Unified Reservoir And Seismic Simulation With Explicit Representation Of Fractures And Faults

2021 ◽  
Author(s):  
Zheng Han ◽  
Guotong Ren ◽  
Rami M. Younis
Keyword(s):  
Reservoir Simulation ◽  
Transient Flow ◽  
Risk Mitigation ◽  
Integration Scheme ◽  
Fractured Reservoir ◽  
Dynamic Rupture ◽  
Time Step ◽  
Discrete Fracture Model ◽  
Seismic Triggering ◽  
Seismic Deformation

Abstract In the context of remote sensing, the vast disparity in characteristic scales between seismic deformation (e.g. milliseconds) and transient flow (e.g. hours) allows a "two-model paradigm" for geophysics and reservoir simulation. In the context of flow-induced geohazard risk mitigation and micro-seismic data integration, this paradigm breaks down. Under micro-seismic deformation, events occur with high-frequency, and over sustained duration during which the rock-fluid coupling is significant. In risk mitigation scenarios, the onset of seismic deformation is directly tied to quasi-static coupling periods. This work develops an approach to reservoir simulation modeling that allows simultaneous resolution of transient (inertial) poromechanics and multiphase fluid flow in the presence of fracture. A mixed discretization scheme combining the extended finite element method (XFEM) and the embedded discrete fracture model (EDFM) is extended using a second-order implicit Newmark time integration scheme for the inertial mechanics. A Lagrange multiplier method is developed to model pressure-dependent contact traction in fractures. The contact constraints are adapted to accommodate fracture opening. Slip-weakening fracture friction models are incorporated. Finally, a time-step controller is proposed to combine local discretization error with contact traction and slip-rate control along the fractures. This strategy allows automatic adaptation to resolve quasi-static, inter-seismic triggering, and co-seismic spontaneous rupture periods within one model. The model is verified to simulate complete induced earthquake sequences, including inter-seismic and dynamic rupture phases. The performance of the adaptive model is illustrated for cases with various set-ups of production and injection periods in a fractured reservoir with explicit fracture representation.

scholarly journals Investigation of Air Pocket Behavior in Pipelines Using Rigid Column Model and Contributions of Time Integration Schemes

Water ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 785
Author(s):  
Arman Rokhzadi ◽  
Musandji Fuamba
Keyword(s):  
Transient Flow ◽  
Time Integration ◽  
Driving Pressure ◽  
Implicit Time ◽  
Numerical Dissipation ◽  
Integration Scheme ◽  
Time Step ◽  
Column Model ◽  
Integration Schemes ◽  
Backward Euler

This paper studies the air pressurization problem caused by a partially pressurized transient flow in a reservoir-pipe system. The purpose of this study is to analyze the performance of the rigid column model in predicting the attenuation of the air pressure distribution. In this regard, an analytic formula for the amplitude and frequency will be derived, in which the influential parameters, particularly, the driving pressure and the air and water lengths, on the damping can be seen. The direct effect of the driving pressure and inverse effect of the product of the air and water lengths on the damping will be numerically examined. In addition, these numerical observations will be examined by solving different test cases and by comparing to available experimental data to show that the rigid column model is able to predict the damping. However, due to simplified assumptions associated with the rigid column model, the energy dissipation, as well as the damping, is underestimated. In this regard, using the backward Euler implicit time integration scheme, instead of the classical fourth order explicit Runge–Kutta scheme, will be proposed so that the numerical dissipation of the backward Euler implicit scheme represents the physical dissipation. In addition, a formula will be derived to calculate the appropriate time step size, by which the dissipation of the heat transfer can be compensated.

scholarly journals Three-Dimensional Elastodynamic Analysis Employing Partially Discontinuous Boundary Elements

Algorithms ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 129
Author(s):  
Yuan Li ◽  
Ni Zhang ◽  
Yuejiao Gong ◽  
Wentao Mao ◽  
Shiguang Zhang
Keyword(s):  
Side Effect ◽  
Domain Boundary ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Integration Scheme ◽  
Computational Accuracy ◽  
Time Step ◽  
Corner Points ◽  
Discontinuous Elements ◽  
The Time Domain

