Model-Based Optimization of Mannitol Production by Using a Sequence of Batch Reactors for a Coupled Bi-Enzymatic Process—A Dynamic Approach
Abstract
:1. Introduction
- Sequential Batch-to-batch Reactors (SeqBR) (Figure 2) consist of a certain number of (usually identical) BR operated in series. The BR content is transferred from every BR to the next one, with adjusting the reactants and/or biocatalyst(s) amounts (concentrations) at the beginning of each BR, to reach optimal levels (off-line determined in this paper) [13,14];
Paper’s Novelty
2. Process Kinetics
The Kinetic Model
3. Optimal BR
3.1. Reactor Model
3.2. Optimal BR Operation
- There is a close connection between the coupling reactions, enzyme concentrations, and the quasi-stationarity of the NADH/NAD ratio over the batch. For all the optimal conditions of Figure 4, Figure 5 and Figure 6, the two enzymatic reactions are well coupled. Thus, the ratio of the high reaction rates R1 and R2 reaches a quasi-stationary level, leading to a quasi-constant NADH/NAD ratio much higher than 10, thus maintaining the process efficiency.
4. Optimal SeqBR
4.1. Control Variable Choice
4.2. The Choice of NBR
4.3. Optimization Problem Formulation for the SeqBR
- Determine the optimal initial conditions for every BR from the series to ensure the highest productivity in mannitol at the SeqBR output, which is the output of the last (NBR)-th BR; and
- Minimize the costly enzymes’ overall consumption (MDH and FDH) while preserving the best connection of the two enzymatic reactions to ensure a quick regeneration of the cofactor and a high fructose reduction rate.
5. Results and Discussion
5.1. Optimization Problem (I), Equations (1+3) of Section 4.3
5.2. Optimization Problem (II), Equations (2+3) of Section 4.3
5.3. Additional Conclusions about the Results of the Optimization Problems (I) and (II)
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Nomenclature
species j concentration | |
species j saturation level | |
, | rate constants |
Min/Max | minimum/maximum |
, R1, R2 | species j reaction rate; reaction rates |
time | |
the batch time | |
V | the BR volume |
fructose conversion | |
W | the objective function of the optimization problem |
Greek Symbols | |
ε | accepted tolerance to achieve the target conversion |
stoichiometric coefficient of species j in the reaction i | |
Index | |
o | initial |
f | final |
Abbreviations | |
arg | the argument of a function |
BR | batch reactor |
BRP | BR with intermittent addition of enzyme solution |
CSTR | continuous stirred-tank reactor |
Conv. | conversion |
DO | dissolved oxygen |
E | enzyme |
F | D-fructose |
FDH | formate dehydrogenase |
FXBR | fixed-bed solid–liquid continuous reactor |
GFS | fructose/glucose syrup |
HCOO- | formate |
M | mannitol |
MACR/MASCR | mechanically agitated solid–liquid (semi-)continuous reactor |
MDH | mannitol dehydrogenase |
NAD(P)H | nicotinamide adenine dinucleotide (phosphate) |
NAD, NAD+ | nicotinamide adenine dinucleotide (oxidized form) |
NLP | nonlinear Programming Problem |
NBR | number of BR connected in series |
SeqBR | sequential batch-to-batch reactor |
SBR | semi-batch reactor |
[X] | concentration of X |
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Reactions | Rate Expressions |
---|---|
Species rate stoichiometry ; | |
Rate constants kc1 = 2 × 10−3; kc2 = 8.3259 × 10−3; 1/h//(U/L) KM1 = 7.2367 × 10−2 M; KM2 = 8.8047 × 10−2 M; KF = 1; KNH = 1; KHC = 5.0061 × 10−2; KNAD = 90.181 |
Parameter | Value [26] |
---|---|
Temperature | 25 °C |
Pressure/pH (buffer solution) | Normal/7 |
Molar initial concentrations | |
Fructose, [F]o ** | 0.1–1 M (tested by [26]) 0.1–3 M (this paper) |
Formate [HCOO]o | [HCOO]o = [F]o |
[NADH]o | 0.008 M (0.1–0.5 M) (this paper) |
[NAD]o | 0.0005 M |
Others: [M]o = [CO2]o = 0 | none |
= CO2 saturation level at 25 °C and pH= 7 | 0.0313 M [35,36] |
Reaction time | 48 h |
Initial FDH (referred to the reactor liquid) | 0.1–2 kU/L (to be optimized) |
Initial MDH (referred to the reactor liquid) | 0.1–2 kU/L (to be optimized) |
