Hollow fiber membrane modules have been used for a variety of applications, functioning as a separator, contactor, or reactor. The most commonly used configuration is a shell-and-tube design in which the fibers are aligned axially but are randomly arranged within a cross-section. A number of factors affect module performance. Some of these factors have been analyzed in the literature, however, the effect of random fiber packing is poorly understood due to the complex geometry of the shell. This thesis describes methods to quantify the effect of random fiber packing on module performance. Using these methods, one can calculate shell-side fluid distribution and shell-side mass transfer coefficients for axial flows through randomly packed bundles.; The randomly packed fiber bundle is modeled as an infinite, periodic medium. A unit cell is used to represent the fiber bundle in which up to 200 fibers are randomly placed at a specific packing fraction. The unit cell is translated in each direction to produce the infinite bundle. The fibers in the unit cell lie parallel to each other, and all fibers have the same properties and dimensions.; To calculate shell-side fluid distribution and mass transfer coefficients, the conservation of momentum and mass equations are solved numerically. To simplify the problem, the analysis focuses on two mass transfer limits: entry and well-developed limits. In the entry limit, mass transfer coefficients are determined by the velocity gradient along the fiber surface. The Boundary Element method is used to solve the conservation of momentum equation. In the well-developed limit, the conservation of momentum and mass equations are solved simultaneously using the Finite Element method combined with the Finite Difference method for constant wall flux and constant wall concentration boundary conditions.; Results show that randomness in fiber packing is detrimental to performance. In the entry limit, mass transfer coefficients are ∼30% lower than expected for regular fiber packings. In the well-developed limit, larger decreases in mass transfer occur. The large decreases are attributed to flow maldistribution resulting from random fiber packing.; The analysis is used to predict hollow fiber module performance for nitrogen production from air. For current commercial units, random fiber packing has a negligible effect on performance. However, as the membrane permeance increases, shell-side concentration boundary layer resistances become significant and module performance deteriorates because of the flow maldistributation induced by random fiber packing.
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