Numerical Simulation of Distributed Dynamic Systems using Hybrid Tools of Intelligent Computing

2013 ◽  
pp. 360-383
Author(s):  
Fethi H. Bellamine ◽  
Aymen Gdouda

Developing fast and accurate numerical simulation models for predicting, controlling, designing, and optimizing the behavior of distributed dynamic systems is of interest to many researchers in various fields of science and engineering. These systems are described by a set of differential equations with homogenous or mixed boundary constraints. Examples of such systems are found, for example, in many networked industrial systems. The purpose of the present work is to review techniques of hybrid soft computing along with generalized scaling analysis for the solution of a set of differential equations characterizing distributed dynamic systems. The authors also review reduction techniques. This paves the way to control synthesis of real-time robust realizable controllers.

Author(s):  
Liubymov Artem ◽  
◽  
Svjatnyj Volodymyr

The concept of developing parallel modeling languages (PML) of complex dynamic systems (CDS) based on the analogy between the principles of operation of serial languages (SL) and MIMD parallelism provides for the purpose of "Functional element of the SL block diagram - MIMD process", which transforms the SL specifications of serial simulators (block diagrams) in the structure of virtual parallel simulators. Virtuality is due to the atypical for MIMD-systems "fine granulation" of the processes generated by this purpose and the connections between the processes, which must be appropriate to the connection schemes of the functional elements of SL simulators. The architecturally relevant implementation of a parallel simulator of any CDS is related to the form of its mathematical description and the corresponding Simulation model. CDS with concentrated parameters are described by systems of ordinary differential equations (ODE) of the first order, systems of equations of different orders, systems of differential-algebraic equations (DAE-Problem), and in network CDS there are sums of derivatives from different variables. CDS with distributed parameters are described by systems of differential equations in partial derivatives, so the development of Simulation-models is associated with the approximation of equations by spatial coordinates and the formation of ODE systems. For these forms of description Simulation-models and corresponding SL-specifications in the form of block diagrams of SL-elements are considered, which is the basis for construction of virtual MIMD-simulators of two possible levels of granulation of processes: the basic level " SL-element - process" provides MIMD-processes "Shallow granulation", in which there is uneven loading of processes and an unfavorable relationship between the volume of computational operations and data exchange operations between processes; The level "Group of SL-elements - process" corresponds to the stage of simulator development, in which the specifications use the composition of SL-elements according to a certain principle, for example, "One equation Simulation model - Group of SLelements to solve the equation - Coarse granulation process"


Author(s):  
Ge Kai ◽  
Wei Zhang

In this paper, we establish a dynamic model of the hyper-chaotic finance system which is composed of four sub-blocks: production, money, stock and labor force. We use four first-order differential equations to describe the time variations of four state variables which are the interest rate, the investment demand, the price exponent and the average profit margin. The hyper-chaotic finance system has simplified the system of four dimensional autonomous differential equations. According to four dimensional differential equations, numerical simulations are carried out to find the nonlinear dynamics characteristic of the system. From numerical simulation, we obtain the three dimensional phase portraits that show the nonlinear response of the hyper-chaotic finance system. From the results of numerical simulation, it is found that there exist periodic motions and chaotic motions under specific conditions. In addition, it is observed that the parameter of the saving has significant influence on the nonlinear dynamical behavior of the four dimensional autonomous hyper-chaotic system.


Author(s):  
Xiangying Guo ◽  
Wei Zhang ◽  
Ming-Hui Yao

This paper presents an analysis on the nonlinear dynamics and multi-pulse chaotic motions of a simply-supported symmetric cross-ply composite laminated rectangular thin plate with the parametric and forcing excitations. Firstly, based on the Reddy’s three-order shear deformation plate theory and the model of the von Karman type geometric nonlinearity, the nonlinear governing partial differential equations of motion for the composite laminated rectangular thin plate are derived by using the Hamilton’s principle. Then, using the second-order Galerkin discretization approach, the partial differential governing equations of motion are transformed to nonlinear ordinary differential equations. The case of the primary parametric resonance and 1:1 internal resonance is considered. Four-dimensional averaged equation is obtained by using the method of multiple scales. From the averaged equation obtained here, the theory of normal form is used to give the explicit expressions of normal form. Based on normal form, the energy phase method is utilized to analyze the global bifurcations and multi-pulse chaotic dynamics of the composite laminated rectangular thin plate. The results obtained above illustrate the existence of the chaos for the Smale horseshoe sense in a parametrical and forcing excited composite laminated thin plate. The chaotic motions of the composite laminated rectangular thin plate are also found by using numerical simulation. The results of numerical simulation also indicate that there exist different shapes of the multi-pulse chaotic motions for the composite laminated rectangular thin plate.


