Effect of Sampling Line Characteristics on the Dynamic Monitoring of

Apr 21, 2009 - To whom correspondence should be addressed. Tel. ... Fax: (520) 626-5397. ... The sampling line simulator can be used to analyze the ef...
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Ind. Eng. Chem. Res. 2009, 48, 5481–5488

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Effect of Sampling Line Characteristics on the Dynamic Monitoring of Fluid Concentrations Harpreet S. Juneja, Junpin Yao, and Farhang Shadman* Chemical and EnVironmental Engineering Department, UniVersity of Arizona, Tucson, Arizona 85721

A novel approach is developed and demonstrated to characterize the sampling line effects during dynamic monitoring of fluid concentrations. The “sampling line” in this study refers to all components between the point of fluid sampling and the point of analyzer sensor. In general, sampling lines introduce errors in measurements by altering the sample properties due to the fluid transport in the line as well as the adsorption and desorption of fluid constituents on the surfaces of the sampling components that come into contact with the sample fluid. A methodology based on a sampling line simulator is developed for taking these effects into account and correcting the measurements. The model is validated by direct experimental measurements using several different analyzers under various conditions. The sampling line simulator can be used to analyze the effect of various sampling configurations and operating conditions; this would be helpful in the design of sampling lines and their location. An algorithm is proposed that can be used to convert concentration values measured and reported by the analyzer to the concentration values at the point of sampling that are the actual and desired values. Introduction The online monitoring of the chemical composition of fluids in transport pipes and processing chambers is typically accomplished by two general analytic techniques: one is placing an in situ sensor exactly at the point of measurement; the second is diverting and transferring a small portion of the fluid to the analytical instrument by using a sampling line. Application of the first technique, while ideal in concept, is limited to relatively few analytical techniques such as some in situ optical methods. Most available analytical instruments, however, cannot be placed at the point of measurement either because of the configuration and size of the sensor or due to the undesirable interference that such a placement will have with the system that is being monitored. Therefore, the most widely used technique involves the second technique, in which a sampling line is used. The effect of this kind of sampling on the analysis is not only due to the sampling line that brings the sample from the measurement point to the analytical instrument, but is also due to all components that exist between the point of sampling (PoS), where measurement is supposed to be made, and the point of analysis (PoA), where the sensor is located and the measurement is actually made. As shown in Figure 1, these will include the lines, flow and pressure control parts, and other components that are an integral part of and usually inside the analytical instrument between the analyzer inlet port and the analyzer sensor. This entire assembly which includes all components between the PoS and the PoA (including all components outside or inside the analytical instrument) is referred to as the sampling line in this paper. The effect of the sampling line on the analysis of sample properties is basically due to the fluid transport effects (dispersion and residence time) in the line as well as the adsorption and desorption of fluid constituents on the surfaces of the sampling line parts that come into contact with the fluid.1 In general, in a transient process, adsorption of a species will lower its concentration in the fluid phase and result in the PoA concentration being smaller than the PoS concentration.2,3 * To whom correspondence should be addressed. Tel.: (520) 6216052. Fax: (520) 626-5397. E-mail: [email protected].

Desorption, on the other hand, has the opposite effect and will result in the measured value at the PoA being higher than the concentration at the PoS.4-8 These errors and alteration of composition by the sampling line are not present during steadystate operations when all components come to equilibrium with the sampled fluid. Under these dynamic equilibrium conditions, adsorption and desorption occur at exactly equal rates and hence have no net effect.9 However, in general and under time-varying process conditions, relating what is measured to what one is trying to measure is far from trivial: the correction cannot be accomplished by a general calibration. The differences between the two values and the effects caused by the sampling line are significant, in most cases involving transient conditions and nonequilibrium sampling, particularly in applications with ultrapure systems. This research is aimed at providing a methodology for detecting and analyzing the sampling line effects during online monitoring of fluid concentrations. To validate this analysis, the sample line effect during purging and cleaning of dielectric oxides during semiconductor processing is used as the model case study. Purging processes are intrinsically transient, and they require control of very low level contamination of molecular contaminants such as moisture and volatile organic compounds.10 Experimental Approach The experimental setup designed and used for studying the effect of the “sampling line” on fluid concentration measure-

Figure 1. Schematic of a typical sampling line consisting of tubing as well as components (valves, regulators, etc.) between point of sampling (PoS) and point of analysis (PoA).

