The Shrinking Core Model

The reaction rate assuming first-order reaction is given by $-\frac{d[B]}{dt} = k_s[C_b]$.

The equation for the reaction rate between $r_O$ and $r_C$ is $t = \frac{7.2}{(1- \frac{(1-X_B)^3}{k_s[C_b]})}$.

The mass balance equation for a single porous particle when no solid product is formed is $D_e\frac{d^2[C_b]}{dx^2} - k_sS_vC_b^n = 0$.

<p>The equation for the apparent activation energy in the grain model is $r_A \approx (kD)^{\frac{1}{2}}$.</p> Signup and view all the answers

<p>$rA = - ks f(Cs)$</p> Signup and view all the answers

<p>$- ks f(Cs) = - km(Cb - Cs)$</p> Signup and view all the answers

<p>$\rac{dnB},{dt} = -<br /> ho_B r_c^2 \rac{dr_c},{dt} = \rac{b k_m C_b},{r_o^2}$</p> Signup and view all the answers

<p>$k_m = \rac{2D},{d_p y r_o y}$</p> Signup and view all the answers

<p>The selection of a reaction model is important in the design of reaction systems because it must closely correspond to what actually takes place and its rate expression must closely predict and describe the actual kinetics without too many mathematical complexities.</p> Signup and view all the answers

<p>The reaction equation for the Shrinking Particle Model is $A(fluid) + bB(solid) = cR(fluid) + dD(removable solid)$.</p> Signup and view all the answers

<p>Examples of reactions that can be described using the Shrinking Particle Model include the dissolution of metals/metal compounds, chlorination of metals, and roasting of cinnabar (HgS).</p> Signup and view all the answers

<p>𝐷𝑒 ∇^2 𝐶𝑏 − 𝜈𝐴 = 0</p> Signup and view all the answers

<p>−𝜌𝐵 𝑑𝑟𝑐 𝑑𝑡 = 𝑏𝑘𝑠 𝐶𝑏</p> Signup and view all the answers

<p>𝑡 ∗ ≃ 𝑔𝐹𝑔 (𝑥) + 𝜎^2 𝑝𝐹𝑝 (𝑥)</p> Signup and view all the answers

<ol> <li>Batch Reactor\n2. Continuously Stirred Tank Reactor (CSTR), Continuous Flow Stirred Tank Reactor (CFSTR), Backmix reactor</li> </ol> Signup and view all the answers

<p>The overall process in the shrinking core model involves the formation of a product on the surface of the particle and a reaction taking place at the interface between the product layer and the unreacted core.</p> Signup and view all the answers

<p>The assumptions made in treating the diffusion through product/ash layer controls are: (i) the rate of reaction is given by the rate of diffusion to the reaction surface, (ii) the movement inwards of the reaction surface is slower than the rate of flow of fluid reactant towards the unreacted core, and (iii) the flux relationship is written for a partially reacted particle and applied to all values of rC.</p> Signup and view all the answers

<p>$-r_B = 4\pi r_o^2 k_m (C_B - C_s)$</p> Signup and view all the answers

<p>$-dn_B = -4\pi\rho_B r_c^2 dr_c$</p> Signup and view all the answers

<p>A plug flow reactor is a type of reactor where the reactants are continually consumed as they flow along the length of the reactor. The concentration varies continuously in the axial direction through the reactor, and the reaction rate also varies axially. It is normally operated at steady-state.</p> Signup and view all the answers

<p>A continuous stirred tank reactor is a well-mixed stirred tank operated continuously. It is normally run at steady-state, with constant reactant and product concentrations over time. The reactants entering the reactor are assumed to be instantaneously distributed over the total reactor volume, resulting in no spatial variations in concentration, temperature, or reaction rate.</p> Signup and view all the answers

<p>In a batch reactor, each fluid element remains in the reactor volume for the same reaction time. In a CSTR, the separate fluid elements have a wide range of residence times.</p> Signup and view all the answers

<p>CSTR</p> Signup and view all the answers

<p>Batch reactor</p> Signup and view all the answers

<p>Plug Flow Reactor (PFR)</p> Signup and view all the answers