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Drying Technology: An International Journal Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/ldrt20
METHODS FOR PROCESSING EXPERIMENTAL DRYING KINETICS DATA a
a
c
d
b
b
Ian C. Kemp , B. Christran Fyhr , Stephane Laurent , Michel A. Roques , Carda E. e
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Groenewold , Evangelos Tsotsas , Alberto A. Sereno , Cathenne B. Bonazzi , Jeanf
Jacques Bimbenet & Mathhues Kind
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a
AEA Technology, SPS (Separation Processes Service), 404 Harwell, Didcot, U.K.
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University of Pau, France
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University of Magdebg, Germany
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University of Magdeburg, Germany
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University of Porto, Portugal
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ENSIA, Massy, France
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University of Karlsruhe, Germany Published online: 06 Feb 2007.
To cite this article: Ian C. Kemp , B. Christran Fyhr , Stephane Laurent , Michel A. Roques , Carda E. Groenewold , Evangelos Tsotsas , Alberto A. Sereno , Cathenne B. Bonazzi , Jean-Jacques Bimbenet & Mathhues Kind (2001): METHODS FOR PROCESSING EXPERIMENTAL DRYING KINETICS DATA, Drying Technology: An International Journal, 19:1, 15-34 To link to this article: http://dx.doi.org/10.1081/DRT-100001350
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DRYING TECHNOLOGY, 19(1), 15–34 (2001)
METHODS FOR PROCESSING EXPERIMENTAL DRYING KINETICS DATA Ian C. Kemp,1,∗ B. Christran Fyhr,1 Stephane Laurent,2 Michel A. Roques,2 Carda E. Groenewold,3 Evangelos Tsotsas,3 Alberto A. Sereno,4 Cathenne B. Bonazzi,5 Jean-Jacques Bimbenet,5 and Mathhues Kind6 1
SPS (Separation Processes Service), AEA Technology, 404 Harwell, Didcot, U.K. 2 University of Pau, France 3 University of Magdeburg, Germany 4 University of Porto, Portugal 5 ENSIA, Massy, France 6 University of Karlsruhe, Germany
ABSTRACT This paper provides a review of methods for processing the data obtained from drying kinetics rigs and pilot-plant trials. Different methods for fitting and smoothing drying curves are compared, aiming to generate curves that are usable in industrial design without losing vital information by oversmoothing. Generally, plots of drying rate need more smoothing than moisture content data. Special care is needed at low drying rates and moisture contents. It is shown that some popular methods of processing data, including use of smoothing programs or fitting to equations, may generate drying curves which are seriously in error. Recommendations are made for reliable methods of processing data; cubic splines have been found ∗
Corresponding author. E-mail:
[email protected] 15
C 2001 by Marcel Dekker, Inc. Copyright
www.dekker.com
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to be effective for moisture–time curves. It is important to retain the original raw experimental data as a cross-check, as smoothing can conceal valuable information. Key Words: Drying curve; Rate data; Smoothing; Recommended methods. INTRODUCTION Numerous articles have appeared describing experimental apparatus to record drying kinetics and even more numerous papers that present results from such experiments. However, the mundane but important subject of how to process the experimental data in the most reliable way has received relatively little attention. The data obtained from drying kinetics experiments typically contains inaccuracies, spurious points, and noise. It is important to remove these and obtain a smoothed curve that can be used for design purposes. However, important information must not be concealed. In particular, oversmoothing or using the wrong method may conceal or distort information, which may lead to substantial errors in the design of a full-scale dryer. The Council of the European Communitities (CEC) has funded eight European research laboratories to work together in drying in the QUID (Quality in Drying) project. Participants are the Universities of Lund, Eindhoven, Karlsruhe, Magdeburg, Pau, Porto, and ENSIA-Massy, and AEA Technology plc. In the course of this work, it was necessary to understand the different methods used for processing the data. The methods used for one type of drying experiment may be inappropriate for another. Nevertheless, a reasonable consensus was reached and is presented here. It is hoped that this will be of use to drying researchers worldwide in giving a unified approach to the reporting of data. In particular, it is hoped that this will present an easy guide to best practice for researchers who are new to the field of drying. METHODS OF OBTAINING DRYING KINETICS DATA There are three principal methods of obtaining drying kinetics data: 1. Periodic sampling or weighing. A sample may be extracted at intervals and its moisture content determined by laboratory methods, or the entire sample of material may be weighed and then reintroduced into the drying apparatus. These methods are slow and tend to give very few points on a moisture–time graph. 2. Continuous weighing. A sample is mounted on a microbalance, or an accurate balance suspended in a drying tunnel, and its weight is recorded