Compared with continuous elements, discontinuous elements advance in processing the discontinuity of physical variables at corner points and discretized models with complex boundaries. However, the computational accuracy of discontinuous elements is sensitive to the positions of element nodes. To reduce the side effect of the node position on the results, this paper proposes employing partially discontinuous elements to compute the time-domain boundary integral equation of 3D elastodynamics. Using the partially discontinuous element, the nodes located at the corner points will be shrunk into the element, whereas the nodes at the non-corner points remain unchanged. As such, a discrete model that is continuous on surfaces and discontinuous between adjacent surfaces can be generated. First, we present a numerical integration scheme of the partially discontinuous element. For the singular integral, an improved element subdivision method is proposed to reduce the side effect of the time step on the integral accuracy. Then, the effectiveness of the proposed method is verified by two numerical examples. Meanwhile, we study the influence of the positions of the nodes on the stability and accuracy of the computation results by cases. Finally, the recommended value range of the inward shrink ratio of the element nodes is provided.

A new dynamic mesh algorithm for studying the 3D transient flow field of tilting pad journal bearings

2016 ◽  
Vol 230 (12) ◽  
pp. 1470-1482 ◽  
Author(s):  
Mengxuan Li ◽  
Chaohua Gu ◽  
Xiaohong Pan ◽  
Shuiying Zheng ◽  
Qiang Li
Keyword(s):  
Flow Field ◽  
Equilibrium Position ◽  
Transient Flow ◽  
Journal Bearings ◽  
Dynamic Mesh ◽  
Static Equilibrium ◽  
Time Step ◽  
Tilting Pad ◽  
Grid Nodes ◽  
Tilting Pad Journal Bearings

A new dynamic mesh algorithm is developed in this paper to realize the three-dimensional (3D) computational fluid dynamics (CFD) method for studying the small clearance transient flow field of tilting pad journal bearings (TPJBs). It is based on a structured grid, ensuring that the total number and the topology relationship of the grid nodes remain unchanged during the dynamic mesh updating process. The displacements of the grid nodes can be precisely recalculated at every time step. The updated mesh maintains high quality and is suitable for transient calculation of large journal displacement in FLUENT. The calculation results, such as the static equilibrium position and the dynamic characteristic coefficients, are consistent with the two-dimensional (2D) solution of the Reynolds equation. Furthermore, in the process of transient analysis, under conditions in which the journal is away from the static equilibrium position, evident differences appear between linearized and transient oil film forces, indicating that the nonlinear transient calculation is more suitable for studying the rotor-bearing system.

Influence of Clearances and Thermal Effects on the Dynamic Behavior of Gear-Hydrodynamic Journal Bearing Systems

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
R. Fargère ◽  
P. Velex
Keyword(s):  
Degrees Of Freedom ◽  
Integration Scheme ◽  
Time Step ◽  
Specific Element ◽  
Normal Contact ◽  
Contact Algorithm ◽  
Gear Teeth ◽  
Proposed Model ◽  
Elastic Couplings ◽  
Definition Of

A global model of mechanical transmissions is introduced which deals with most of the possible interactions between gears, shafts, and hydrodynamic journal bearings. A specific element for wide-faced gears with nonlinear time-varying mesh stiffness and tooth shape deviations is combined with shaft finite elements, whereas the bearing contributions are introduced based on the direct solution of Reynolds' equation. Because of the large bearing clearances, particular attention has been paid to the definition of the degrees-of-freedom and their datum. Solutions are derived by combining a time step integration scheme, a Newton–Raphson method, and a normal contact algorithm in such a way that the contact conditions in the bearings and on the gear teeth are simultaneously dealt with. A series of comparisons with the experimental results obtained on a test rig are given which prove that the proposed model is sound. Finally, a number of results are presented which show that parameters often discarded in global models such as the location of the oil inlet area, the oil temperature in the bearings, the clearance/elastic couplings interactions, etc. can be influential on static and dynamic tooth loading.

Vibration analysis of multiple degrees of freedom mechanical system with dry friction

2012 ◽  
Vol 227 (7) ◽  
pp. 1505-1514 ◽  
Author(s):  
SD Yu ◽  
BC Wen
Keyword(s):  
Mechanical System ◽  
Dry Friction ◽  
Degrees Of Freedom ◽  
Simple Procedure ◽  
Mathematical Problem ◽  
Equations Of Motion ◽  
Inequality Constraints ◽  
Integration Scheme ◽  
Time Step ◽  
Multiple Degrees Of Freedom

