A Simplified Numerical Model to Predict the Velocity Field in a Catalytic Cracking Unity in Oil Refineries

2001 ◽  
Author(s):  
J. A. Souza ◽  
J. V. C. Vargas ◽  
O. F. von Meien ◽  
D. I. Vlassov
Keyword(s):  
Finite Element ◽  
Velocity Field ◽  
Catalytic Cracking ◽  
Momentum Conservation ◽  
Light Olefins ◽  
Future Application ◽  
Conservation Equations ◽  
Oil Refineries ◽  
Backward Euler ◽  
Finite Differences Method

Abstract This paper introduces a general computational model for determining the velocity field in either reacting or non-reacting duct flows. The model is then applied to a catalytic cracking unit (FCC) of an oil refinery, to determine the velocity field inside the riser, where reactions take place to convert heavy petroleum fractions in lighter products, like middle distillates and light olefins, with high rates of conversion and productivity. The correct approach to simulate this process is to avoid the plug flow assumption and to solve the full fluid flow problem, based on the mass and momentum conservation equations in a complete formulation, which are shown in the literature to be computationally very expensive and time consuming, mainly in a three-dimensional (3-D) simulation. Since, the main objective of the simulation is the accurate determination of the concentration of the noble products, a very accurate velocity field is not mandatory. Therefore, bidimensional flow is assumed, and a modified set of unsteady mass and momentum conservation equations is proposed and the resulting 2-D differential equations are discretized in space using an upwind cell centered finite differences method, and the equations integrated in time with an implicit backward Euler scheme. The coarsest possible mesh is determined such that the solution relative error is within 5 % when compared to a steady state accurate finite element solution, which was obtained with a 2-D isoparametric, four-noded, linear element that was implemented to solve the complete Navier-Stokes equations for the finite element analysis program, FEAP [1]. The objective of this work is to propose an alternative technique that gives a simplified treatment to the velocity field, to make possible the numerical calculation of the products concentrations in the riser and future application in optimization and real time control. Each cell, in this specific situation, can be understood as a perfect mixing reactor.

scholarly journals A Finite Element Splitting Method for a Convection-Diffusion Problem

2020 ◽  
Vol 20 (4) ◽  
pp. 717-725 ◽  
Author(s):  
Vidar Thomée
Keyword(s):  
Finite Element ◽  
Splitting Method ◽  
Diffusion Problem ◽  
Euler Method ◽  
Euler Approximation ◽  
Convection Diffusion ◽  
Time Stepping ◽  
Backward Euler ◽  
Spatially Periodic ◽  
Forward Euler

AbstractFor a spatially periodic convection-diffusion problem, we analyze a time stepping method based on Lie splitting of a spatially semidiscrete finite element solution on time steps of length k, using the backward Euler method for the diffusion part and a stabilized explicit forward Euler approximation on {m\geq 1} intervals of length {k/m} for the convection part. This complements earlier work on time splitting of the problem in a finite difference context.

scholarly journals Solvent-Free Synthesis of SAPO-34 Zeolite with Tunable SiO2/Al2O3 Ratios for Efficient Catalytic Cracking of 1-Butene

Catalysts ◽  
2021 ◽  
Vol 11 (7) ◽  
pp. 835
Author(s):  
Xia Xiao ◽  
Zhongliang Xu ◽  
Peng Wang ◽  
Xinfei Liu ◽  
Xiaoqiang Fan ◽  
...  
Keyword(s):  
Catalytic Cracking ◽  
Acid Sites ◽  
Solvent Free ◽  
Zeolite Catalysts ◽  
Light Olefins ◽  
Molar Ratio ◽  
Coordination Environment ◽  
Starting Mixture ◽  
Synthesis Methodology ◽  
Solvent Free Synthesis

Solvent-free synthesis methodology is a promising technique for the green and sustainable preparation of zeolites materials. In this work, a solvent-free route was developed to synthesize SAPO-34 zeolite. The characterization results indicated that the crystal size, texture properties, acidity and Si coordination environment of the resulting SAPO-34 were tuned by adjusting the SiO2/Al2O3 molar ratio in the starting mixture. Moreover, the acidity of SAPO-34 zeolite was found to depend on the Si coordination environment, which was consistent with that of SAPO-34 zeolite synthesized by the hydrothermal method. At an SiO2/Al2O3 ratio of 0.6, the SP-0.6 sample exhibited the highest conversion of 1-butene (82.8%) and a satisfactory yield of light olefins (51.6%) in the catalytic cracking of 1-butene, which was attributed to the synergistic effect of the large SBET (425 m2/g) and the abundant acid sites (1.82 mmol/g). This work provides a new opportunity for the design of efficient zeolite catalysts for industrially important reactions.

