Abstract Membranes are excellent alternatives for gas separations due to their low installation and maintenance costs. In industrial environment, membranes are usually organized in modules with spiral-wound or hollow fiber geometries. Because of their wide range of applications, the development of reliable mathematical models for industrial membrane operations is encouraged. In the present work, a mathematical model is proposed to describe gas separations in spiral-wound membranes, based on a phenomenological approach. The proposed model was validated in four case studies of common separations: (i) ammonia; (ii) hydrogen; (iii) C O 2 from natural gas and (iv) C O 2 from flue gas. It is shown that the proposed model is able to represent the analyzed phenomena accurately. The robustness and good performance of the model for several operation conditions were evaluated through sensitivity analyses. In addition, a novel numerical approach is proposed to solve the analyzed mathematical model. The proposed procedure presents good efficiency and accuracy and is faster and more efficient than the well-known shooting method, largely employed to perform membrane simulations, allowing the use of the model in real time applications.

中文翻译：

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用于气体分离的螺旋缠绕膜的建模。第一部分：迭代二维渗透模型

摘要 由于安装和维护成本低，膜是气体分离的绝佳替代品。在工业环境中，膜通常组织成具有螺旋缠绕或中空纤维几何形状的模块。由于它们的广泛应用，鼓励为工业膜操作开发可靠的数学模型。在目前的工作中，基于现象学方法，提出了一个数学模型来描述螺旋缠绕膜中的气体分离。提出的模型在四个常见分离案例研究中得到验证：(i) 氨；(ii) 氢气；(iii) 来自天然气的CO 2 和(iv) 来自烟道气的CO 2 。结果表明，所提出的模型能够准确地表示所分析的现象。通过敏感性分析评估了该模型在多种操作条件下的稳健性和良好性能。此外，提出了一种新的数值方法来求解所分析的数学模型。所提出的程序具有良好的效率和准确性，并且比众所周知的射击方法更快、更有效，主要用于执行膜模拟，允许在实时应用中使用模型。