This article presents a simple procedure for predicting time-domain vibrational behaviors of a multiple degrees of freedom mechanical system with dry friction. The system equations of motion are discretized by means of the implicit Bozzak–Newmark integration scheme. At each time step, the discontinuous frictional force problem involving both the equality and inequality constraints is successfully reduced to a quadratic mathematical problem or the linear complementary problem with the introduction of non-negative and complementary variable pairs (supremum velocities and slack forces). The so-obtained complementary equations in the complementary pairs can be solved efficiently using the Lemke algorithm. Results for several single degree of freedom and multiple degrees of freedom problems with one-dimensional frictional constraints and the classical Coulomb frictional model are obtained using the proposed procedure and compared with those obtained using other approaches. The proposed procedure is found to be accurate, efficient, and robust in solving non-smooth vibration problems of multiple degrees of freedom systems with dry friction. The proposed procedure can also be applied to systems with two-dimensional frictional constraints and more sophisticated frictional models.

Identifying Cable Tension Loss and Deck Damage in a Cable-Stayed Bridge Using a Moving Vehicle

2011 ◽  
Vol 133 (2) ◽  
Author(s):  
Shih-Hsun Yin ◽  
Chung-Yu Tang
Keyword(s):  
Computational Study ◽  
Vertical Displacement ◽  
Relative Displacement ◽  
Future Research ◽  
Integration Scheme ◽  
Time Step ◽  
Cable Tension ◽  
Displacement Response ◽  
Cable Stayed Bridge ◽  
Response Vector

This paper presents a computational study on a new method of detecting multiple simultaneous damages in a cable-stayed bridge by use of the analysis of the vertical dynamic response of a vehicle passing the bridge. First, the study uses a finite-element method to simulate the vehicle cable-stayed bridge system. Then, the vertical vibration interaction between the bridge and the vehicle is solved by a time-step integration scheme. In this research, we consider that two kinds of damage including cable tension loss and deck damage may occur simultaneously at different locations. The differences between the vertical displacement responses of a vehicle passing the damaged bridge and the healthy bridge are sampled and called the relative displacement response vector of the vehicle. The proper orthogonal decomposition (POD) is utilized to decompose the relative displacement response vector of the vehicle passing the bridge with unknown multiple damages into an optimal set of basis vectors formed from the ones of the vehicle moving over the known damaged bridges. The associated system parameters variation with the unknown multiple damages can be reconstructed further. Discussions are given concerning the feasibility and limitation of the proposed detection technique as well as directions for future research.

scholarly journals A Semi-Implicit Version of the MPAS-Atmosphere Dynamical Core

2015 ◽  
Vol 143 (9) ◽  
pp. 3838-3855 ◽  
Author(s):  
Steven Sandbach ◽  
John Thuburn ◽  
Danail Vassilev ◽  
Michael G. Duda
Keyword(s):  
Time Integration ◽  
Standard Test ◽  
Newton Iteration ◽  
Atmospheric Modeling ◽  
Implicit Time ◽  
Integration Scheme ◽  
Baroclinic Wave ◽  
Time Step ◽  
Integration Schemes ◽  
Helmholtz Problem

Abstract An important question for atmospheric modeling is the viability of semi-implicit time integration schemes on massively parallel computing architectures. Semi-implicit schemes can provide increased stability and accuracy. However, they require the solution of an elliptic problem at each time step, creating concerns about their parallel efficiency and scalability. Here, a semi-implicit (SI) version of the Model for Prediction Across Scales (MPAS) is developed and compared with the original model version, which uses a split Runge–Kutta (SRK3) time integration scheme. The SI scheme is based on a quasi-Newton iteration toward a Crank–Nicolson scheme. Each Newton iteration requires the solution of a Helmholtz problem; here, the Helmholtz problem is derived, and its solution using a geometric multigrid method is described. On two standard test cases, a midlatitude baroclinic wave and a small-planet nonhydrostatic gravity wave, the SI and SRK3 versions produce almost identical results. On the baroclinic wave test, the SI version can use somewhat larger time steps (about 60%) than the SRK3 version before losing stability. The SI version costs 10%–20% more per step than the SRK3 version, and the weak and strong scalability characteristics of the two versions are very similar for the processor configurations the authors have been able to test (up to 1920 processors). Because of the spatial discretization of the pressure gradient in the lowest model layer, the SI version becomes unstable in the presence of realistic orography. Some further work will be needed to demonstrate the viability of the SI scheme in this case.

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