Biomod/2013/NanoUANL/Reactor: Difference between revisions
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Accumulation = <math>\tfrac{d[P]}{dt}</math> | Accumulation = <math>\tfrac{d[P]}{dt}</math> | ||
<math>F_0 = F_0(1-x_S)-V(-r_S)+\frac{d[P]}{dt}</math> | |||
The intake and outflow were determined by diffusion. For the simplification of the diffusion phenomenon we considered: | The intake and outflow were determined by diffusion. For the simplification of the diffusion phenomenon we considered: |
Revision as of 21:09, 17 October 2013
What is a reactor?
Introduction
The CCMV capsid could be considered as a continuous stirred-tank reactor with an accumulation of the product inside the capsid. This type of reactor is a common and ideal type in chemical engineering. The open system will be treated as it operates on a steady-state assumption, where the conditions of the reactor will not change with time. The reactor proposed is a complete opposite type from tubular plug-flow and stirred batch reactors, and can be very useful when studying the behavior of a gas, liquid or solid.
The reactor is modeled by that of a Continuous Ideally Stirred-Tank Reactor (CISTR), assuming perfect mixing in the container.
Enzymatic Reaction
The general reaction scheme is described as follows:
[math]\displaystyle{ E + S \leftrightarrow ES \rightarrow E^0 + P }[/math]
With a reaction rate of:
[math]\displaystyle{ \frac{d[ES]}{dt}=k_1[E][S]-k_{-1}[ES]-k_2[ES] }[/math]
This equation is affected by the constants k1 , k-1 and k2.
Considerations
We established the following considerations in our system:
- Uniform distribution throughout the reactor
- k1 and k2 >> k-1
- One enzyme per reactor/VLP
- Tortuosity approaches zero during diffusion
Mass balance
Material balances are important, as a first step in devising a new process (or analyzing an existing one). They are almost always a prerequisite for all calculations for process engineering problems. The concept of mass balance is based on the physical principle that matter cannot be either created nor destroyed, only transformed. The law of mass transformation balances describe the mass of the inputs of the process with the output, as waste, products or emissions. This whole process is accounting for the material used in a reaction.
Mass balance was presented as such:
ACCUMULATION = INPUT - OUTPUT - DISAPPEARANCE BY REACTION
where
Input= F0
Output= F0(1-XS)
Disappearance = V(-rS)
Accumulation = [math]\displaystyle{ \tfrac{d[P]}{dt} }[/math]
[math]\displaystyle{ F_0 = F_0(1-x_S)-V(-r_S)+\frac{d[P]}{dt} }[/math]
The intake and outflow were determined by diffusion. For the simplification of the diffusion phenomenon we considered:
- Constant temperature
- Constant pressure
- Species B stays in a stationary state (it does not diffuse in A)
- The container (VLP) has a spherical shape
A mass balance, applied to a spherical envelope is as follows:
[math]\displaystyle{ \frac{d}{dr}(r^2N_{Ar})=0 }[/math]
where NAr represents molar flux. When NBr=0 we obtain
[math]\displaystyle{ \frac{d}{dr}(r^2\frac{cD_{AB}}{1-x_A}\frac{dx_A}{dr})=0 }[/math]
At a constant temperature the product (cDAB) is equally constant and xA=1-xB, the equation can be integrated into the following expression1:
[math]\displaystyle{ F_A=4\pi r_1^2N_{Ar}|_{r=r1}= \frac{4\pi cD_{AB}}{1/r_1-1/r_2} \ln\frac{x_{B2}}{x_{B1}} }[/math]
where x are the fractions, c is the concentration and r are the respective radius.
This equation defines the nanoreactor inflow; a similar analysis yields the reactor outflow.
Diffusion coefficient
The ionic silver diffusion coefficient in solution is described by Nerst's equation (1888)2:
[math]\displaystyle{ D_{AB}°= \frac{RT}{F^2} \frac{\lambda^o_+\lambda^o_-}{\lambda^o_++\lambda^o_-} \frac{|Z_-|+|Z_+|}{|Z_+Z_-|} }[/math]
where
- F = Faraday's constant [A·s/geq]
- DAB° = Diffusion coefficient at infinite dilution [m2/s]
- λ+° = Cationic conductivity at infinite dilution
- λ-° = Anionic conductivity at infinite dilution
- Z+ = Cation valence
- Z- = Anionic valence
- T = Absolute temperature [K]
Boiling temperature
Via Joback's method, we estimate the normal boiling temperature:
[math]\displaystyle{ T_b=\mathbf{198} + \sum_{k} N_k(tbk) }[/math]
in which Nk is the number of times that the contribution group is present in the compound.