A Finite Element Procedure of a Cyclic Thermoviscoplasticity Model for Solder and Copper Interconnects

1998 ◽  
Vol 120 (1) ◽  
pp. 24-34 ◽  
Author(s):  
C. Fu ◽  
D. L. McDowell ◽  
I. C. Ume
Keyword(s):  
Finite Element ◽  
Electronic Packaging ◽  
Copper Interconnects ◽  
Implicit Time ◽  
Integration Scheme ◽  
Single Element ◽  
Ofhc Copper ◽  
Computation Efficiency ◽  
Backward Euler ◽  
Finite Element Procedure

A finite element procedure using a semi-implicit time-integration scheme has been developed for a cyclic thermoviscoplastic constitutive model for Pb-Sn solder and OFHC copper, two common metallic constituents in electronic packaging applications. The scheme has been implemented in the commercial finite element (FE) code ABAQUS (1995) via the user-defined material subroutine, UMAT. Several single-element simulations are conducted to compare with previous test results, which include monotonic tensile tests, creep tests, and a two-step ratchetting test for 62Sn36Pb2Ag solder; a nonproportional axial-torsional test and a thermomechanical fatigue (TMF) test for OFHC copper. At the constitutive level, we also provide an adaptive time stepping algorithm, which can be used to improve the overall computation efficiency and accuracy especially in large-scale FE analyses. We also compare the computational efforts of fully backward Euler and the proposed methods. The implementation of the FE procedure provides a guideline to apply user-defined material constitutive relations in FE analyses and to perform more sophisticated thermomechanical simulations. Such work can facilitate enhanced understanding thermomechanical reliability issue of solder and copper interconnects in electronic packaging applications.

Production of Low‐carbon Light Olefins from Catalytic Cracking of Crude Bio‐oil

2013 ◽  
Vol 26 (2) ◽  
pp. 237-244 ◽  
Author(s):  
Yan‐ni Yuan ◽  
Tie‐jun Wang ◽  
Quan‐xin Li
Keyword(s):  
Catalytic Cracking ◽  
Light Olefins ◽  
Low Carbon ◽  
Bio Oil

Tracing Streamlines on Unstructured Grids From Finite Volume Discretizations

SPE Journal ◽  
2008 ◽  
Vol 13 (04) ◽  
pp. 423-431 ◽  
Author(s):  
Sebastien F. Matringe ◽  
Ruben Juanes ◽  
Hamdi A. Tchelepi
Keyword(s):  
Finite Element ◽  
Velocity Field ◽  
Finite Difference ◽  
Finite Volume ◽  
Unstructured Grids ◽  
Control Volume ◽  
Next Generation ◽  
Flux Approximation ◽  
Streamline Tracing ◽  
Tracing Method

