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Criteria for a unique steady state for enzymatic depectinization of bael (Aegle marmelos) juice in a continuous stirred tank reactor†
Reaction Chemistry & Engineering ( IF 3.4 ) Pub Date : 2018-03-29 00:00:00 , DOI: 10.1039/c7re00212b Sourav Sengupta 1, 2, 3, 4 , Amit Jain 1, 2, 3, 4 , Sirshendu De 1, 2, 3, 4
Reaction Chemistry & Engineering ( IF 3.4 ) Pub Date : 2018-03-29 00:00:00 , DOI: 10.1039/c7re00212b Sourav Sengupta 1, 2, 3, 4 , Amit Jain 1, 2, 3, 4 , Sirshendu De 1, 2, 3, 4
Affiliation
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The depectinization kinetics of bael (Aegle marmelos) juice using the enzyme pectinase was evaluated and it was observed to follow the Michaelis–Menten model. The suitable reaction time and enzyme concentration were estimated to be 60 min and 0.25% w/w, respectively. The conditions to obtain a unique steady state for such a reaction in a continuous stirred tank reactor were determined using the fixed point theorem and contraction mapping. The phase space plot was generated using parameters 
and 
, involving the operating conditions and kinetic constants (V is the reactor volume, vmax and KM are the kinetic parameters of the Michaelis–Menten model, v0 is the volumetric flow rate and CA0 is the feed concentration of the substrate), and the envelope of a unique steady state was developed. From the iso-conversion curves, the values of α and β were identified so that the reactor can operate at a unique steady state. It was found that β > 4 results in a feasible steady state. The range of α was reduced at a higher β in order to get a unique steady state. The critical residence time of the reactor decreased with the enzyme concentration and became invariant beyond 0.20% w/w. Deviation of the CSTR from ideal behavior led to an increase in the critical residence time. The present analysis is extendable to other reaction kinetic models as well, for appropriate design and scale up of commercial reactors so as to prevent the occurrence of multiple steady states leading to inaccurate product specifications.
中文翻译：
在连续搅拌釜反应器中 对贝尔（Aegle marmelos）果汁进行酶促脱胶的独特稳态的标准†
评价了使用果胶酶对贝尔（Aegle marmelos）果汁的去果胶动力学，并观察其遵循了Michaelis-Menten模型。合适的反应时间和酶浓度估计分别为60分钟和0.25％w / w。使用定点定理和收缩映射法确定在连续搅拌釜反应器中获得这种反应的独特稳态的条件。相空间图是使用参数和生成的，其中包括操作条件和动力学常数（V是反应堆体积，v max和K M是Michaelis–Menten模型的动力学参数，v 0是体积流量和Ç A0是在基板的进料浓度）和一个唯一的稳定状态的包络线被开发。从等转换曲线中，可以确定α和β的值，以便反应堆可以在独特的稳态下运行。发现β > 4导致可行的稳态。当β值较高时，α的范围会减小为了获得独特的稳态。反应器的临界停留时间随酶浓度而降低，并且在超过0.20％w / w时保持不变。CSTR与理想行为的偏离导致临界停留时间的增加。本分析还可以扩展到其他反应动力学模型，以用于商业反应器的适当设计和按比例放大，从而防止出现多个稳态导致产品规格不准确的情况。
更新日期：2018-03-29
and , involving the operating conditions and kinetic constants (V is the reactor volume, vmax and KM are the kinetic parameters of the Michaelis–Menten model, v0 is the volumetric flow rate and CA0 is the feed concentration of the substrate), and the envelope of a unique steady state was developed. From the iso-conversion curves, the values of α and β were identified so that the reactor can operate at a unique steady state. It was found that β > 4 results in a feasible steady state. The range of α was reduced at a higher β in order to get a unique steady state. The critical residence time of the reactor decreased with the enzyme concentration and became invariant beyond 0.20% w/w. Deviation of the CSTR from ideal behavior led to an increase in the critical residence time. The present analysis is extendable to other reaction kinetic models as well, for appropriate design and scale up of commercial reactors so as to prevent the occurrence of multiple steady states leading to inaccurate product specifications.
中文翻译：
在连续搅拌釜反应器中 对贝尔（Aegle marmelos）果汁进行酶促脱胶的独特稳态的标准†
评价了使用果胶酶对贝尔（Aegle marmelos）果汁的去果胶动力学，并观察其遵循了Michaelis-Menten模型。合适的反应时间和酶浓度估计分别为60分钟和0.25％w / w。使用定点定理和收缩映射法确定在连续搅拌釜反应器中获得这种反应的独特稳态的条件。相空间图是使用参数
和生成的，其中包括操作条件和动力学常数（V是反应堆体积，v max和K M是Michaelis–Menten模型的动力学参数，v 0是体积流量和Ç A0是在基板的进料浓度）和一个唯一的稳定状态的包络线被开发。从等转换曲线中，可以确定α和β的值，以便反应堆可以在独特的稳态下运行。发现β > 4导致可行的稳态。当β值较高时，α的范围会减小为了获得独特的稳态。反应器的临界停留时间随酶浓度而降低，并且在超过0.20％w / w时保持不变。CSTR与理想行为的偏离导致临界停留时间的增加。本分析还可以扩展到其他反应动力学模型，以用于商业反应器的适当设计和按比例放大，从而防止出现多个稳态导致产品规格不准确的情况。
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