A framework is developed by integrating the results of Monte-Carlo simulations with Karhunen-Loeve expansion to study the effect of input random processes that are weakly correlated. Weakly correlated stochastic processes need a large number of independent random variables to capture the higher frequency content of the process [1]. Conventional stochastic methods like Polynomial Chaos Expansion (PCE) are not ideal to propagate their effect, as the number of terms needed in PCE are prohibitively large. For complex non-linear systems, this difficulty is even more pronounced. The present study investigates the problem of a 1D pressure driven flow through a 2D saturated `Debye type' porous media. We study the effect of random input solid-pore geometry of the porous media on the output flow field. The input process is weakly correlated [2] and need a large number of input random variables to represent it with a reasonable level of accuracy. Monte-Carlo simulations (MCS), a sampling based method, is applied to simulate the flow through a large number of media samples and to generate the flow-field statistics. Lattice Boltzmann method is used as the simulation tool. Subsequently, using the flow-field statistics, the output flow-field is characterized using a KL expansion step. The associated KL random variables are found to be from the Pearson Type VII family. This characterization helps to reconstruct realistic and statistically accurate samples of the output flow-field of any desired number, without the need of performing further computationally expensive simulations.