10.1021/ie8016169 CCC: $40.75  2009 American Chemical Society Published on Web 04/21/2009

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Figure 2. Generic sampling line configuration.

ments consists of three parts: the first part is the signal generation part, which generates the concentration that is being sampled and is to be monitored (the PoS concentration). In this setup the system to be monitored is the purge chamber that contains the dielectric samples which are undergoing purge and outgassing. The second part is the sampling line, which takes the sample from the PoS to the PoA. Finally, the third part is the analyzer/sensor where the actual measurement is conducted and the PoA signal is recorded. The generic and general sampling line configuration is illustrated in Figure 2. Two types of experiments are conducted on this experimental setup. In the first set of experiments, the behavior of the sampling line is characterized by a detailed and systematic study of the processes that take place in the sampling line. For these experiments, the sampling line is exposed to a step change in concentration, generated by the sample source at the PoS (step change from the purge level to a challenge level) for the selected compounds. The response of the sampling line to this step input is monitored until the system comes to equilibrium with the challenge species. Once the system reaches its equilibrium, the feed is switched to purge; during this stage, isothermal desorption takes place. Similar experiments are performed for a wide range of challenge concentrations at the temperatures of interest. In the second type of experiments, different types of PoS profiles (both transient and steady state) are generated at the sample source section over a wide range of concentrations and temperatures. These PoS profiles represent the concentration that is to be monitored. The signal will be changed in the sampling line as the sample is sent from the PoS to the PoA. Figure 3 shows the actual experimental setup; the details are given in our earlier publications.9,11,12 The model impurity compound used in this study was moisture; the inert purge gas was nitrogen; the experiments were performed using moisture concentration from 0.5 to 1500 parts per million (ppm) over temperatures ranging from room temperature to 380 °C. Some experiments

Figure 3. Schematic diagram of the experimental setup.

were also performed with isopropyl alcohol (IPA) in a concentration range from 150 to 1500 ppm at room temperature. The analytical instruments used at the PoA were an atmospheric pressure ionization mass spectrometer (APIMS), a cavity ring down spectroscope (CRDS), and an electron impact mass spectrometer (EIMS). APIMS has the ability to detect moisture in the parts per trillion (ppt) range, CRDS can detect moisture in the sub-parts per billion (ppb) range, while EIMS detects moisture from ppm to percentage level.9 In all the systems (APIMS, CRDS, and EIMS) the sampling line consists of the line that brings the sample from the PoS to the analyzer, as well as the internal tubings, and flow control elements inside the analyzer. In addition to these components, the sampling line in CRDS has a filter, and in EIMS has the inlet capillary. In order to characterize these two different sampling systems (CRDS and EIMS), experiments were performed for moisture concentration ranging from 0.5 to 1500 ppm at room temperature (25 °C), using nitrogen as purge gas. APIMS can be characterized in a similar way. Sampling Line Simulator A process model is developed for the generic sampling line system, as shown in Figure 2. This model provides the process link between the PoS and the PoA and allows us to calculate one from the other. In general, it is relatively simple to calculate a concentration temporal profile at the PoA, if the profile at the PoS is given and the properties of the sampling line are fully known and specified. However, since numerical calculations use the given boundary condition at the inlet of the sampling line and progress is the direction of flow, it is not straightforward to do the reverse and calculate the profile at the PoS, if the PoA profile is known. The second case is what is required in practice since in general the PoA is the measured (known) profile and the PoS is the desired (unknown) profile. The sampling lines are typically long tubes; the effect of other components in this line can also be represented by their equivalent pipe length. For some cases, different components in a sampling system have significantly different properties. These sampling systems can be best represented by a series of sections; each section is modeled as described here but with its

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Figure 4. Response of different sampling line configurations to a step down change in PoS.

own set of parameters. Using this approach, the entire sampling line is represented as a nonideal tubular chamber in which the analyte is affected by various transport mechanisms (convection and dispersion) as well as adsorption and desorption on chamber surfaces. This model is representative enough to account for most sampling line configurations. The conservation equation for the analyte in the sampling line fluid phase is as follows: As ∂c ∂c ∂2c ) -u + DL 2 + [kdcs - kac(S0 - cs)] ∂t ∂x LA ∂x The initial and boundary conditions for a purge process are I.C.: B.C.1:

