8.7.6 Example Calculations for Membrane Oxygenators

The following examples illustrate the calculation of the area of a membrane blood

oxygenator using the above equations.

Example 8.3 Determine the hollow fiber membrane surface area for a blood oxygenator

operating under the following conditions. Assume the fibers are made from microporous

polypropylene having a membrane porosity of 40 %. The gas permeabilities are then based

on diffusion through a stagnant layer of gas trapped within the pores of the membrane. The

length of each fiber is 50 cm with a wall thickness of 50 microns. The inside diameter of a

fiber is 400 microns. The blood flowrate through the lumen of the fibers in the device is

5,000 ml/min and the gas flowrate is 5,000 ml/min, both at 37 C and 1 atm. The pO2 of the

entering blood is 40 mmHg and the exiting blood must be at a pO2 of 95 mmHg. The pCO2

of the entering blood is 45 mmHg and the exiting blood has a pCO2 of 40 mmHg. The

entering gas contains no carbon dioxide and is saturated with water. The pO2 of the entering

gas is therefore 713 mmHg. Estimate the surface area required to meet these specifications

for both oxygen and carbon dioxide. The gas side mass transfer resistance may be

considered negligible because of the negligible gas solubility. Hence the bulk of the mass

transfer resistance is a result of the boundary layer formed within the blood.

See the PDF file for examples 8.3 and 4 for the MathCad details

SOLUTION. Using the equations developed above, the membrane area calculated for

oxygen uptake is about 12.3 m2 whereas that for carbon dioxide removal is calculated to be

2.5 m2. In this example, we must change the blood pO2 from 40 to 95 mmHg in order to

sustain life for the adult cardiac output of 5,000 ml/min. We find that the total amount of

oxygen transported, Qoxygen , is about 250 ml/min based on the required change in blood pO2

levels. This is the value typically reported for an adult. A proper calculation of the

membrane area for oxygen transport requires a value of m based on a representative oxygen

partial pressure in the blood, see Equation 6.36 or 37. Therefore, we must adjust the value

of m, or the reference pO2 , until the amount of oxygen transferred is the same based on the

changes in the blood pO2 and the gas pO2, thus satisfying the mass balance on oxygen on

the blood side and gas sides. For the problem stated in this example, the value of m is

calculated to be 25.15 which results in a reference pO2 of 62 mmHg which is close to the

average of the arterial and venous pO2 levels of 67.5 mmHg. The amount of carbon dioxide

exchanged is calculated to be 289 ml/min and is the same whether based on the blood or gas

sides. This value for an adult should be about 200 ml/min. Therefore, we are removing too

much carbon dioxide which will tend to make the blood basic and lead to alkalosis. The

respiratory exchange ratio (R) is defined as the ratio of carbon dioxide output to oxygen

uptake and should be about 0.8. Here we see that R is about 1.17. For a given membrane

area, we can control the amount of carbon dioxide removed by adjusting the pCO2 of the

incoming gas. In this example, its value was zero. The next example illustrates the effect of

the entering gas pCO2 on the carbon dioxide removal rate for a given membrane area.

Example 8.4 Use the membrane area calculated for oxygen from Example 8.3. Find the

entering gas pCO2 needed to provide an oxygen uptake of 250 ml/min and a carbon dioxide

removal of 200 ml/min.

SOLUTION. Equations 8.41 and 8.46 are rearranged to solve for the exiting blood partial

pressures. By adjusting the entering gas pCO2 from 0 up to 15 mmHg, we can decrease the

carbon dioxide output to the required value of 200 ml/min, while keeping the oxygen

uptake at 250 ml/min, thus achieving the normal respiratory exchange ratio of 0.8. We also

find that the membrane area needs to be increased by 0.3 m2 to maintain the delivery of the

same amount of oxygen. This is due to the decreased driving force for oxygen transport as a

result of the carbon dioxide that was added to the feed gas.

Once again see the PDF files for the MathCad details of how thesecalculations are done.

Hollow fiber membrane blood oxygenators in use today typically have surface areas in the

range from about 1.5 - 5 m2. In the above examples, it was assumed that blood flowed through the

lumen of the hollow fibers in fully developed laminar flow. This assumption provides a

conservative or worst case estimate of oxygenator performance. Hence, the surface areas calculated

in the above examples are several times larger than what can be achieved in actual practice. Since

the major resistance for oxygen transport resides in the blood, increasing the blood side oxygen

mass transfer coefficient can have a significant effect on the size of the oxygenator. This can be

accomplished by such methods as pulsating flow, small obstructions in the fiber to cause radial

mixing, or a helical arrangement of the hollow fibers to induce secondary flows (swirls). Having

the blood flow across the outside of the hollow fibers can also significantly increase the mass

transfer rate of oxygen into the blood. This is a result of repetitive mixing of the blood as it crosses

successive hollow fibers effectively decreasing the boundary layer resistance to oxygen transport.

Generally, it is recommended that experiments be performed to measure the oxygen

transport rates for a given oxygenator design. Mathematical models, such as the one developed

above or in the papers by Vaslef et al. 1994 and Wickramasinghe et al. 2005, can then be used to

correlate the results, and provide accurate measurements of the blood-side mass transfer

coefficient. A calibrated model can then be used to explore operations under a wide range of

operating conditions and assist in the optimal development of the device. For example, Vaslef et al.

1994 and Wickramasinghe et al. 2005 were able to assess the performance of cross flow hollow

fiber oxygenators using water and other blood analogues. Subsequent tests using bovine blood

provided excellent comparisons between their measurements and model predictions of the oxygen

transport rates.

Use of a mathematical model to predict oxygen transfer rates inHollow fiber membrane oxygenators, Vaslef et al. ASAIO J 1994(read the paper as well, the following summarizes the key points)

6) Not sure whatthey mean bythis.

Now go to PDF forthe derivation

Other oxygenatorshad similar results