One Simple BR ; j = species index (F, M, HCOO, NADH, NAD, CO2). Reaction stoichiometry is given in Table 1. 48 h (batch time, this paper). Initial conditions are given in Table 2. , (negligible inactivation of MDH and FDH); E = enzymes (MDH and FDH); If , then ≈ (excess being removed from the liquid phase). |
SeqBR, that is a Series of (k = 1,…,NBR ) Simple BR ; j = species index (F, M, HCOO, NADH, NAD, CO2). Reaction stoichiometry is given in (Table 1); 40 h (batch time; this paper). Initial conditions: ; ; k = 1,…, NBR; variables to be optimized ; ; ; k = 1,…, NBR; variables to be optimized = 0.0005 M (for the first BR, as recommended in Table 2). The condition of reactors connected in series leads to the following constraints: ; k = 2,…, NBR; = 0 (for the first BR); ; k = 2,…, NBR; = 0 (for the first BR); ; k = 2,…, NBR; Other adopted hypotheses: , (negligible inactivation of MDH and FDH); E = enzymes (MDH and FDH); If , then ≈ (excess being removed from the liquid phase). |
Variable | Model Validation by [10] [F]o = 0.1−1 M | ||
---|---|---|---|
[F]o | 0.1 M | 0.5 M | 1 M |
FDH (U/L) | 1000 | 1000 | 1000 |
MDH (U/L) | 1000 | 1000 | 1000 |
F conversion Model [10] | 1 | 0.95 | 0.68 |
F conversion Experimental [26] | 0.99 | 0.95 | 0.68 |
Enzyme | Optimal BR [F]o = 0.1M [NADH]o = 0.008 M | Experimental [26] | ||||||
FDH (U/L) | 500 | 500 | 500 | 1000 | ||||
MDH (U/L) | 214 | 385 | 879 | 1000 | ||||
F conv. | 0.89 | 0.93 | 0.95 | 0.98 | ||||
Enzyme | Optimal BR [F]o = 1 M [NADH]o = 0.008 M | Experimental [26] | ||||||
FDH (U/L) | 500 | 1000 | 500 | 1000 | 500 | 1000 | 1000 | 1000 |
MDH (U/L) | 1192 | 1192 | 1248 | 1246 | 1388 | 1388 | 1000 | 1000 |
F conv. | 0.58 | 0.76 | 0.59 | 0.78 | 0.61 | 0.82 | 0.68 | 0.68 |
Enzyme | Optimal BR [F]o = 3 M [NADH]o = 0.5 M; | Experimental [26] | ||||||
FDH (U/L) | 500 | 500 | 500 | 300 | 100 | No data | ||
MDH (U/L) | 500 | 100 | 50 | 100 | 100 | |||
F conv. | 1 | 0.99 | 0.80 | 0.87 | 0.50 |
Initial Conditions (Maximum Amount) | Mannitol Production (Total Operating Time) (M/h) | MDH Total Consumption (kU/L) | FDH Total Consumption (kU/L) |
---|---|---|---|
max[F]o = 1 M [Alternative (a)] | |||
SeqBR (10 BR) max [NADH]o = 0.1 M | 5.059/400 | 1.112 | 1.755 |
10 repeated runs of the optimal BR [F]o = 1 M; [NADH]o = 0.008 M (from Table 5) | 8.2/480 | 13.88 | 10 |
10 repeated runs of the experimental BR of [26] [F]o = 1 M; [NADH]o = 0.008 M (from Table 5) | 6.8/480 | 10 | 10 |
max[F]o = 3 M [Alternative (b)] | |||
SeqBR (10 BR) max [NADH]o = 0.5 M | 17.692/400 | 1.112 | 1.755 |
10 repeated runs of the optimal BR [F]o = 3 M; max [NADH]o = 0.5 M (from Table 5) | 26.1/480 | 1 | 3 |
Initial Conditions (Maximum Amount) | Manitol Production (Total Operating Time) (M/h) | MDH Total Consumption (kU/L) | FDH Total Consumption (kU/L) |
---|---|---|---|
max[F]o = 1 M [Alternative (a)] | |||
SeqBR (10 BR) max [NADH]o = 0.1 M | 6.79/400 | 1.12 | 3 |
10 repeated runs of the optimal BR [F]o = 1 M; [NADH]o = 0.008 M (from Table 5) | 8.2/480 | 13.88 | 10 |
10 repeated runs of the experimental BR of [26] [F]o = 1 M; [NADH]o = 0.008 M (from Table 5) | 6.8/480 | 10 | 10 |
max[F]o = 3 M [Alternative (b)] | |||
SeqBR (10 BR) max [NADH]o = 0.5 M | 28.93/400 | 1.72 | 5.34 |
10 repeated runs of the optimal BR [F]o = 3 M; max [NADH]o = 0.5 M (from Table 5) | 26.1/480 | 1 | 3 |
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Maria, G.; Peptănaru, I.M. Model-Based Optimization of Mannitol Production by Using a Sequence of Batch Reactors for a Coupled Bi-Enzymatic Process—A Dynamic Approach. Dynamics 2021, 1, 134-154. https://doi.org/10.3390/dynamics1010008
Maria G, Peptănaru IM. Model-Based Optimization of Mannitol Production by Using a Sequence of Batch Reactors for a Coupled Bi-Enzymatic Process—A Dynamic Approach. Dynamics. 2021; 1(1):134-154. https://doi.org/10.3390/dynamics1010008
Chicago/Turabian StyleMaria, Gheorghe, and Ioana Mirela Peptănaru. 2021. "Model-Based Optimization of Mannitol Production by Using a Sequence of Batch Reactors for a Coupled Bi-Enzymatic Process—A Dynamic Approach" Dynamics 1, no. 1: 134-154. https://doi.org/10.3390/dynamics1010008