t ) 0, c ) cin x ) 0, uc0 ) uc - DL

∂c ∂x

∂c ∂c ) uc or )0 ∂x ∂x where c is the species concentration in bulk gas; cin is the challenge concentration of the species; c0 is the purge gas species concentration, which is assumed to be zero; t is the time; u is the velocity; DL is the dispersion coefficient; A is the crosssectional area of the dispersion reactor; L is the equivalent length; As is the exposed surface area for adsorption/desorption of species; kd is the desorption rate coefficient; cs is the concentration of species on the surface; ka is the adsorption rate coefficient; and S0 is the number of active surface sites. DL, A, L, As, ka, kd, and S0 are model parameters. The conservation equation for the analyte adsorbed on the sampling line surface is as follows: B.C.2:

x ) L, uc - DL

∂cs ) -[kdcs - kac(S0 - cs)] ∂t The initial condition for a purge process is I.C.:

t ) 0, cs ) cs0

where cs0 is the concentration of the species on the surface that is equilibrated with cin. Results and Discussion Significance of the Sampling Line Effect. Figure 4 shows the normalized response (normalized values of the PoA) for three analyzers (APIMS, CRDS, and EIMS) when the inlet to

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Figure 5. Error in monitoring a ramp input concentration.

the sampling line (PoS) was dropped from a finite value to zero at time zero. The response delay due to sensors alone in these analyzers is negligible. Therefore, the observed lag in response is essentially entirely due to the sampling line effect. As expected, the sampling effect is different for different systems. However, in all cases the contribution of the sampling line is very significant. There is about 12-15 min of delay to get 90% response and about 25 min of delay to get 95% response. “Response” here refers to the value of the PoA as a fraction of the PoS value. The sampling line effect is particularly important for fast changing (highly transient) signals. To illustrate this, a linear ramp input signal, which is represented by the equation PoS(t) ) mt, was introduced at the sample source. The response to this signal as measured by CRDS at the PoA and the error due to the sampling line were evaluated. In particular, the error in the signal is represented by the root-mean square (RMS) of the difference between PoA and PoS: RMS(PoA - PoS) ) [(PoA - PoS)2]1/2 is determined as a function of the parameter m, which is the measure of the rate of change in the input signal. Figure 5 shows that the rms is a strong function of m and increases as the rate of change in signal with time (degree of transience) increases. In fact, in the extreme situation, when the signal is steady and constant with time, the sampling line error approaches zero. Characterization of Sampling Line. The sampling line model developed in the previous section is useful in characterizing the sampling line and in making the appropriate correction to the measured PoA. To use this model, some of its key parameters need to be characterized first. This is done by comparing and fitting the model to the experimental data. Figure 6 is the result of this model application for the EIMS analyzer. The experimental results are for a step down concentration of 150 ppm at 25 °C. The model fits the experimental data well. This indicates that the model’s fundamental assumptions and characteristics are correct. The parameters found for one concentration fit when the concentration is changed as shown in Figure 7. Figure 7 shows the application of the model to experimental results for an organic contaminant (isopropyl alcohol; IPA). Experiments were conducted for two different step down input signals (magnitudes of 820 and 1500 ppm) at 25 °C on the EIMS. First, the model was fitted to experimental data at the PoA for the 820 ppm signal. Then, utilizing the coefficients found from fitting the model to the 820 ppm signal experiment,

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Figure 6. Model fit to experimental results.

Figure 7. Application of the process model to experimental results for an organic contaminant.

the model was used for another experiment to calculate the PoA for a 1500 ppm magnitude step down. Application of the Model to Correct for the Sampling Line Delay. Once the sampling line model is developed and calibrated, it can be used to correct for the sampling line effects and obtain the true and desired measurements (PoS) from the reading of the analyzer (PoA). Basically there are two ways to find the PoS, for a given PoA. The method of choice depends on the type of information available for a given system. These methods are as follows: Method A: Assume a reasonable mathematical functional form for the desired PoS (polynomial, exponential, etc.) with unknown function parameters (constant coefficients). Then use the PoS function as the inlet boundary condition and find the parameters in the PoS function that give the best fit to the known and given PoA data. Method B: If the system generating the PoS has an operational model with unknown parameters, link that model to the sampling line model; then solve the two model equations simultaneously to fit the output to the PoA. The simultaneous solution will give information on the PoS. An example of method A is shown in Figure 8. A mathematical function containing two exponential terms is assumed for the PoS. This PoS function when clubbed together with the sampling line model gives a good fit of the PoA to experimental data.

