<br>通过超声波技术提高生物柴油产量：一项数学研究,ACS Omega

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通过超声波技术提高生物柴油产量：一项数学研究
ACS Omega ( IF 3.7 ) Pub Date : 2024-04-25 , DOI: 10.1021/acsomega.4c01729
Xianbing Cao ₁ , Sk Mosaraf Ahammed ₂ , Siddhartha Datta ₃ , Jahangir Chowdhury ₄ , Priti Kumar Roy ₂

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生物柴油是替代性可再生能源之一，因其清洁、绿色能源而受到广泛关注。生物柴油的生产可以使用不同的来源，但最合适和经济的方法依赖于甲醇与来自麻风树果实的非食用植物油的酯交换反应。摩尔比、容器直径、催化剂浓度和超声波都对酯交换过程合成生物柴油有重大影响。在这些因素中，容器的直径和通过传质限制产生的超声波效应对反应的成功完成具有重大影响。在这项研究工作中，我们开发了一个数学模型来分析氢氧化钾催化剂存在下的三步酯交换过程和副皂化反应。该模型考虑了混合强度变化（包括超声波）对不同相传质的影响。使用修正的 Dittus-Boelter 相关性计算传质速率。 Pontryagin 采用最小原理的最优控制方法，以最小的成本最大化生物柴油的产量。这项研究的新颖性是我们从分析和数值结果中得出的，考虑到工业过程，超过 97% 的生物柴油产量转化率将在 50 kHz 超声波频率下获得，即 6:1 的甲醇：使用最优控制理论，在 50 分钟内麻风树与油的摩尔比和 1 m 的容器直径。

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Enhancement of Biodiesel Production via Ultrasound Technology: A Mathematical Study

Biodiesel is one of the alternative renewable energy sources that has received a lot of attention since it is clean, green energy. Different sources can be used for the production of biodiesel, but the most appropriate and economical method relies on the transesterification of methanol with the nonedible vegetable oil from the fruit of the Jatropha curcas plant. Molar ratio, vessel diameter, catalyst concentration, and ultrasound all have a substantial influence on the synthesis of biodiesel by the transesterification process. Among these factors, the diameter of the vessel and the ultrasonic effect through mass transfer limitations have a significant impact on successful reaction completion. In this research work, we have developed a mathematical model to analyze the three-step transesterification process and side saponification reaction in the presence of a potassium hydroxide catalyst. The model considers the influence of mixing intensity variations, including ultrasound, on the mass transfer in different phases. The mass transfer rate is calculated using the modified Dittus–Boelter correlation. An optimal control approach through the minimum principle by Pontryagin is applied to maximize the production of biodiesel at minimal cost. The novelty of this research, which we have derived from our analytical as well as numerical results, considering industrial processes, is that more than 97% biodiesel yield conversion is to be obtained at 50 kHz ultrasound frequency, a 6:1 methanol-to-Jatropha-oil molar ratio, and 1 m of vessel diameter within 50 min using optimal control theory.

更新日期：2024-04-25

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