Intelligent Time-Stepping for Practical Numerical Simulation

2021 ◽  
Author(s):  
Soham Sheth ◽  
Francois McKee ◽  
Kieran Neylon ◽  
Ghazala Fazil

Abstract We present a novel reservoir simulator time-step selection approach which uses machine-learning (ML) techniques to analyze the mathematical and physical state of the system and predict time-step sizes which are large while still being efficient to solve, thus making the simulation faster. An optimal time-step choice avoids wasted non-linear and linear equation set-up work when the time-step is too small and avoids highly non-linear systems that take many iterations to solve. Typical time-step selectors use a limited set of features to heuristically predict the size of the next time-step. While they have been effective for simple simulation models, as model complexity increases, there is an increasing need for robust data-driven time-step selection algorithms. We propose two workflows – static and dynamic – that use a diverse set of physical (e.g., well data) and mathematical (e.g., CFL) features to build a predictive ML model. This can be pre-trained or dynamically trained to generate an inference model. The trained model can also be reinforced as new data becomes available and efficiently used for transfer learning. We present the application of these workflows in a commercial reservoir simulator using distinct types of simulation model including black oil, compositional and thermal steam-assisted gravity drainage (SAGD). We have found that history-match and uncertainty/optimization studies benefit most from the static approach while the dynamic approach produces optimum step-sizes for prediction studies. We use a confidence monitor to manage the ML time-step selector at runtime. If the confidence level falls below a threshold, we switch to traditional heuristic method for that time-step. This avoids any degradation in the performance when the model features are outside the training space. Application to several complex cases, including a large field study, shows a significant speedup for single simulations and even better results for multiple simulations. We demonstrate that any simulation can take advantage of the stored state of the trained model and even augment it when new situations are encountered, so the system becomes more effective as it is exposed to more data.

1990 ◽  
Vol 10 (1) ◽  
pp. 33-58 ◽  
Author(s):  
Koji Sekiguchi ◽  
R.Kerry Rowe ◽  
Kwan Yee Lo

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1799
Author(s):  
Irene Gómez-Bueno ◽  
Manuel Jesús Castro Díaz ◽  
Carlos Parés ◽  
Giovanni Russo

In some previous works, two of the authors introduced a technique to design high-order numerical methods for one-dimensional balance laws that preserve all their stationary solutions. The basis of these methods is a well-balanced reconstruction operator. Moreover, they introduced a procedure to modify any standard reconstruction operator, like MUSCL, ENO, CWENO, etc., in order to be well-balanced. This strategy involves a non-linear problem at every cell at every time step that consists in finding the stationary solution whose average is the given cell value. In a recent paper, a fully well-balanced method is presented where the non-linear problems to be solved in the reconstruction procedure are interpreted as control problems. The goal of this paper is to introduce a new technique to solve these local non-linear problems based on the application of the collocation RK methods. Special care is put to analyze the effects of computing the averages and the source terms using quadrature formulas. A general technique which allows us to deal with resonant problems is also introduced. To check the efficiency of the methods and their well-balance property, they have been applied to a number of tests, ranging from easy academic systems of balance laws consisting of Burgers equation with some non-linear source terms to the shallow water equations—without and with Manning friction—or Euler equations of gas dynamics with gravity effects.


2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Jin-Woong Lee ◽  
Chaewon Park ◽  
Byung Do Lee ◽  
Joonseo Park ◽  
Nam Hoon Goo ◽  
...  

