Superposition Method (TLSM) have been recently developed and applied to model and visualize mechanical interactions between pressurized fractures [15] and boreholes [26]. TLSM and LSM are proposed as fast, gridless alternatives to commonly used, grid-dependent fracture propagation models, which are computationally more demanding and henceforth more expensive.…”

Section: Methods Of Solution: Lsm and Tlsmmentioning

confidence: 99%

Hydraulic Fracture Propagation in a Poro-Elastic Medium with Time-Dependent Injection Schedule Using the Time-Stepped Linear Superposition Method (TLSM)

Pham

2020

Energies

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The Time-Stepped Linear Superposition Method (TLSM) has been used previously to model and analyze the propagation of multiple competitive hydraulic fractures with constant internal pressure loads. This paper extends the TLSM methodology, by including a time-dependent injection schedule using pressure data from a typical diagnostic fracture injection test (DFIT). In addition, the effect of poro-elasticity in reservoir rocks is accounted for in the TLSM models presented here. The propagation of multiple hydraulic fractures using TLSM-based codes preserves infinite resolution by side-stepping grid refinement. First, the TLSM methodology is briefly outlined, together with the modifications required to account for variable time-dependent pressure and poro-elasticity in reservoir rock. Next, real world DFIT data are used in TLSM to model the propagation of multiple dynamic fractures and study the effect of time-dependent pressure and poro-elasticity on the development of hydraulic fracture networks. TLSM-based codes can quantify and visualize the effects of time-dependent pressure, and poro-elasticity can be effectively analyzed, using DFIT data, supported by dynamic visualizations of the changes in spatial stress concentrations during the fracture propagation process. The results from this study may help develop fracture treatment solutions with improved control of the fracture network created while avoiding the occurrence of fracture hits.

“…The proprietary, gridless, fracture propagation simulator (TLSM) can be coupled with the gridless simulator for fluid flow in fractured porous media (CAM). The fundamental theory and key algorithms for both types of simulators have been published in leading applied mathematics journals [17,[77][78][79].…”

Section: Merging Gridless Solutions For Flow and Fracturementioning

confidence: 99%

Comparison of Flow Solutions for Naturally Fractured Reservoirs Using Complex Analysis Methods (CAM) and Embedded Discrete Fracture Models (EDFM): Fundamental Design Differences and Improved Scaling Method

Khanal

2020

Geofluids

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The present study compares flow paths in reservoirs with natural fractures, solved with Complex Analysis Methods (CAM), to those solved with Embedded Discrete Fracture Models (EDFM). One aim is to define scaling rules for the strength (flux) of the discrete natural fractures used in CAM models, which was previously theoretically defined based on the expected flow distortion. A major hurdle for quantitative benchmarks of CAM with EDFM results is that each of the two methods accounts for natural fractures with different assumptions and input parameters. For example, EDFM scales the permeability of the natural fractures based on a cubic equation, while CAM uses a flux strength. The results from CAM and EDFM are used to scale the flux strength of the natural fractures and improve the equivalent permeability contrast estimation for CAM. The permeability contrast for CAM is calculated from the ratio of the enhanced velocity inside natural fractures to the unperturbed matrix fluid velocity. A significant advantage of flow and pressure models based on CAM is the high resolution without complex gridding. Particle tracking results are presented for fractures with different hydraulic conductivity ranging from highly permeable to impervious.