Solving the output concentration of computer in multiple mixed flow reactors in series — Second-order reversible reaction

2011 ◽  
Author(s):  
Wenjie Zhao ◽  
Huixuan Zhang
Keyword(s):  
Second Order ◽  
Reversible Reaction ◽  
Mixed Flow ◽  
Flow Reactors ◽  
In Series ◽  
Output Concentration

scholarly journals A SIMPLE ROBUST CONTROL APPROACH FOR CR(VI) REGULATION OF WASTEWATER AT ELECTROCHEMICAL MIXED-FLOW REACTORS IN SERIES

2009 ◽  
Vol 196 (10) ◽  
pp. 1278-1290 ◽  
Author(s):  
Hector Puebla ◽  
Miriam G. Rodríguez ◽  
Sergio A. Martínez-Delgadillo ◽  
Víctor X. Mendoza ◽  
Sergio Gómez-Callejas
Keyword(s):  
Robust Control ◽  
Mixed Flow ◽  
Flow Reactors ◽  
Control Approach ◽  
In Series

Reactor Design for Complex Reactions

2001 ◽  
Author(s):  
L. K. Doraiswamy
Keyword(s):  
Batch Reactor ◽  
Plug Flow ◽  
Reaction Network ◽  
Reactor Design ◽  
Batch Reactors ◽  
Complex Reaction ◽  
Mixed Flow ◽  
Flow Reactors ◽  
Design Procedures ◽  
Reactor Types

Procedures were formulated in Chapter 5 for treating complex reactions. We now turn to the design of reactors for such reactions. Continuing with the ethylation reaction, we consider the following reactor types for which design procedures were formulated earlier in Chapter 4 for simple reactions: batch reactors, continuous stirred reactors (or mixed-flow reactors), and plug-flow reactors. However, we use the following less formal nomenclature: A = aniline, B = ethanol, C = monoethyaniline, D = water, E = diethylaniline, F = diethyl ether, and G = ethylene. The four independent reactions then become Using this set of equations as the basis, we now formulate design equations for various reactor types. Detailed expositions of the theory are presented in a number of books, in particular Aris (1965, 1969) and Nauman (1987). Consider a reaction network consisting of N components and M reactions. A set of N ordinary differential equations, one for each component, would be necessary to mathematically describe this system. They may be concisely expressed in the form of Equation 5.5 (Chapter 5), or . . . d(cV)/dt = vrV (11.1) . . . The use of this equation in developing batch reactor equations for a typical complex reaction is illustrated in Example 11.1.

The effect of aqueous sulphate on basaltic glass dissolution rates

2008 ◽  
Vol 72 (1) ◽  
pp. 39-41 ◽  
Author(s):  
T. K. Flaathen ◽  
E. H. Oelkers ◽  
S. Gislason
Keyword(s):  
Steady State ◽  
Rate Equation ◽  
Rate Increase ◽  
Basaltic Glass ◽  
Mixed Flow ◽  
Dissolution Rates ◽  
Flow Reactors ◽  
Glass Dissolution ◽  
Sulphate Concentration

AbstractSteady-state dissolution rates of basaltic glass were measured in mixed-flow reactors at 50ºC at pH 3 and 4 as a function of aqueous sulphate concentration. Dissolution rates in the presence of 0.1 moles/kg SO42- were found to be ~3 times greater than those in corresponding SO42- free solutions. This rate increase is found to be approximately consistent with that calculated using a rate equation previously proposed by Gislason and Oelkers (2003). These results suggest that the addition of sulphate to injected CO2 may facilitate CO2 sequestration in basalts by accelerating basaltic glass dissolution rates thus more rapidly releasing aqueous Ca and Mg to solution.

Macro- to nanoscale study of the effect of aqueous sulphate on calcite growth

2008 ◽  
Vol 72 (1) ◽  
pp. 141-144 ◽  
Author(s):  
A. I. Vavouraki ◽  
C. V. Putnis ◽  
A. Putnis ◽  
E. H. Oelkers ◽  
P. G. Koutsoukos
Keyword(s):  
Atomic Force Microscopy ◽  
Growth Rates ◽  
Kinetics And Mechanism ◽  
Two Dimensional ◽  
Mixed Flow ◽  
Flow Reactors ◽  
Force Microscopy ◽  
Atomic Force

AbstractCalcite growth rates were measured in the presence of sulphate using mixed-flow reactors and in situ Atomic Force Microscopy. Preliminary observations reveal that the kinetics and mechanism of the calcite growth was altered by the presence of sulphate. Calcite growth rates in the presence of sulphate (≥ mM) were decreased and two-dimensional nuclei tend to grow on top of existing nuclei, rather than spreading. The height of new nuclei was ~4 Å, 1 Å greater than that of pure calcite growth. This difference reflects the incorporation of tetrahedral SO2-4 anions into the calcite lattice.

A Novel PID Controller with Second Order Lead/Lag Filter for Stable and Unstable First Order Process with Time Delay

2018 ◽  
Vol 13 (1) ◽  
Author(s):  
Praveen Kumar Medarametla ◽  
Manimozhi Muthukumarasamy
Keyword(s):  
Time Delay ◽  
Pid Controller ◽  
Chemical Reactor ◽  
Initial Guess ◽  
Second Order ◽  
Maximum Sensitivity ◽  
Tuning Parameter ◽  
First Order ◽  
In Series ◽  
Made In

AbstractA novel Proportional-Integral-Derivative (PID) controller is proposed for stable and unstable first order processes with time delay. The controller is cascaded in series with a second order filter. Polynomial approach is employed to derive the controller and filter parameters. Simple tuning rules are derived by analysing the maximum sensitivity of the control loop. Formulae are provided for initial guess of tuning parameter. The range of tuning parameter around the initial guess and the corresponding range of maximum sensitivity is specified based on time delay to time constant ratio. Promising results are obtained with the proposed method is compared against recently proposed methods in the literature. The comparison is made in terms of various performance indices for servo and regulatory responses separately. The proposed method is implemented for an isothermal chemical reactor at an unstable equilibrium point.

