Continuous Prediction Model of Carbon Content in 120 t Converter Blowing Process

A continuous prediction model of carbon content of 120 t BOF is established in this paper. Based on the three-stage decarburization theory and combined with the production process of 120 t converter, the effects of oxygen lance height and top blowing oxygen flow rate are also considered in the model. The explicit finite difference method is used to realize continuous prediction of carbon content in the converter blowing process. The model parameters such as ultimate carbon content in molten pool are calculated according to the actual data of 120 t BOF, which improves the hit rate of the model. Process verification and end-point verification for the continuous prediction model have been carried out, and the results of process verification indicate that the continuous prediction model established in the paper basically accords with the actual behavior of decarburization. Moreover, the hit ratio of the continuous prediction model reached 85% for the prediction of end-point carbon content within a tolerance of ±0.02%.

Removing the stability limit of the time–space domain explicit finite difference schemes for acoustic modeling with stability condition-based spatial operators

The time step and grid spacing in explicit finite-difference (FD) modeling are constrained by the Courant-Friedrichs-Lewy (CFL) condition. Recently, it has been found that spatial FD coefficients may be designed through simultaneously minimizing the spatial dispersion error and maximizing the CFL number. This allows one to stably use a larger time step or a smaller grid spacing than usually possible. However, when using such a method, only second-order temporal accuracy is achieved. To address this issue, I propose a method to determine the spatial FD coefficients, which simultaneously satisfy the stability condition of the whole wavenumber range and the time–space domain dispersion relation of a given wavenumber range. Therefore, stable modeling can be performed with high-order spatial and temporal accuracy. The coefficients can adapt to the variation of velocity in heterogeneous models. Additionally, based on the hybrid absorbing boundary condition, I develop a strategy to stably and effectively suppress artificial reflections from the model boundaries for large CFL numbers. Stability analysis, accuracy analysis and numerical modeling demonstrate the accuracy and effectiveness of the proposed method.

Modelling and performance analysis for cumene production process in a four-layer packed bed reactor

A mathematical model is developed and designed for the cumene reactor in cumene production process in Hindustan Organic Chemicals Limited (HOCL), Kochi with improved operating conditions. High purity cumene is produced by the alkylation of benzene with propylene in this catalytic condensation process where solid phosphoric acid (SPA) is used as the catalyst. The mathematical model has been derived from mass and energy balance equations considering the reactor as fixed packed bed reactor and two different numerical methods are presented here to solve the modelling equations. The explicit finite difference method (FDM) involves the approximation of derivatives into finite differences, and in the other one, orthogonal collocation (OC), Ordinary Diffeential Equations (ODEs) are formed at the collocation points and are solved using Runge–Kutta fourth order numerical scheme. Here the analysis shows that the predictions from the model are in good alignment with the plant data. The combined feed has the optimum value of 1:2:8 for propylene, propane and benzene and the profiles of temperature and concentration can be obtained along the reactor. The model has been implemented in COMSOL Multiphysics as a packed bed reactor using the same parameters collected from the plant of study. It has been found that the reaction occurs at a satisfactory level even with a low temperature than the reactor temperature at the plant by changing the catalytic particle size. The reaction performance is also analysed for the physical properties like porosity and catalyst size.

An explicit method to calculate implicit spatial finite differences

The finite-difference solution of the second-order acoustic wave equation is a fundamental algorithm in seismic exploration for seismic forward modeling, imaging, and inversion. Unlike the standard explicit finite difference (EFD) methods that usually suffer from the so-called "saturation effect", the implicit FD methods can obtain much higher accuracy with relatively short operator length. Unfortunately, these implicit methods are not widely used because band matrices need to be solved implicitly, which is not suitable for most high-performance computer architectures. We introduce an explicit method to overcome this limitation by applying explicit causal and anti-causal integrations. We can prove that the explicit solution is equivalent to the traditional implicit LU decomposition method in analytical and numerical ways. In addition, we also compare the accuracy of the new methods with the traditional EFD methods up to 32nd order, and numerical results indicate that the new method is more accurate. In terms of the computational cost, the newly proposed method is standard 8th order EFD plus two causal and anti-causal integrations, which can be applied recursively, and no extra memory is needed. In summary, compared to the standard EFD methods, the new method has a spectral-like accuracy; compared to the traditional LU-decomposition implicit methods, the new method is explicit. It is more suitable for high-performance computing without losing any accuracy.

Numerical Study of Cylindrical Tropical Woods Pyrolysis Using Python Tool

In this paper, the thermal behavior of large pieces of wood pyrolysis has been modeled. Two mathematical models coupling heat transfer equations to chemical kinetics were used to predict the pyrolytic degradation of a 25 mm radius wood sample, assumed to be dry in the first model and wet in the second, when heated to 973.15 K. The reactions involved in the pyrolysis process are assumed to be endothermic. The diffusion of bounded water during the process is taken into account in the second model, where the heat transfer equation has been coupled to that of the diffusion of moisture. This model, although simple, provides more information on the drying and pyrolysis processes during the heating of wood, which is its originality. It can therefore be advantageously used to calculate the temperature distribution in a pyrolysis bed. The equations of the two models, discretized by an explicit finite difference method, were solved numerically by a program written in Python. The validation of both models against experimental work in the literature is satisfactory. The two models allow examination of the temperature profile in the radial direction of wood samples and highlighting of the effect of temperature on some thermal, physical and physicochemical characteristics.

Fast and Accurate Numerical Solution of Allen–Cahn Equation

Simulation speed depends on code structures. Hence, it is crucial how to build a fast algorithm. We solve the Allen–Cahn equation by an explicit finite difference method, so it requires grid calculations implemented by many for-loops in the simulation code. In terms of programming, many for-loops make the simulation speed slow. We propose a model architecture containing a pad and a convolution operation on the Allen–Cahn equation for fast computation while maintaining accuracy. Also, the GPU operation is used to boost up the speed more. In this way, the simulation of other differential equations can be improved. In this paper, various numerical simulations are conducted to confirm that the Allen–Cahn equation follows motion by mean curvature and phase separation in two-dimensional and three-dimensional spaces. Finally, we demonstrate that our algorithm is much faster than an unoptimized code and the CPU operation.