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Solid Suspension and Solid-Liquid Mass Transfer in Stirred Reactors

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Handbook of Multiphase Flow Science and Technology

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Abstract

Stirred tank reactors are among the most commonly used reactors for solid-liquid operations in the chemical industry. A generalized design procedure of the solid-liquid stirred tank is presented here for the benefit of a practicing engineer. The different aspects of solid-liquid reactor design like mixing, solid suspension, heat transfer, and mass transfer are discussed. This chapter covers details of impeller design and impeller selection procedure. A case study of uranium oxide dissolution in nitric acid is chosen to demonstrate the design procedure. Finally, the optimized design of the hardware for the same case study with general recommendations is presented.

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Abbreviations

a :

Stoichiometric coefficient of reactant A (−)

a p :

Interfacial area in (m2/m3)

A :

Liquid reactant(−)

A i :

Tank side heat transfer area (m2)

A o :

Jacket side or coil side heat transfer area (m2)

B :

Solid reactant(−)

C :

The mass of solids per unit volume of slurry \( \left(\frac{\mathrm{kg}}{{\mathrm{m}}^3}\right) \)

c :

Cylindrical tank bottom clearance (m)

C A :

Intermediate concentration of \( A\left(\frac{\mathrm{kmol}}{{\mathrm{m}}^3}\right) \)

C AL :

Concentration of A in the liquid phase \( \left(\frac{\mathrm{kmol}}{{\mathrm{m}}^3}\right) \)

C AS :

Concentration of A on the solid surface \( \left(\frac{\mathrm{kmol}}{{\mathrm{m}}^3}\right) \)

C AC :

Concentration of A in the unreacted core \( \left(\frac{\mathrm{kmol}}{{\mathrm{m}}^3}\right) \)

C B :

Concentration of \( B\left(\frac{\mathrm{kmol}}{{\mathrm{m}}^3}\right) \)

C B0 :

Initial concentration of \( B\left(\frac{\mathrm{kmol}}{{\mathrm{m}}^3}\right) \)

CBT :

Curved blade turbine(−)

C D :

Drag coefficient(−)

Cp j :

Specific heat of utility fluid \( \left(\frac{J}{\mathrm{kg}K}\right) \)

Cp T :

Specific heat of the mixture \( \left(\frac{J}{\mathrm{kg}K}\right) \)

d p :

Particle diameter (m)

D :

Impeller diameter (m)

DT :

Disk turbine(−)

D A :

Diffusivity of the liquid phase reactant \( A\left(\frac{{\mathrm{m}}^2}{\mathrm{s}}\right) \)

D e :

Effective diffusivity of liquid reactant in the ash layer \( \left(\frac{{\mathrm{m}}^2}{\mathrm{s}}\right) \)

FBT :

Flat blade turbine(−)

F j :

Volumetric flow rate of the utility fluid \( \left(\frac{{\mathrm{m}}^3}{\mathrm{s}}\right) \)

g :

Gravitational acceleration \( \left(\frac{\mathrm{m}}{{\mathrm{s}}^2}\right) \)

H :

Height of the liquid in the reactor (m)

HE – 3 :

3 bladed – high efficiency impeller(−)

H b :

Height of bed of the solids (m)

H C :

Cloud height (m)

H S :

Height of the solids’ suspension (m)

HTC :

Heat transfer coefficient \( \left(\frac{W}{{\mathrm{m}}^2K}\right) \)

h i :

Process side or tank side heat transfer coefficient \( \left(\frac{W}{{\mathrm{m}}^2K}\right) \)

h ji :

Tank side heat transfer coefficient when the jacket is used \( \left(\frac{W}{{\mathrm{m}}^2K}\right) \)

h o :

Utility side heat transfer coefficient \( \left(\frac{W}{{\mathrm{m}}^2K}\right) \)

h sj :

Utility side heat transfer coefficient for the simple jacket \( \left(\frac{W}{{\mathrm{m}}^2K}\right) \)

h bj :

Utility side heat transfer coefficient for the baffled jacket \( \left(\frac{W}{{\mathrm{m}}^2K}\right) \)

h lc :

Utility side heat transfer coefficient for the limpet coil \( \left(\frac{W}{{\mathrm{m}}^2K}\right) \)

h c :

Utility side heat transfer coefficient for the internal coil \( \left(\frac{W}{{\mathrm{m}}^2K}\right) \)

h ci :

Tank side heat transfer coefficient when the internal coil is used \( \left(\frac{W}{{\mathrm{m}}^2K}\right) \)

ΔHR:

Heat of reaction \( \left(\frac{J}{\mathrm{kmol}}\right) \)

K :

Thermal conductivity of the reaction mixture \( \left(\frac{W}{\mathrm{m}K}\right) \)

K j :

Thermal conductivity of the utility fluid \( \left(\frac{W}{\mathrm{m}K}\right) \)

k SL :

Mass transfer coefficient between solid and liquid \( \left(\frac{\mathrm{m}}{\mathrm{s}}\right) \)

k′ :

First order rate constant for the surface reaction \( \left(\frac{\mathrm{m}}{\mathrm{s}}\right) \)

L :

Half thickness of the flat pate (m)

(LMTD)j:

Log mean temperature difference (K)

M :

Mass of the slurry (kg)

MF :

Mass of solid per total mass of slurry(−)

MT :

Mixing time (s)

MTC :

Mass transfer coefficient between solid and liquid \( \left(\frac{\mathrm{m}}{\mathrm{s}}\right) \)

m j :

Mass flow rate of the utility fluid \( \left(\frac{\mathrm{kg}}{\mathrm{s}}\right) \)

