In the porous media literature, unidirectional fibrous systems are broadly categorized as ordered or disordered. The former class, easily tractable for analysis purposes but limited in its relation to reality, involves square, hexagonal and various staggered arrays. The latter class involves everything else. While the dimensionless hydraulic permeability of ordered fibrous media is known to be a deterministic function of their porosity Delta, the parameters affecting the permeability of disordered fiber arrays are not very well understood. The objective of this study is to computationally investigate flow across many unidirectional arrays of randomly placed fibers and derive a correlation between K and some measure of their microstructure. In the process, we explain the wide scatter in permeability values observed computationally as well as experimentally. This task is achieved using a parallel implementation of the Boundary Element Method (BEM). Over 600 simulations are carried out in two-dimensional geometries consisting of 576 fiber cross-sections placed within a square unit cell by a Monte Carlo procedure. The porosity varies from 0.45 to 0.90. The computed permeabilities are compared with earlier theoretical results and experimental data. Analysis of the computational results reveals that the permeability of disordered arrays with phi < 0.7 is reduced as the non-uniformity of the fiber distribution increases. This reduction can be substantial at low porosities. The key finding of this study is a direct correlation between K and the mean nearest inter-fiber spacing delta(-)1, the latter depending on the microstructure of the fibrous medium.