AbstractPredicting mechanical properties such as yield strength (YS) and ultimate tensile strength (UTS) is an intricate undertaking in practice, notwithstanding a plethora of well-established theoretical and empirical models. A data-driven approach should be a fundamental exercise when making YS/UTS predictions. For this study, we collected 16 descriptors (attributes) that implicate the compositional and processing information and the corresponding YS/UTS values for 5473 thermo-mechanically controlled processed (TMCP) steel alloys. We set up an integrated machine-learning (ML) platform consisting of 16 ML algorithms to predict the YS/UTS based on the descriptors. The integrated ML platform involved regularization-based linear regression algorithms, ensemble ML algorithms, and some non-linear ML algorithms. Despite the dirty nature of most real-world industry data, we obtained acceptable holdout dataset test results such as R2 > 0.6 and MSE < 0.01 for seven non-linear ML algorithms. The seven fully trained non-linear ML models were used for the ensuing ‘inverse design (prediction)’ based on an elitist-reinforced, non-dominated sorting genetic algorithm (NSGA-II). The NSGA-II enabled us to predict solutions that exhibit desirable YS/UTS values for each ML algorithm. In addition, the NSGA-II-driven solutions in the 16-dimensional input feature space were visualized using holographic research strategy (HRS) in order to systematically compare and analyze the inverse-predicted solutions for each ML algorithm.


2014 ◽  
Vol 50 (2) ◽  
pp. 477-480 ◽  
Author(s):  
Theodoros T. Zygiridis ◽  
Nikolaos V. Kantartzis ◽  
Theodoros D. Tsiboukis

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.


Author(s):  
Fabien Bigot ◽  
François-Xavier Sireta ◽  
Eric Baudin ◽  
Quentin Derbanne ◽  
Etienne Tiphine ◽  
...  

Ship transport is growing up rapidly, leading to ships size increase, and particularly for container ships. The last generation of Container Ship is now called Ultra Large Container Ship (ULCS). Due to their increasing sizes they are more flexible and more prone to wave induced vibrations of their hull girder: springing and whipping. The subsequent increase of the structure fatigue damage needs to be evaluated at the design stage, thus pushing the development of hydro-elastic simulation models. Spectral fatigue analysis including the first order springing can be done at a reasonable computational cost since the coupling between the sea-keeping and the Finite Element Method (FEM) structural analysis is performed in frequency domain. On the opposite, the simulation of non-linear phenomena (Non linear springing, whipping) has to be done in time domain, which dramatically increases the computation cost. In the context of ULCS, because of hull girder torsion and structural discontinuities, the hot spot stress time series that are required for fatigue analysis cannot be simply obtained from the hull girder loads in way of the detail. On the other hand, the computation cost to perform a FEM analysis at each time step is too high, so alternative solutions are necessary. In this paper a new solution is proposed, that is derived from a method for the efficient conversion of full scale strain measurements into internal loads. In this context, the process is reversed so that the stresses in the structural details are derived from the internal loads computed by the sea-keeping program. First, a base of distortion modes is built using a structural model of the ship. An original method to build this base using the structural response to wave loading is proposed. Then a conversion matrix is used to project the computed internal loads values on the distortion modes base, and the hot spot stresses are obtained by recombination of their modal values. The Moore-Penrose pseudo-inverse is used to minimize the error. In a first step, the conversion procedure is established and validated using the frequency domain hydro-structure model of a ULCS. Then the method is applied to a non-linear time domain simulation for which the structural response has actually been computed at each time step in order to have a reference stress signal, in order to prove its efficiency.


Author(s):  
Sheikh Md Rabiul Islam

In this paper analysis of a RLC circuit model that has been described optimal time step and minimize of error using numerical method. The goal is to reach the optimal time response due to the input for which optimal output response reaches a minimum error and also compared with ODE solver of MATLAB packages for the different cell (mesh) size of the RLC model. Table is constructed of the model to evaluate optimal time step and also CPU time into the simulation using MATLAB 7.6.0(R2008a).The values of register, capacitor and inductor as well as electromagnetic force are obtained through the mathematical relations of the model. The general analysis of the RLC circuit due to the optimal time step and minimum error is developed after several analysis and operations. The theoretical results show effectiveness of optimized of the model. Keywords: Optimal time step; MATLAB; Trapezoidal; Implicit Euler; Runge-Kutta method; RLC circuit. DOI: http://dx.doi.org/10.3329/diujst.v7i1.9650   Daffodil International University Journal of Science and Technology Vol.7(1) 2012 67-73


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