scholarly journals On the Linear Differential Equation of the Second Order

1915 ◽  
Vol 34 ◽  
pp. 45-60 ◽  
Author(s):  
S. Brodetsky
Keyword(s):  
Differential Equation ◽  
Linear Differential Equation ◽  
General Equation ◽  
Second Order ◽  
General Properties ◽  
In Series ◽  
Linear Differential ◽  
Image Position

The linear differential equation of the second orderis not in general integrable by any method at present available. At the same time, several equations of this type have been integrated, either in terms of finite functions or by means of expansions in series. Some properties of the integrals of the general equation have also been obtained. It is the object of this paper to develop some general properties of these integrals, which throw some light on the nature of the solutions, even if not obtainable in explicit terms.

Small-scale statistics in high-resolution direct numerical simulation of turbulence: Reynolds number dependence of one-point velocity gradient statistics

2007 ◽  
Vol 592 ◽  
pp. 335-366 ◽  
Author(s):  
T. ISHIHARA ◽  
Y. KANEDA ◽  
M. YOKOKAWA ◽  
K. ITAKURA ◽  
A. UNO
Keyword(s):  
Reynolds Number ◽  
High Resolution ◽  
Longitudinal Velocity ◽  
Second Order ◽  
Distribution Functions ◽  
Small Scale ◽  
Kolmogorov Length Scale ◽  
Velocity Gradients ◽  
In Series ◽  
Derivatives Of

One-point statistics of velocity gradients and Eulerian and Lagrangian accelerations are studied by analysing the data from high-resolution direct numerical simulations (DNS) of turbulence in a periodic box, with up to 40963 grid points. The DNS consist of two series of runs; one is with kmaxη ~ 1 (Series 1) and the other is with kmaxη ~ 2 (Series 2), where kmax is the maximum wavenumber and η the Kolmogorov length scale. The maximum Taylor-microscale Reynolds number Rλ in Series 1 is about 1130, and it is about 675 in Series 2. Particular attention is paid to the possible Reynolds number (Re) dependence of the statistics. The visualization of the intense vorticity regions shows that the turbulence field at high Re consists of clusters of small intense vorticity regions, and their structure is to be distinguished from those of small eddies. The possible dependence on Re of the probability distribution functions of velocity gradients is analysed through the dependence on Rλ of the skewness and flatness factors (S and F). The DNS data suggest that the Rλ dependence of S and F of the longitudinal velocity gradients fit well with a simple power law: S ~ −0.32Rλ0.11 and F ~ 1.14Rλ0.34, in fairly good agreement with previous experimental data. They also suggest that all the fourth-order moments of velocity gradients scale with Rλ similarly to each other at Rλ > 100, in contrast to Rλ < 100. Regarding the statistics of time derivatives, the second-order time derivatives of turbulent velocities are more intermittent than the first-order ones for both the Eulerian and Lagrangian velocities, and the Lagrangian time derivatives of turbulent velocities are more intermittent than the Eulerian time derivatives, as would be expected. The flatness factor of the Lagrangian acceleration is as large as 90 at Rλ ≈ 430. The flatness factors of the Eulerian and Lagrangian accelerations increase with Rλ approximately proportional to RλαE and RλαL, respectively, where αE ≈ 0.5 and αL ≈ 1.0, while those of the second-order time derivatives of the Eulerian and Lagrangian velocities increases approximately proportional to RλβE and RλβL, respectively, where βE ≈ 1.5 and βL ≈ 3.0.

Epidote dissolution and its role within carbon storage

2020 ◽  
Author(s):  
Chiara Marieni ◽  
Giuseppe Saldi ◽  
Pascale Benezeth ◽  
Eric Oelkers
Keyword(s):  
Carbon Storage ◽  
Flow Reactor ◽  
Carbon Mineralization ◽  
Thermal Conditions ◽  
High Reactivity ◽  
Batch Reactors ◽  
Mixed Flow ◽  
Flow Reactors ◽  
Fluid Fraction ◽  
Ph Range

&lt;p&gt;In the past 20 years, basaltic aquifers have been studied as a key geologic carbon storage host due to their high reactivity and widespread distribution. However, many basaltic reservoirs contain substantial alteration minerals and their potential as cation sources for carbon mineralization processes still need to be assessed. A common alteration phase in high temperatures (&amp;#8805; 200 &amp;#176;C) basalts is epidote. To help determine the possible contribution of this mineral to CO2 sequestration through the release of its constituting cations, the dissolution rates of epidote from the Green Monster Mine (Alaska) were experimentally measured. Far-from equilibrium experiments were conducted over the pH range 2-11 using both batch reactors at 25 &amp;#176;C, and mixed-flow reactors at 100 and 200 &amp;#176;C. Furthermore, mixed-flow reactor experiments at pH ~9 on epidote in presence of CO2 were carried out at 200 &amp;#176;C to study its carbonation potential and to quantify the yields of this reaction compared to basaltic glass. The determination of the extent of this process was monitored by inorganic carbon analyses on both solid and fluid fraction using non-dispersive infra-red (NDIR) CO2 gas analyses. Preliminary results suggest that epidote and potentially other alteration Ca-silicate phases can provide Ca2+ as efficiently as fresh basalts at 25 and 100 &amp;#176;C to promote the precipitation of calcium carbonate. Further experimental and modelling work is ongoing to confirm these findings at different thermal conditions and as a function of injected fluid chemistry.&lt;/p&gt;

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