Summary The accuracy of streamline reservoir simulations depends strongly on the quality of the velocity field and the accuracy of the streamline tracing method. For problems described on complex grids (e.g., corner-point geometry or fully unstructured grids) with full-tensor permeabilities, advanced discretization methods, such as the family of multipoint flux approximation (MPFA) schemes, are necessary to obtain an accurate representation of the fluxes across control volume faces. These fluxes are then interpolated to define the velocity field within each control volume, which is then used to trace the streamlines. Existing methods for the interpolation of the velocity field and integration of the streamlines do not preserve the accuracy of the fluxes computed by MPFA discretizations. Here we propose a method for the reconstruction of the velocity field with high-order accuracy from the fluxes provided by MPFA discretization schemes. This reconstruction relies on a correspondence between the MPFA fluxes and the degrees of freedom of a mixed finite-element method (MFEM) based on the first-order Brezzi-Douglas-Marini space. This link between the finite-volume and finite-element methods allows the use of flux reconstruction and streamline tracing techniques developed previously by the authors for mixed finite elements. After a detailed description of our streamline tracing method, we study its accuracy and efficiency using challenging test cases. Introduction The next-generation reservoir simulators will be unstructured. Several research groups throughout the industry are now developing a new breed of reservoir simulators to replace the current industry standards. One of the main advances offered by these next generation simulators is their ability to support unstructured or, at least, strongly distorted grids populated with full-tensor permeabilities. The constant evolution of reservoir modeling techniques provides an increasingly realistic description of the geological features of petroleum reservoirs. To discretize the complex geometries of geocellular models, unstructured grids seem to be a natural choice. Their inherent flexibility permits the precise description of faults, flow barriers, trapping structures, etc. Obtaining a similar accuracy with more traditional structured grids, if at all possible, would require an overwhelming number of gridblocks. However, the added flexibility of unstructured grids comes with a cost. To accurately resolve the full-tensor permeabilities or the grid distortion, a two-point flux approximation (TPFA) approach, such as that of classical finite difference (FD) methods is not sufficient. The size of the discretization stencil needs to be increased to include more pressure points in the computation of the fluxes through control volume edges. To this end, multipoint flux approximation (MPFA) methods have been developed and applied quite successfully (Aavatsmark et al. 1996; Verma and Aziz 1997; Edwards and Rogers 1998; Aavatsmark et al. 1998b; Aavatsmark et al. 1998c; Aavatsmark et al. 1998a; Edwards 2002; Lee et al. 2002a; Lee et al. 2002b). In this paper, we interpret finite volume discretizations as MFEM for which streamline tracing methods have already been developed (Matringe et al. 2006; Matringe et al. 2007b; Juanes and Matringe In Press). This approach provides a natural way of reconstructing velocity fields from TPFA or MPFA fluxes. For finite difference or TPFA discretizations, the proposed interpretation provides mathematical justification for Pollock's method (Pollock 1988) and some of its extensions to distorted grids (Cordes and Kinzelbach 1992; Prévost et al. 2002; Hægland et al. 2007; Jimenez et al. 2007). For MPFA, our approach provides a high-order streamline tracing algorithm that takes full advantage of the flux information from the MPFA discretization.

Catalytic Cracking of Lower-Valued Hydrocarbons for Producing Light Olefins

2010 ◽  
Vol 14 (2) ◽  
pp. 75-84 ◽  
Author(s):  
Yong-Ki Park ◽  
Chul Wee Lee ◽  
Na Young Kang ◽  
Won Choon Choi ◽  
Sun Choi ◽  
...  
Keyword(s):  
Catalytic Cracking ◽  
Light Olefins

Solutions for Non-Newtonian Flow Into Elliptical Openings

1991 ◽  
Vol 58 (3) ◽  
pp. 820-824 ◽  
Author(s):  
A. Bogobowicz ◽  
L. Rothenburg ◽  
M. B. Dusseault
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Steady State ◽  
Hydrostatic Pressure ◽  
Velocity Field ◽  
Velocity Fields ◽  
Newtonian Flow ◽  
Element Analysis ◽  
Elliptical Opening ◽  
Elliptical Coordinates

A semi-analytical solution for plane velocity fields describing steady-state incompressible flow of nonlinearly viscous fluid into an elliptical opening is presented. The flow is driven by hydrostatic pressure applied at infinity. The solution is obtained by minimizing the rate of energy dissipation on a sufficiently flexible incompressible velocity field in elliptical coordinates. The medium is described by a power creep law and solutions are obtained for a range of exponents and ellipse eccentricites. The obtained solutions compare favorably with results of finite element analysis.

Catalytic cracking of C5 raffinate to light olefins over lanthanum-containing phosphorous-modified porous ZSM-5: Effect of lanthanum content

2013 ◽  
Vol 109 ◽  
pp. 189-195 ◽  
Author(s):  
Joongwon Lee ◽  
Ung Gi Hong ◽  
Sunhwan Hwang ◽  
Min Hye Youn ◽  
In Kyu Song
Keyword(s):  
Catalytic Cracking ◽  
Light Olefins ◽  
Lanthanum Content
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