scholarly journals A decoupled scheme to solve the mass and momentum conservation equations of the improved Darcy–Brinkman–Forchheimer framework in matrix acidization

AIP Advances ◽  
2021 ◽  
Vol 11 (12) ◽  
pp. 125305
Author(s):  
Yuanqing Wu ◽  
Jisheng Kou ◽  
Yu-Shu Wu ◽  
Shuyu Sun ◽  
Yilin Xia
Keyword(s):  
Momentum Conservation ◽  
Conservation Equations ◽  
Matrix Acidization

Invariant Forms of Conservation Equations and Some Examples of Their Exact Solutions

2014 ◽  
Author(s):  
Siavash H. Sohrab
Keyword(s):  
Momentum Conservation ◽  
Enskog Equation ◽  
Cauchy Stress ◽  
Cauchy Stress Tensor ◽  
Scale Invariant ◽  
Spherical Droplet ◽  
Conservation Equations ◽  
Invariant Model ◽  
Cylindrically Symmetric ◽  
Tangential Forces

A scale-invariant model of statistical mechanics is described leading to invariant Boltzmann equation and the corresponding invariant Enskog equation of change. A modified form of Cauchy stress tensor for fluid is presented such that in the limit of vanishing intermolecular spacing all tangential forces vanish in accordance with perceptions of Cauchy and Poisson. The invariant forms of mass, thermal energy, linear momentum, and angular momentum conservation equations derived from invariant Enskog equation of change are described. Also, some exact solution of the conservation equations for the problems of normal shock, flow over a flat plate, and flow within a spherical droplet located at the stagnation point of opposed cylindrically-symmetric gaseous jets are presented.

scholarly journals CFD Simulation of Silica Gel as an Adsorbent on Finned Tube Adsorbent Bed

2018 ◽  
Vol 67 ◽  
pp. 01014 ◽  
Author(s):  
Andre Kurniawan ◽  
Nasruddin ◽  
Asep Rachmat
Keyword(s):  
Silica Gel ◽  
Outer Surface ◽  
Cooling System ◽  
Cooling Water ◽  
Momentum Conservation ◽  
Hot Water ◽  
Adsorption Rate ◽  
Conservation Equations ◽  
Absolute Adsorption ◽  
Adsorption Technology

The adsorption technology is becoming the more expected solution by today’s researchers for fix the energy and environmental issues. The main part of the cooling system adsorption is adsorbent and adsorbate. One of the most widely used adsorbents in research of adsorption technology is silica gel. A new silica gel-water adsorption chiller design was developed that composed of two sorption chambers with compact fin tube heat exchangers as adsorber, condenser, and evaporator. Energy, mass, and momentum conservation equations of the adsorption systems have been used for the CFD two and three dimensional models. The geometry of simulation is simply made within silica gel layer between two fins. The simulation is also implemented using a finite volume method through the CFD software Fluent. User defined functions are given to modify the energy, mass, and momentum conservation equations. The simulation of adsorption process is adjusted at unsteady condition. Adsorption and desorption processes are simulated with room temperature for cooling water inlet at temperature 305.15 °K, hot water inlet at temperature 353.15 °K, mass flow rate cooling water inlet at 0.3 kg/s and pressure 32 KPa. For the whole adsorbent bed area, the result shows that the highest absolute adsorption rate at the outer surface, while the lowest rate is at the center. After adsorption was finished, the condition is reversed. The highest absolute adsorption rate is achieved at center, while the lowest rate is achieved at the outer surface.

Invariant Forms of Conservation Equations and Some Examples of Their Exact Solutions

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Siavash H. Sohrab
Keyword(s):  
Exact Solutions ◽  
Momentum Conservation ◽  
Immiscible Fluids ◽  
Enskog Equation ◽  
Cauchy Stress ◽  
Liquid Droplets ◽  
Scale Invariant ◽  
Conservation Equations ◽  
Cylindrically Symmetric ◽  
Laminar And Turbulent Flow

A scale-invariant model of statistical mechanics is described leading to invariant Boltzmann equation and the corresponding invariant Enskog equation of change. A modified form of Cauchy stress tensor for fluid is presented such that in the limit of vanishing intermolecular spacing, all tangential forces vanish in accordance with perceptions of Cauchy and Poisson. The invariant forms of mass, thermal energy, linear momentum, and angular momentum conservation equations derived from invariant Enskog equation of change are described. Also, some exact solutions of the conservation equations for the problems of normal shock, laminar, and turbulent flow over a flat plate, and flow within a single or multiple concentric spherical liquid droplets made of immiscible fluids located at the stagnation point of opposed cylindrically symmetric gaseous finite jets are presented.

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.