N :

Speed of the impeller (rev/s)

N B0 :

Initial number of moles of B (kmol)

N jd :

Critical speed for just draw down of the solids (rev/s)

N js :

Critical speed for just off – bottom suspension (rev/s)

N P :

Impeller power number(−)

Nu :

Nusselt number used for the tank side heat transfer correlation(−)

N De :

Dean number for the limpet coil(−)

N pr :

Prandtl number used for the utility side heat transfer correlation(−)

N Re :

Raynolds number used for the utility side heat transfer correlation(−)

N Nu :

Nusselt number used for the utility side heat transfer correlation(−)

PBT :

45 degree pitched blade turbine(−)

PBTD – 4:

4 – blade 45 degree pitched blade turbine downflow(−)

PBTD – 6:

6 – blade 45 degree pitched blade turbine downflow(−)

Pr:

Prandtl number used for the tank side heat transfer correlation(−)

PTU :

45 degree pitched blade turbine upflow(−)

P js :

Power consumption at critical suspension speed (W)

Q :

The total heat load of the system (W)

Re :

Impellers Raynolds number used for the tank side heat transfer correlation(−)

Re p :

Particle Raynolds Number(−)

R 0 :

Initial radius of the shrinking particle at time t = 0 (m)

R :

Radius of the particle (m)

RT :

Reaction time (sec)

r c :

Radius of the unreacted core of the particle (m)

r :

Radius of the unreacted core of the particle at any time t (m)

S :

Zweitering’s constant dependent on tank and impeller dimensions(−)

Sh :

Sharewood number(−)

Sc :

Schmidt number(−)

t :

time (s)

t R :

thickness of the reactor (m)

T :

Tank diameter (m)

T j :

Utility side temperature in K

T jt :

Utility fluid inlet temperature (K)

T jo :

Utility fluid outlet temperature (K)

T R :

Reaction temperature (K)

T T :

Tank temperature in K

T w :

Temperature of the wall (K)

Δtg:

The temperature difference between the bulk of the utility fluid and the wall (K)

V :

Volume of the reaction mixture (m3)

V j :

Volume of the jacket or coil (m3)

v t :

Terminal settling velocity \( \left(\frac{\mathrm{m}}{\mathrm{s}}\right) \)

vs:

Hindered settling velocity \( \left(\frac{\mathrm{m}}{\mathrm{s}}\right) \)

X :

Solid loading by weight % (mass of solid / mass of liquid × 100)

X v :

Solid loading by volume % (volume of solid / volume of slurry × 100)

X B :

Conversion of reactant B (−)

Z :

The constant used in the GMB correlation(−)

β :

Volumetric expansion coefficient (K−1)

φ :

The volume of solids divided by the volume of solid – free liquid(−)

μ avg :

Average dynamic viscosity of slurry (Pas)

μ j :

Viscosity of the utility fluid (Pas)

μ L :

Dynamic viscosity of liquid (Pas)

γ :

Kinamatic viscosity \( \left(\frac{{\mathrm{m}}^2}{\mathrm{s}}\right) \)

ρ avg :

Average slurry density \( \left(\frac{\mathrm{kg}}{{\mathrm{m}}^3}\right) \)

ρ B :

Molar density of reactant B in \( \left(\frac{\mathrm{kmol}}{{\mathrm{m}}^3}\right) \)

ρ L :

Density of liquid \( \left(\frac{\mathrm{kg}}{{\mathrm{m}}^3}\right) \)

ρ s :

Density of solid \( \left(\frac{\mathrm{kg}}{{\mathrm{m}}^3}\right) \)

Δρ:

Density difference between solid and liquid \( \left({\rho}_s-{\rho}_L\right)\left(\frac{\mathrm{kg}}{{\mathrm{m}}^3}\right) \)

τ :

Time required for complete conversion (sec)

τ FD :

Time to complete the reaction by film diffusion (sec)

τ SR :

Time to complete the reaction by surface reaction (sec)

ε :

Particle hold – up(−)

ε p :

Power consumption per unit mass \( \left(\frac{\mathrm{Watt}}{\mathrm{kg}}\right) \)

(Nθ)CS:

Dimensionless mixing time at critical suspension speed(−)

θ :

Mixing time (s)

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Author information

Authors and Affiliations

  1. Department of Chemical Engineering, Institute of Chemical Technology, Mumbai, India

    Sumit S. Joshi, Vishawnath H. Dalvi & Jyeshtharaj B. Joshi

  2. FluiDimensions – Engineering Simulations and Consulting, Pune, India

    Vivek S. Vitankar

  3. Homi Bhabha National Institute, Bhabha Atomic Research Center (BARC), Anushakti Nagar, Mumbai, India

    Jyeshtharaj B. Joshi

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  1. Sumit S. Joshi
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  2. Vivek S. Vitankar
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  3. Vishawnath H. Dalvi
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  4. Jyeshtharaj B. Joshi
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Editors and Affiliations

  1. Mechanical and Manufacturing Engineering, University of New South Wales, Sydney, NSW, Australia

    Guan Heng Yeoh

  2. Homi Bhabha National Institute (HBNI); Institute of Chemical Technology, Mumbai, Maharashtra, India

    Jyeshtharaj B. Joshi

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Joshi, S.S., Vitankar, V.S., Dalvi, V.H., Joshi, J.B. (2023). Solid Suspension and Solid-Liquid Mass Transfer in Stirred Reactors. In: Yeoh, G.H., Joshi, J.B. (eds) Handbook of Multiphase Flow Science and Technology. Springer, Singapore. https://doi.org/10.1007/978-981-287-092-6_49

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