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

Energies ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 3256
Author(s):  
Ruud Weijermars ◽  
Jihoon Wang
Keyword(s):  
Pressure Change ◽  
Hydraulic Fractures ◽  
Superposition Method ◽  
Fracture Treatment ◽  
Energy Extraction ◽  
Principal Stresses ◽  
Linear Superposition ◽  
Two Generations ◽  
Stress States ◽  
Stress Reversals

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.

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

Energies ◽  
2020 ◽  
Vol 13 (24) ◽  
pp. 6474
Author(s):  
Tri Pham ◽  
Ruud Weijermars
Keyword(s):  
Hydraulic Fracture ◽  
Fracture Propagation ◽  
Fracture Network ◽  
Time Dependent ◽  
Reservoir Rock ◽  
Hydraulic Fractures ◽  
Superposition Method ◽  
Stress Concentrations ◽  
Linear Superposition ◽  
Dynamic Fractures

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.

Evaluating Shakedown for Structures Based on the Element Bearing-Ratio

2011 ◽  
Vol 137 ◽  
pp. 16-23 ◽  
Author(s):  
Wei Zhang ◽  
Lu Feng Yang ◽  
Chuan Xiong Fu ◽  
Jian Wang
Keyword(s):  
Yield Criterion ◽  
Solution Procedure ◽  
Superposition Method ◽  
Linear Superposition ◽  
Non Linear Programming ◽  
Elastic Plastic ◽  
Non Linear ◽  
Efficiency And Effectiveness ◽  
Linear Programming Formulation ◽  
Element Bearing

Based on Melan’s theorem, an improved numerical solution procedure for evaluating shakedown loads by non-linear superposition method is presented, and the relationship between the classical non-linear programming formulation of shakedown problem and the numerical method is disclosed. The stress term in classical optimization problem is replaced by the element bearing-ratio (EBR) in the procedure, and series of residual EBR fields can be generated by the D-value of the elastic-plastic EBR fields and the elastic EBR fields at every incremental loading step. The shakedown load is determined by performing the incremental non-linear static analysis when the yield criterion is arrived either by the elastic-plastic EBR fields or residual EBR fields. By introducing the EBR, the proposed procedure can be easily used to those complex structures with multi-material and complicated configuration. The procedure is described in detail and some numerical results, that show the efficiency and effectiveness of the proposed method, are reported and discussed.

Strain field reconstruction of crossbeam structure based on load-strain linear superposition method

2021 ◽  
Author(s):  
Yangyang Cheng ◽  
Zhaohua Li ◽  
Guangjun Wang ◽  
Chang Peng ◽  
Lei Zhang ◽  
...  
Keyword(s):  
Strain Field ◽  
Superposition Method ◽  
Linear Superposition ◽  
Field Reconstruction

A Quick Computation of Factor of Safety for Biaxial Stress States

1998 ◽  
Vol 120 (4) ◽  
pp. 721-726
Author(s):  
K. Deb
Keyword(s):  
Factor Of Safety ◽  
Biaxial Stress ◽  
Principal Stresses ◽  
Design Charts ◽  
Failure Theory ◽  
Safe Stress ◽  
Design Activities ◽  
Stress States ◽  
Failure Theories

Determination of overall factor of safety of a design involves repeated calculation of factor of safety at critical points in the design. For a given stress state at a point, the factor of safety is calculated by first finding the principal stresses and then comparing them with the maximum safe stress that can be applied without causing failure of the material according to an appropriate failure theory. In this paper, we suggest quick and ready-to-use expressions and graphs for calculating factor of safety for biaxial stress states for a number of commonly-used failure theories. These graphs can be directly used as design charts for computing factor of safety in engineering design activities.

On a class of non-coaxial plasticity models for granular soils

2005 ◽  
Vol 462 (2067) ◽  
pp. 725-748 ◽  
Author(s):  
H.S Yu ◽  
X Yuan
Keyword(s):  
Simple Shear ◽  
Shear Loading ◽  
Granular Soils ◽  
Strain Rates ◽  
Principal Stresses ◽  
Constitutive Theories ◽  
Strain Behaviour ◽  
Plastic Potential ◽  
Stress States ◽  
Soil Behaviour

The non-coaxiality of the directions of principal stresses and principal plastic strain rates in granular soils under stress rotations has long been observed and recognized in soil tests using both simple shear and hollow cylinder apparatuses. A few constitutive theories have also been proposed in the literature to account for the effect of stress rotations and the subsequent non-coaxial soil behaviour, particularly in the context of shear band analysis. However, the lack of corresponding general numerical methods makes it difficult to investigate the influence of non-coaxial stress–strain behaviour on the results of geotechnical boundary value problems. This paper presents a numerical evaluation of a class of non-coaxial, elastic–plastic models that are developed by combining the conventional plastic potential theory and the double shearing theory. The general non-coaxial constitutive theories are first formulated and then a finite element implementation of the theories is carried out. To evaluate the non-coaxial theories, the problem of simple shear of soils is chosen to investigate the predicted behaviour of soils under simple shear loading conditions where the axes of principal stresses rotate. In particular, the influence of initial stress states and the degree of non-coaxiality are examined. It is found that the numerical results predicted using the non-coaxial model are in general agreement with the experimental observations reported in the literature.

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