Most End-Stage Renal Disease (ESRD) patients receiving dialysis therapy are in a state of
constant metabolic acidosis which is associated with high cardiovascular morbidity and
mortality. In an attempt to improve the quality and efficacy of ESRD patients suffering from
acidosis many experimental approaches have been used to investigate acid–base balance
during dialysis sessions. However, these experimental approaches are expensive and time
consuming. To reduce acidosis morbidity, a compartmental mathematical model is used
in this paper. The model takes into account the exchange of small solutes, bicarbonate
(HCO−
3 ) and carbon dioxide, across a non-uniform trans-membrane dialyzer. Blood and
dialysate flows are simulated using the Navier–Stokes and Darcy equations respectively.
Since the trans-membrane (TM) flux would not be uniform, both blood- and dialysateside
equations are coupled with interfacial conditions calculated by Kedem–Katchalsky
equations. Numerical results and clinical data are in close agreement within a satisfactory
range, thus confirming that mathematical models can predict dialysis operative parameters
with accuracy. Numerical results also confirm that acid–base balance for ESRD patients
can be achieved during HCO−
3 dialysis therapy.