2021 ◽  
Vol 73 (04) ◽  
pp. 60-61
Author(s):  
Chris Carpenter

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 199149, “Rate-Transient-Analysis-Assisted History Matching With a Combined Hydraulic Fracturing and Reservoir Simulator,” by Garrett Fowler, SPE, and Mark McClure, SPE, ResFrac, and Jeff Allen, Recoil Resources, prepared for the 2020 SPE Latin American and Caribbean Petroleum Engineering Conference, originally scheduled to be held in Bogota, Colombia, 17–19 March. The paper has not been peer reviewed. This paper presents a step-by-step work flow to facilitate history matching numerical simulation models of hydraulically fractured shale wells. Sensitivity analysis simulations are performed with a coupled hydraulic fracturing, geomechanics, and reservoir simulator. The results are used to develop what the authors term “motifs” that inform the history-matching process. Using intuition from these simulations, history matching can be expedited by changing matrix permeability, fracture conductivity, matrix-pressure-dependent permeability, boundary effects, and relative permeability. Introduction This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 199149, “Rate-Transient-Analysis-Assisted History Matching With a Combined Hydraulic Fracturing and Reservoir Simulator,” by Garrett Fowler, SPE, and Mark McClure, SPE, ResFrac, and Jeff Allen, Recoil Resources, prepared for the 2020 SPE Latin American and Caribbean Petroleum Engineering Conference, originally scheduled to be held in Bogota, Colombia, 17-19 March. The paper has not been peer reviewed. This paper presents a step-by-step work flow to facilitate history matching numerical simulation models of hydraulically fractured shale wells. Sensitivity analysis simulations are performed with a coupled hydraulic fracturing, geomechanics, and reservoir simulator. The results are used to develop what the authors term “motifs” that inform the history-matching process. Using intuition from these simulations, history matching can be expedited by changing matrix permeability, fracture conductivity, matrix-pressure-dependent permeability, boundary effects, and relative permeability. Introduction The concept of rate transient analysis (RTA) involves the use of rate and pressure trends of producing wells to estimate properties such as permeability and fracture surface area. While very useful, RTA is an analytical technique and has commensurate limitations. In the complete paper, different RTA motifs are generated using a simulator. Insights from these motif simulations are used to modify simulation parameters to expediate and inform the history- matching process. The simulation history-matching work flow presented includes the following steps: 1 - Set up a simulation model with geologic properties, wellbore and completion designs, and fracturing and production schedules 2 - Run an initial model 3 - Tune the fracture geometries (height and length) to heuristic data: microseismic, frac-hit data, distributed acoustic sensing, or other diagnostics 4 - Match instantaneous shut-in pressure (ISIP) and wellhead pressure (WHP) during injection 5 - Make RTA plots of the real and simulated production data 6 - Use the motifs presented in the paper to identify possible production mechanisms in the real data 7 - Adjust history-matching parameters in the simulation model based on the intuition gained from RTA of the real data 8 -Iterate Steps 5 through 7 to obtain a match in RTA trends 9 - Modify relative permeabilities as necessary to obtain correct oil, water, and gas proportions In this study, the authors used a commercial simulator that fully integrates hydraulic fracturing, wellbore, and reservoir simulation into a single modeling code. Matching Fracturing Data The complete paper focuses on matching production data, assisted by RTA, not specifically on the matching of fracturing data such as injection pressure and fracture geometry (Steps 3 and 4). Nevertheless, for completeness, these steps are very briefly summarized in this section. Effective fracture toughness is the most-important factor in determining fracture length. Field diagnostics suggest considerable variability in effective fracture toughness and fracture length. Typical half-lengths are between 500 and 2,000 ft. Laboratory-derived values of fracture toughness yield longer fractures (propagation of 2,000 ft or more from the wellbore). Significantly larger values of fracture toughness are needed to explain the shorter fracture length and higher net pressure values that are often observed. The authors use a scale- dependent fracture-toughness parameter to increase toughness as the fracture grows. This allows the simulator to match injection pressure data while simultaneously limiting fracture length. This scale-dependent toughness scaling parameter is the most-important parameter in determining fracture size.


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