An analytical approach to the gas pressure drop in hollow fiber membranes

The gas pressure drop in the bore of hollow fiber membranes has attracted much attention. Numerical methods are generally employed to deal with such complex problems. However, numerical methods cannot provide a clear picture on how the pressure drop is affected by the physical properties of fibers (e.g., fiber inner diameter, fiber length, and intrinsic permeance) and the operating conditions (e.g., downstream pressure). This article attempts to elucidate the interaction mechanism based on an analytical approach. The pressure drop in hollow fibers is formulated by an elliptic integral function, and the effectiveness factor of the transmembrane pressure is proposed to characterize the effect. A dimensionless parameter is obtained, which contains all the dominant factors responsible for generating the pressure drop in hollow fibers. It is shown that the dimensionless parameter serves as the indicator of the significance of the effect of the pressure buildup in hollow fibers. To some degree, this parameter is also a convenient tool for rationalizing hollow fiber modules design.