Figure 8. Example of application of method A to correct for error in experimental measurements.

Figure 9. Example of application of method B to correct for error in experimental measurements.

An example of the use of method B is given in Figure 9. In this case a model for a sample source system was available to determine the PoS and was linked with the sampling line model. The model for the source is that of a reactor containing samples of low-k dielectrics which are undergoing purge and outgassing; the detailed description of this reactor and its model is given in our earlier publications.9,11,12 In Figure 9, the experimental results are at 25 °C for the EIMS analyzer setup, as shown in Figure 2. The input for the system was a step down function. The magnitude of the step down signal was 1500 ppm. The linked reactor and the sampling line model (method B) gave a very good fit to the experimental data. The method allowed prediction of the actual PoS (desired concentration as shown by a line). The results also show a significant difference between the PoA and the PoS profiles. This difference confirms the significant error that is introduced by the sampling line that is corrected using the described method. Parametric Study of the Sampling Line Effects. Using the sampling process model, the effect of various configuration and operational parameters of the sampling line can be analyzed. These results would be helpful in designing the sampling line and also in the selection of its operating conditions to minimize the signal delay in a transient process due to the existence of the sampling line.

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Figure 10. Effect of sampling line temperature on PoA.

Figure 11. Effect of sampling line volume on PoA.

An important operational parameter is the temperature of the sampling line. Figure 10 illustrates this effect for the case of moisture as measured by CRDS. As the temperature is increased from 25 to 100 °C, the profile at the PoA moves toward the profile at the PoS. Increasing the temperature of the sampling line system decreases the adsorption of species on the surface of the sampling line and hence decreases the error, where the error is the difference between the PoS and the PoA. This approach can be used for practical purposes to minimize the sampling line effect if the sampling lines can be heated. Figure 11 shows the effect of changing the total volume of the sampling system. The results are for a step down signal of magnitude 1500 ppm at 25 °C for the EIMS analyzer as per the setup shown in Figure 2. As the volume is decreased, the PoA profile moves toward the profile at the PoS. This is because the residence time as well as the adsorption/desorption of the contaminant on the sampling line decreases. Volumetric flow rate of gas is another key factor that affects the sampling line effect. Figures 12 and 13 show the effect of flow rate on the sampling system. In this parametric study section, the data of Figures 12 and 13 were directly from experimental results; the data of other figures in this section were generated by the sampling process modeling. As the flow rate through the sampling system increases, the dispersion of species decreases; the residence time decreases because the sample gas with higher velocity physically takes less time to

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Figure 12. Effect of sampling line flow rate on PoA.

Figure 13. Effect of sampling line flow rate on PoA.

traverse the sampling system. The decrease in dispersion and residence time in turn causes the PoA to move toward the PoS, thereby decreasing the error. The volumetric flow rate and sampling line volume effects are interdependent and can best be shown as the residence time, defined as the ratio of the volume to the flow rate.13 To illustrate the residence time effect, the response time to a step signal input is analyzed. The results are shown in Figure 14. In this figure, the response time refers to the amount of time it takes the error (difference between the PoS and the PoA) to reach less than 1% or 5% or 10%. Increasing the residence time increases the response time. The results are for a step down signal of magnitude 3300 ppb at 25 °C for the CRDS analyzer as per the setup shown in Figure 2. Another illustration of the effect of residence time is shown in Figure 15. In this figure the system response is shown for the case where a short perturbation was introduced at the PoS. The results show that the signal modification and the error in measured perturbation increase as the sampling line residence time increases. A key parameter in the design and setup of a sampling system is the length of the sampling line. Figure 16 shows the effect of changing the length of the sampling line. The results are for a step down profile in the PoS from magnitude 1050 to 0 ppb at 25 °C for the CRDS analyzer as per the setup shown in Figure 2. The effect of length on the PoA is primarily due to the change

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Figure 14. Effect of sampling line residence time on response time.

Figure 17. Effect of sampling line surface site density on PoA.

Figure 15. Effect of sampling line residence time on PoA.

Figure 18. PoA profile for different materials for sampling line system.

