Regression Method Essay

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The traditional method for the determination of the time lag resorts to a limited portion of the downstream pressure rise curve to perform the required extrapolation to the time axis. When a numerical model is available, an alternative method to obtain the membrane properties is to fit the variation of the pressure change in the downstream reservoir as a function of time using a nonlinear least squares method [30]. By minimizing the sum of squares of the differences between the experimental data and the numerical model, the optimal combination of S and D can be obtained. The nonlinear regression method has three advantages in diminishing the noise effect: 1) it uses the whole range of pressure data instead of only the quasi-steady state…show more content…
The details of the CV system used in this work are described elsewhere [15,16]. The design of the downstream compartment allows varying the volume for gas accumulation from 77.6×10-6 m3 to 1009.7×10-6 m3; at the same time, the effects of resistance to gas accumulation reported in ref. [31-33] are minimized. The absolute pressure transducer (MKS model 627B11TBC1B) to monitor gas accumulation operates in a range of 0 to 1333 Pa (10 torr), with an accuracy of 0.0133 Pa (0.0001 torr) and a maximum error of 0.12% of the pressure reading. This level of precision is typical of the best precision from pressure transducers currently available on the market. Prior to each experiment, the system is evacuated using a rotary vacuum pump (Edwards model RV3) for at least 48 h, and just before the experiment, leak tests for both upstream and downstream sides of the membrane are performed. During the leak tests, the vacuum pump is disconnected from the system and gas accumulation (if any) in the downstream reservoir is monitored for a period of time (from 20 minutes to 1 hour depending on the duration of the experiment). The membrane used in the tests was a solution-cast, high molecular polyphenylene oxide (PPO) film prepared by a spin-coating technique. The details of membrane preparation are described elsewhere [34]. Other relevant experimental parameters are summarized in Table
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