*Article* **Modeling and Economic Optimization of the Membrane Module for Ultrafiltration of Protein Solution Using a Genetic Algorithm**

#### **Tuan-Anh Nguyen 1,\* and Shiro Yoshikawa 2**


Received: 8 November 2019; Accepted: 16 December 2019; Published: 18 December 2019

**Abstract:** The performance of cross-flow ultrafiltration is greatly influenced by permeate flux behavior, which depends on many factors, including solution properties, membrane characteristics, and operating conditions. Currently, most research focuses on improving membrane performance, both in terms of permeability and selectivity. Only a few studies have paid attention to how the membrane module is configured and operated. In this study, the geometric design and operating conditions of a membrane module are considered as multivariable optimization variables. The objective function is the annual cost. The cost consists of a capital investment depending on the plant scale and an operating expense associated with energy consumption. In the optimization problem, the channel dimensions (width × length × height), and operating conditions (the inlet pressure and recirculation flow rate) were considered as decision variables. The operating configuration of the membrane plant is assumed to be feed and bleed mode, and a model including the pressure drop is introduced. The model is used to simulate the membrane plant and calculate the membrane area and energy usage, which are directly related to the total cost. The genetic algorithm is used for the optimization. The e ffect of individual parameters on the total cost is discussed.

**Keywords:** modeling; optimization; ultrafiltration; membrane module; cross-flow; protein solution
