CHE 499 (Spring 04) LAST NAME FIRST Problem

che 499 (spring 04) __________________ last name, first problem set #9 1. a “drug patch” is designed to slowly deliver a drug (species

CHE 499 (Spring 04) __________________
LAST NAME, FIRST
Problem set #9
1. A “drug patch” is designed to slowly deliver a drug (species A)
through the body tissue to an infected zone of tissue beneath the
skin. The drug patch consists of a sealed reservoir containing the
drug encapsulated within a porous polymer matrix. The patch is
implanted just below the skin. It is designed to release 2.010-11
mol/s of the drug uniformly over a surface area of 1 cm2. The mean
distance from the drug patch to the infected area of tissue is 5 mm.
To be effective, the drug concentration must be at least 0.2 mol/m3 at
the top edge of the infected zone. Determine the time (in hours) it
will take for the drug to begin to be effective for treatment. The
effective molecular diffusion coefficient of the drug through the body
tissue is 110-6 cm2/s.
2. Estimate the clearance of urea in a co-current and a
counter-current hollow-fiber dialyzer. The device has 1.2 m2 of
membrane surface area where blood flows within the hollow fiber and
the dialysate flows in a single-pass on the shell side. The blood flow
rate is 300 cm3/min and the dialysate flow rate is 600 cm3/min. The
membrane permeability for urea, Pm, is 10-3 cm/s, the mass transfer
coefficient on the blood side, kb, is 1.05410-3 cm/s, and the mass
transfer coefficient on the dialysate side, kd, is 2.8810-3 cm/s.
3. Figure 1 shows the schematic of a blood dialysis system, where CUB,
CUR, and CUM are, respectively, the concentrations of urea in the
body, the reservoir, and in the blood leaving the membrane unit. CUM
is related to CUB by the following relation
ln = - 0.874
At the start of the dialysis process the urea concentration in the
blood within the body CUB is 1.0 g/liter. The volume of blood VB is
6.0 liters, the blood flow rate Qb is 5.94 liters/hr, and CUR is
constant at 0.05 g/liter. Determine the time required for the urea
concentration in the body (CUB) to drop to 0.2 g/liter.

Figure 1 Schematic of a blood dialysis system.
4. Figure 1 shows the schematic of a blood dialysis system, where CUB,
CUR, and CUM are, respectively, the concentrations of urea in the
body, the reservoir, and in the blood leaving the membrane unit. The
operating parameter Qb and the design parameter VR are fixed by the
following two conditions
= 0.05
and = exp = 0.5
Other parameters are given as
mDU,m = 10-5 cm2/s, Rout  Rin = 50 m, Rin = 50 m, fV = 0.2
Ain = 2NfLRin = 500 cm2, k = 10-3 s-1, b = 1, VB = 5 L,  = Rin/Rout
= 0.5
Note: B = VB/Q, L =  =  = 
fV = the volume fraction of the bead inside the reactor
1) Determine Q and VR.
2) Determine Q and VR if k = 0.2 s-1.

Figure 1 Schematic of a blood dialysis system.