# Stacking Effect

In this section we  study the effect of stacking on the outlet concentration.

By evaluating the integral :

$$Sh=-\frac{1}{2{\pi{r}{\Delta{c}}}} \int{( \frac{\partial{c}}{\partial{x}}n_x+\frac{\partial{c}}{\partial{y}}n_y+\frac{\partial{c}}{\partial{z}}n_z} )dS$$

over the surface of the particle we calcuate Sherwood number and we use it to calculate the mass transfere coefficient from the fact that $Sh=\frac{KL}{D}$ .

Studied geometries:

Due to memory constrains our study was limited by some specific geometries through which Comsol Multiphsics 3.5a can solve. We start with a very simple case through which we show the variation of the Sherwood number .

(A)$\varepsilon=0.7$            (B)$\varepsilon=0.6$               (C)$\varepsilon=0.55$

In our study spheres where inserted inside the box where we consider that these spheres act as a catalyst in the packed bed reactor. We studied three cases where void fration has been taken as 0.7 in case(A), 0.6 in case (B), 0.55 in case(C) respectively. Free Mesh has been taken in all the three different geometry.

Concentration profile has been analyzed for all the different cases.

Configuration(A)-Concentration profile

Configuration(B)-Concentration profile

Configuration(C)-Concentration profile

In the above figure we find that for the configuration (A) which has highest void fraction, concentration at the outlet of the box is maximum, which means that less catalysts are present inside the box and less reactants are consumed. For the configuration (C) which has the least void fraction, which means more catalysts are present inside the box, more reactants are consumed and less  outlet concentration is observed. For the Configuration (B) which has the value of  void fraction in between Case A and Case B, Value of the Concentration found at the outlet for configuration (B) is in between the Value of concentration for configuration (A) and configuration (B).

Outlet concentration as function of k for different geometries

Above figure represents the variation of the outlet concentration with the different reactivity constant for system having different void fraction. One having higher void fraction has more outet concentration and one with lower void fraction has lesser outer concentration.

CONCLUSION:

The objective of our project was to study the effect of stacking on the hydrodynamic and the mass transfer inside a fixed bed reactor.

Ranz-marshall correlation has been validated for a single sphere inside the box for 2D as well as 3D. Outlet concentration profile has been studied in the case of stacking with different void fraction and the effect of stacking on the concentration has been studied.

Hydrodynamic and mass transfer with cylinder inside the box has been studied by changing the orientation of cylinder. Correlation of Sherwood with Reynolds and Schmidt for a single cylinder placed inside finite box has been obtained.

When the diffusivity of fluid is decreased peclet number increases and the boundary layer thickness $\delta$ decreases. For $D_e$  less than $10^{-6}$, we were not able to refine the mesh because when the number of cells increase the memory required by the simulation increases beyond the available limit and Comsol was giving "out of memory error" so we were not able to carry out our study for wide range of parameters as well as for complex geometry.The advance version of the comsol or may be some different code would be better for studying complex geometry where we can use wide range of physical parameters.