The active sulfonic group was grafted on a preprepared Seven Bore Hollow Fiber membranes (SBHF) of PolyEtherSulfone (PES), it is used for esterification catalyzation as a novel catalytic membrane with a smart surface and excellent mechanical properties. A kinetic model incorporated the grafting mechanism, describes the polymerization physically and mathematically. Surface chain grafting occurs by both monomer and backbone polymer. The kinetics of isothermal ($25^\circ C$) graft polymerization of the active functional group onto the prepared SBHF PES membranes was previously studied. The polymerization initiated with $0.5N\ H_2SO_4$, then use the Styrene monomer of concentrations ranging $12\%$ vol. for polymerizations, which was terminated using a $0.5N\ H_2SO_4$ formulating the active sulfonic groups attached to the pores of the SBHF PES membranes. The degree of sulfonation was determined using the experimental results and compared with that forecasted by several methods: determine the conversion of the activation step experimentally, by the acid-base back titration method, calculation by the $H^+$ and predicted by the developed mathematical model. It has a good harmony with such experimentally achieved results. The degree of sulfonation is determined, using four approaching ways, they are very close: 21.89, 23, 21.57 and 22.67%. The IEC was, also, determined and it equals 0.1316 meq/g.