The electro-kinetic characteristics of different material bioreactor columns for treating water and waste water are experimentally studied. Separate columns of unsaturated gravels (~6mm) and ball clay were assessed for electro-kinetic characteristics by dosing water at a hydraulic loading rate of 50ml/min and 10ml/min. Similarly locally available organic materials such as sawdust, Moringa oleifera sheets and textile clothe pieces were also empirically analyzed. Size effects of the bio-reactor columns were also studied. The effluent from textile clothe and gravel reactor respectively showed an increase in pH while a depreciation in pH in the effluent was observed in the Moringa Oleifera reactor and sawdust reactor. This may be due to leaching of acidic organic components for sawdust and Moringa Oleifera . In gravels effluent pH depreciated with increase in flow rate but the general trend of the effluent pH curve showed an initial improvement before it slowed down to an asymptote for a specific constant dosage and height. A multi-parameter stochastic linear model for change in pH as a function of column height, dosage rate, time for specific volume discharge and change in electrical conductivity between influent and effluent was derived. A general stochastic model was also developed to characterize pH change in any bioreactor irrespective of the material media. Thirty centimeters of gravel exhibited an increase in conductivity with increase in flow rate while conductivity dipped with increasing flow rate when the gravel column height was halved. The measure of organic compounds in water decreased with increasing percolation rate through gravel. The chemical oxygen demand ratio within the gravel improved to unity showing increased containment of organic compounds with time. Organic textile clothes reactor also illustrated increased conductivity with increasing flow but conductivity dipped with increase in column height. For Moringa Oleifera reactors, a dosage of water at 10ml/min showed a significant improvement in conductivity with increase in column height. An initial depreciation in temperature curve was observed within clay and gravel reactor. With increase in depth there was an increase in temperature within the gravel as the saturation by water improved. In sawdust reactors this was not the trend. A birth process model is proposed to simulated temperature within a bioreactor as a function of time irrespective of any specific material used as bioreactor media.