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be430_final - BE.430/2.795/6.561/10.539/HST.544 Final Exam...

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BE.430/2.795//6.561/10.539/HST.544 Final Exam Handed out: Monday, Dec. 6, 2004 Due: Thursday, Dec. 9 by 5pm
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Problem 1 (30 %) ALG Notes Problem 2.6.3 – Parts a – f (not g) (Page 199) Problem 2 (35 %) When patients are on hemodialysis therapy for enhancement of subpar renal function, their blood must be treated with the anticoagulant heparin so that potential problems with clotting within the dialysis device can be minimized. However, the heparin concentration in the blood returned to the patient must be carefully controlled in order to diminish the risk of bleeding. One approach to accomplishing this is use of an enzyme reactor, in which porous spherical beads whose channels throughout are coated with heparinase. The beads are packed tightly into a cylindrical vessel, through which the blood flows; the fluid flow may be considered to be governed by the Darcy Equation, so that the flow velocity profile is uniform across the radial cross-section of the reactor and is proportional to the pressure drop across the axial dimension of the reactor. The rate of transport of heparin from the flowing blood to the beads is governed by a convective mass transport coefficient, with the heparin concentration driving force being the difference between its local concentration in the fluid and its concentration at the bead surface. From the surface, heparin diffuses into the bead and undergoes irreversible degradative reaction (governed by Michaelis-Menten enzyme/substrate kinetics) due to the activity of the heparinase coating the interior pore channels. The objective for use of this enzyme reactor is to reduce the concentration of heparin in the outlet to below a specified critical level, so we need to determine key parameters for its proper design. a. Develop a comprehensive set of model equations for this situation, which can be employed to determine the heparin concentration at the reactor outlet as a function of all other system parameters, including: heparin concentration at the reactor inlet, blood flow rate, heparin diffusion coefficient (assume it is the same in both the bulk blood fluid and the bead pore channel fluid).
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be430_final - BE.430/2.795/6.561/10.539/HST.544 Final Exam...

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