Numerical Evaluation of An Improper Integral for Pressure Drop Calculation in Hollow Fiber Membrane

Abstract

The decrease in gas pressure within the bore of hollow fibers in membrane separation has received considerable interest. Typically, such complex problems are commonly addressed by the utilization of numerical methods. The pure numerical approaches are inadequate in providing a comprehensive understanding of the influence of physical features of fibers (such as length, inner diameter, and intrinsic gas permeance) and operating parameters (such as membrane pressure) on the pressure drop. Another approach is to present the pressure profile by an analytical expression. The integral equation derived from this approach requires a calculation of an improper integral. The improper integral is numerically estimated by a commercial mathematical package or by consulting tables from handbooks, which limit the application and is also implicit in nature. In this study, a simple technique is proposed so that the improper integral is easily and explicitly evaluated by any numerical integration scheme. The effect of fiber length, intrinsic gas permeance on the pressure profile at the permeate side of membrane are also discussed. The pressure profiles serve as a first indication for the design of hollow fiber membrane module.