Eulerian Two-Fluid Model for Aerosol Removal in Filtered Containment Venting Scrubbers

2018 ◽  
Author(s):  
Ji-Su Kim ◽  
Jong Woon Park ◽  
Minkyung Kim
Keyword(s):  
Water Droplet ◽  
Removal Rate ◽  
Fluid Model ◽  
Computer Code ◽  
Momentum Conservation ◽  
Particle Removal ◽  
Conservation Equations ◽  
One Dimensional ◽  
Flow Variables ◽  
Two Fluid

Eulerian steady one-dimensional two-fluid mass and momentum conservation equations for gas and water droplet coupled with the particle removal rate are formulated. The major flow variables are phasic velocities and pressure and they are obtained by integrating the four conservation equations and one particle removal rate along the horizontal throats of the venturi scrubbers by using the forth-order Runge-Kutta method. Popular correlations are used for the impaction parameter, the gas-to-water droplet drag coefficient and the droplet size. All the equations are integrated into one computer code named REMAERO based on the MATLAB. It is found that most particles are removed at the throat entrance as already known from the previous experiments and this is due to the particle removal rate proportional to the particle concentration. Particle removal efficiencies from the present method shows better agreement with existing experimental data than previous one-dimensional models.

scholarly journals A New Model for Predicting Dynamic Surge Pressure in Gas and Drilling Mud Two-Phase Flow during Tripping Operations

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
Xiangwei Kong ◽  
Yuanhua Lin ◽  
Yijie Qiu ◽  
Hongjun Zhu ◽  
Long Dong ◽  
...  
Keyword(s):  
Wave Velocity ◽  
Drill Pipe ◽  
Mass Conservation ◽  
Momentum Conservation ◽  
Operating Speed ◽  
Drilling Mud ◽  
Two Phase ◽  
Influx Rate ◽  
Conservation Equations ◽  
Calculation Results

Investigation of surge pressure is of great significance to the circulation loss problem caused by unsteady operations in management pressure drilling (MPD) operations. With full consideration of the important factors such as wave velocity, gas influx rate, pressure, temperature, and well depth, a new surge pressure model has been proposed based on the mass conservation equations and the momentum conservation equations during MPD operations. The finite-difference method, the Newton-Raphson iterative method, and the fourth-order explicit Runge-Kutta method (R-K4) are adopted to solve the model. Calculation results indicate that the surge pressure has different values with respect to different drill pipe tripping speeds and well parameters. In general, the surge pressure tends to increase with the increases of drill pipe operating speed and with the decrease of gas influx rate and wellbore diameter. When the gas influx occurs, the surge pressure is weakened obviously. The surge pressure can cause a significant lag time if the gas influx occurs at bottomhole, and it is mainly affected by pressure wave velocity. The maximum surge pressure may occur before drill pipe reaches bottomhole, and the surge pressure is mainly affected by drill pipe operating speed and gas influx rate.

Establishment and Solution of the RNC Flow Network Model

2014 ◽  
Vol 548-549 ◽  
pp. 1783-1789
Author(s):  
Li Ying Sun ◽  
Lu Jie Zhen ◽  
Yi Tong Li
Keyword(s):  
Network Model ◽  
Mass Conservation ◽  
Momentum Conservation ◽  
Conservation Equation ◽  
Two Phase ◽  
Conservation Equations ◽  
Flow Network ◽  
Cycle System ◽  
Variable Step ◽  
The Mathematical Model

The mathematical model based on graph theory and the refrigerant natural cycle system of gas-liquid two-phase flow network is established. Incidence matrix was used to describe the relationships between the various components. The node conservation equations, branch equations, momentum conservation equation in return circuit and mass conservation equations of system are established. The model was solved by using variable step gird iterative method. Then refrigerant state of each node and refrigerant flow of each branch in network model are obtained. Establishment and solution of the RNC network model provides an effective way for the further performance analysis of system.

scholarly journals Thermodynamically consistent Darcy–Brinkman–Forchheimer framework in matrix acidization

2021 ◽  
Vol 76 ◽  
pp. 8
Author(s):  
Yuanqing Wu ◽  
Jisheng Kou ◽  
Shuyu Sun ◽  
Yu-Shu Wu
Keyword(s):  
Numerical Experiments ◽  
Good Description ◽  
Energy Balance Equation ◽  
Momentum Conservation ◽  
Conservation Equation ◽  
Scale Model ◽  
Recovery Stage ◽  
Tertiary Recovery ◽  
Matrix Acidization ◽  
Momentum Conservation Equation

Matrix acidization is an important technique used to enhance oil production at the tertiary recovery stage, but its numerical simulation has never been verified. From one of the earliest models, i.e., the two-scale model (Darcy framework), the Darcy–Brinkman–Forchheimer (DBF) framework is developed by adding the Brinkman term and Forchheimer term to the momentum conservation equation. However, in the momentum conservation equation of the DBF framework, porosity is placed outside of the time derivation term, which prevents a good description of the change in porosity. Thus, this work changes the expression so that the modified momentum conservation equation can satisfy Newton’s second law. This modified framework is called the improved DBF framework. Furthermore, based on the improved DBF framework, a thermal DBF framework is given by introducing an energy balance equation to the improved DBF framework. Both of these frameworks are verified by former works through numerical experiments and chemical experiments in labs. Parallelization to the complicated framework codes is also realized, and good scalability can be achieved.

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