Figure 16. Effect of sampling line length on PoA.

in the surface area available for adsorption of species on the sampling system walls.14,15 Figure 17 shows the effect of the surface site density of the sampling lines. Increasing surface site density increases the number of available sites for the molecules to adsorb or desorb; consequently, larger signal change is caused by the sampling

lines. The results are for a step down signal of magnitude 1050 ppb at 25 °C for the CRDS analyzer as per the setup shown in Figure 2. The sampling line material and particularly its surface have significant effects on the alteration of the PoS signal. Changing the material changes the adsorption/desorption rate constant as well as the total surface sites available for reaction. Figure 18 shows the signal profile for a step down input of magnitude 1050 ppb at 25 °C for the CRDS analyzer as per the setup shown in Figure 2 for three different materials.16 The results show that the delay due to a quartz surface is greater than those due to the other two surfaces (stainless steel and materials in CRDS components). This is because the adsorption rate constant of moisture for a quartz surface is greater than those for the other two surfaces. Therefore, the effect of adsorption/desorption is larger for the quartz surface. Representation of Components in the Sampling Line. The sampling system often is more than just a straight tubing and includes components such as valves, regulators, and filters. In this work and the approach developed here, all components are represented by their equivalent sampling line lengths. As an example, CRDS has an internal particle filter which has a large surface area. The adsorption of moisture on the filter is significant and may mask any moisture adsorbed on other parts of the sampling system. Figure 19 shows the experimental and process model results

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Figure 19. Determination of equivalent length for sampling line components.

when the equivalent length for the particle filter is 0.5 m. The process model fits well to experimental results. Conclusions A methodology for detecting and analyzing the sampling line effects during online monitoring of fluid concentrations has been developed. The sampling line includes the lines, flow and pressure control parts, and other components that are an integral part of and usually inside the analytical instrument between the analyzer inlet port (point of sampling) and the analyzer sensor (point of analysis). A process model is developed for the generic sampling line system. This model provides the process link between the point of sampling and the point of analysis and allows us to calculate one from the other. The model is validated using detailed experiments, including different configurations of the sampling line, different concentrations and temperatures, and different interacting species, which provide information on the characterization of the sampling system. Model predictions agree well with the experimental data; the analysis provided useful information on the values of the sampling line process model parameters. While the approach developed here is generally applicable, the parameters in process model equations should be selected to fit the specific sampling line configuration. The parametric study shows the effects of different process parameters, namely the temperature, the total volume of the sampling system, the purge gas flow rate, the residence time, and the surface site density, on the change in the profile of PoS. Increasing the temperature, decreasing the total volume of the sampling line, decreasing the residence time, and decreasing the surface site density minimize the effect of the sampling line and decrease the error difference between the PoS and the PoA. Acknowledgment The authors thank the SRC and Sematech for partial support of this research through Engineering Research Center for Environmentally Benign Semiconductor Manufacturing. Partial support from Tiger Optics LLC is also acknowledged here. Appendix: A Practical Application Algorithm Step 1: Generate a known input signal at the PoS using a known source. Step input is a good choice since it is easy to generate. Step 2: Measure signal at the PoA.

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Step 3: Compare the PoS and the PoA, to estimate the significance of sampling line effect and the need for correction. Step 4: To characterize the sampling line, carry out experiments to generate several temporal profiles of the PoA for given temporal profiles of the PoS. Estimate the sampling line parameters by fitting the model developed here to these pairs of corresponding PoS/PoA profiles. For relatively simple sampling lines (such as stainless steel tubings), some of the parameters needed to characterize the line (such as adsorption/ desorption rate parameters) are available in the literature. Step 5: Once the sampling line is characterized, there are primarily two ways to calculate the PoS, for a given PoA in any future uses of the system: Either assume a reasonable mathematical functional form (which contains adjustable parameters to be determined) for the PoS or, if the system generating the PoS has an operational model, link that model to the sampling line model. Using one of these two approaches, solve the sampling line process model developed above to fit the data in hand (given the PoA). This fitting process will give the desired PoS profile. Notation A ) cross-sectional area of dispersion reactor As ) exposed surface area for adsorption/desorption of species c ) concentration of species in bulk gas cin ) challenge concentration of the species cs ) concentration of species on the surface c0 ) purge gas species concentration DL ) dispersion coefficient ka ) adsorption rate coefficient kd ) desorption rate coefficient L ) equivalent length of the sampling line PoA ) point of analysis (sensor location, measured concentration) PoS ) point of sampling (desired concentration) S0 ) number of active surface sites t ) time u ) velocity x ) position on the sampling line

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ReceiVed for reView October 23, 2008 ReVised manuscript receiVed March 7, 2009 Accepted March 27, 2009 IE8016169