Critical temperature
Using a similar approach, also by Joback, we estimate the critical temperature:
[math]\displaystyle{ T_c=T_b\Bigg[ \mathbf{0.584}+\mathbf{0.965} \bigg\{\sum_{k} N_k(tck) \bigg\} - \bigg\{\sum_{k} N_k(tck) \bigg\}^2 \Bigg]^{-1} }[/math]
Joback Method Contributions (Table C1. Prausnitz)
Group | tbk, K | tck, K | Group | tbk, K | tck, K | Group | tbk, K | tck, K | Group | tbk, K | tck, K |
---|---|---|---|---|---|---|---|---|---|---|---|
CH3 | 23.58 | 0.0141 | CH2(ss) | 27.15 | 0.01 | ACOH | 76.34 | 0.0240 | NH | 50.17 | 0.0295 |
CH2 | 22.88 | 0.0181 | CH(ss) | 21.78 | 0.0122 | O | 22.42 | 0.0168 | NH(ss) | 52.82 | 0.0130 |
CH | 21.74 | 0.0164 | C(ss) | 21.32 | 0.0042 | O(ss) | 31.22 | 0.0098 | N | 11.74 | 0.0169 |
C | 18.25 | 0.0067 | =CH(ds) | 26.73 | 0.0082 | C=O | 76.75 | 0.0380 | =N-(ds) | 74.60 | 0.0255 |
=CH2 | 18.18 | 0.0113 | =C(ds) | 31.01 | 0.0143 | C=O(ds) | 94.97 | 0.0284 | =NH | X | X |
=CH | 24.96 | 0.0129 | F | -0.03 | 0.0111 | CH=O | 72.20 | 0.0379 | CN | 125.66 | 0.0496 |
=C | 24.14 | 0.0117 | Cl | 38.13 | 0.0105 | COOH | 169.09 | 0.0791 | NO2 | 152.54 | 0.0437 |
=C= | 26.15 | 0.0026 | Br | 66.86 | 0.0133 | COO | 81.10 | 0.0481 | SH | 63.56 | 0.0031 |
≡CH | 9.20 | 0.0027 | I | 93.84 | 0.0068 | =O | -10 | 0.0143 | S | 68.78 | 0.0119 |
≡C | 27.38 | 0.0020 | OH | 92.88 | 0.0741 | NH2 | 73.23 | 0.0243 | S(ss) | 52.10 | 0.0019 |
[FALTA EPECIFICAR Q SIGNIFICA ss Y ds Y CENTRAR DATOS DE SER POSIBLE]
Conductivity
The conductivity of the compound is determined by the Sastri method:
[math]\displaystyle{ \lambda_L=\lambda_ba^m }[/math]
where
- λL = thermic conductivity of the liquid [ W/(m·K)]
- λb = thermic conductivity at normal boiling point [ W/(m·K)]
- Tbr = Tb/Tc = normal boiling reduced temperature
- Tr = T/Tc = reduced temperature
- Tc = critical temperature [K]
and
[math]\displaystyle{ m=1-\bigg(\frac{1-T_r}{1-T_{br}}\bigg)^n }[/math]
with a = 0.16 and n = 0.2 for the compound
Contribución de Sastri (Table 10.5. Prausnitz)
Hydrocarbon Groups | Δλb | Non-Hydrocarbon Groups | Δλb | Non-Hydrocarbon Groups | Δλb |
---|---|---|---|---|---|
CH3 | 0.0545 | O | 0.0100 | N(ring) | 0.0135 |
CH2 | 0.0008 | OH2 | 0.0830 | CN | 0.0645 |
CH | -0.0600 | OH3 | 0.0680 | NO2 | 0.0700 |
C | -0.1230 | CO(ketone) | 0.0175 | S | 0.0100 |
=CH2 | 0.0545 | CHO(aldehyde) | 0.0730 | F4 | 0.0568 |
=CH | 0.0020 | COO(ester) | 0.0070 | F5 | 0.0510 |
=C | -0.0630 | COOH(acid) | 0.0650 | Cl | 0.0550 |
=C= | 0.1200 | NH2 | 0.0880 | Br | 0.0415 |
Ring1 | 0.1130 | NH | 0.0065 | I | 0.0245 |
NH(ring) | 0.0450 | H6 | 0.0675 | ||
N | -0.0605 | 3 member ring | 0.1500 | ||
Ring7(other) | 0.1100 |
1Poly-cyclical compounds
2Alifatic Phenol and Alcohol
3Alcohols don't described in 2
4Perfluorines in Carbons
5Perfluorines don't described in 2
6Methanes, Formic Acids, Formats
7Non-Poly-cyclical hydrocarbons
[PORQUE LA ECUACION DE LAMBDA ES MAS PEQUEÑA Q LAS DEMAS? CENTRAR TABLA DE SER POSIBLE]
Silver density
[PENDIENTE]
References
- Bird R. B, Stewart W.E. & Lightfoot E.N., Fenómenos de Trasporte, Reverté Ediciones SA de CV 2006, pages 17-9 – 17-11.
- Anthony L. Hines & Robert N. Maddox, Mass Transfer Fundamentals and Applications, Prentince Hall PTR 1985, pages 34-35
- Poling, Prausnitz & O’Connel, The Properties of Gases and Liquids, 5th Edition. McGrawl-Hill 2001, pages
[ESPECIFICAR PAGINAS PRAUSNITZ]