A system and method of achieving both convective and diffusive transport of plasma across a membrane accompanied by the selective removal of plasma components using sorbents followed by reinfusion of the purified plasma in a blood circulation system is achieved by pumping blood through a filter comprising a bundle of "U" shaped hollow fibers immersed in a closed plasma chamber containing sorbents in an electrolyte solution. As blood flows through the entry arm, due to positive transmembrane pressure difference, plasma filtration into the plasma chamber occurs. The entering plasma causes an increase in the chamber pressure but does not exceed the pressure in the entry arm. The increase in chamber pressure exceeds the pressure in the exit arm of filter where the transmembrane pressure difference is negative and the direction of filtration reverses causing reverse filtration/reinfusion of plasma from the chamber into the blood in the exit arm. The phenomena of positive and reverse filtration from the hollow fiber filter establishes the circulation of plasma fluid in the plasma chamber. The plasma filtering through the entry arm, which corresponds to the arterial end of the system, passes through the plasma chamber solution containing the sorbents where plasma components get selectively depleted. The sorbents may be in any usable form which are not permeable to the filter. The purified plasma reenters the filter along the exit arm corresponding to the venous end where negative transmembrane pressure exists.