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continuously. This gives a much larger number of points on the moisture–time graph. However, the small changes in weight involved can be concealed by random noise, e.g., due to vibration of the sample in the airstream. 3. Intermittent weighing. The sample is mounted on a balance in an air stream as above, and, at intervals, the airflow is cut off or diverted, so that an accurate weight reading can be obtained when the system has stabilised (which takes a few seconds). It has been found that this does not affect the kinetics unless drying times are very short (a few minutes). 4. Indirect methods. The rate of water vapour evolution can be measured, e.g., by measuring the air humidity emerging from the sample chamber, using an infrared gas analyser or simular apparatus. The rate of moisture loss is then back-calculated. The best choice from these approaches will depend on many factors; particle size, initial and final moisture content, predominant drying regime (unhindered or falling-rate), air velocity, level of accuracy required for the data, and availability of measurement equipment. The configuration of the drying apparatus is also important. Tests can be done on single particles on a microbalance or in a drying tunnel, or on thin layers, medium or deep beds, the latter using cross-circulation, through-circulation, fluidisation or conduction heating. In general, on a larger scale, the signal is stronger (bigger weight change or higher outlet humidity), but information is concealed because the data is the average from a large number of particles rather than a few. For beds and thick layers, it is difficult or impossible to ensure that all the particles have the same temperature and exposure history. Even for thin layers, some scaledown is necessary to obtain a fundamental drying kinetics curve, and this is difficult to do reliably (1). The recording method and the size of the sample affect the method to be used. For fundamental single-particle kinetics, as recorded in the Magdeburg drying tunnel, the signal-to-noise ratio is weaker and the moisture–time curve shows considerable random scatter. For bulk drying experiments and slow drying materials, the weighing can be more accurate and is less susceptible to vibration, so the initial curve can be quite smooth. However, less information is obtained on the fundamental kinetics because of the higher number of transfer units (NTUs). During recent work in the QUID project, results from single and multiple particle tests in the University of Magdeburg drying tunnel have been compared with thin-layer tests at SPS at Harwell (2). The drying curves obtained were broadly similar but the critical moisture content was higher for the thin-layer tests because the rig uses a higher velocity. (Low velocities make layer effects worse in a thinlayer test, as the number of transfer units increases. Conversely, high velocities gave too much vibration and signal noise in the drying tunnel.) The thin-layer
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test may thus be more representative for particles experiencing a higher relative velocity in an industrial dryer, e.g., particles above 1 mm diameter in pneumatic conveying and cascading rotary dryers. Conversely, the single particle test might seem more appropriate for small particles at low relative velocity. Unfortunately, particles this small are very difficult to suspend effectively in an airstream and this problem is not yet fully resolved. If a fundamental single particle drying kinetics curve can be obtained, it can now be scaled up effectively to fluidised bed kinetics curves (3–5). Small particles can be studied in fluidised bed or deep layer tests, but these give markedly different drying kinetics curves to single particles due to layer effects, even when the drying is falling-rate (6). The effect is less marked for large particles, e.g., food; drying is mainly falling-rate, and the number of transfer units (NTU) is small.
TYPES OF DATA TO BE PROCESSED There are several important points to consider initially: 1. Form of the data. The major distinction is whether the raw data is in the form of moisture content data (e.g., from continuous weighing rigs or direct moisture measurement) or humidity data (e.g., from infra-red gas analyzers). The former is more common. 2. Quality and quantity of the data. There may be very few points (e.g., from periodic sampling methods), or a large number (hundreds or thousands) from a computer data logging system. Likewise, the data may be fairly smooth or include significant random scatter. 3. Methods used to process the data. Questions include the type of curve or equation to fit to the data and whether to do smoothing before or after curve fitting. There are a number of useful curves that are interrelated: a. Drying curve—moisture content vs. time. (X vs. t). Obtained directly from weight loss-time data. Integral of (b). b. Drying rate curve—drying rate vs. time. (−dX/dt vs. t, or N vs. t). Obtained directly from humidity–time data. Differential of (a). It tends to be much more jagged than the moisture content curve, with lots of random variation. c. Time-independent or Krischer curve—drying rate vs. moisture content. (−dX/dt vs. X , or N vs. X ). Usually derived from the combination of (a) and (b). This curve is used as the basis for the characteristic curve scaling method.
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Figure 1. Drying rate and temperature curves for a particle in a crossflow dryer.
d. Temperature-time plot—shows how the sample temperature varies during the experiment. Figure 1 shows the four interrelated curves obtained by simulation of a single particle undergoing convective drying in a hot air stream at a constant 150◦ C. Under the chosen conditions, this material is assumed to show an induction (initial heating) stage, an unhindered drying (constant rate) period, and a hindered drying (falling rate) period. It is useful and, indeed, common, to interconvert between the three different types of drying curve. For example, a set of moisture–time data (a) may be recorded in an experiment. This batch drying curve is then differentiated to give the drying rate-time curve (b), and the Krischer rate–moisture curve (c) is then produced by combining the other two curves. A characteristic curve (7,8) can then be fitted to the data from the Krischer curve. If it is now desired to design a dryer at different inlet conditions, the new maximum drying rate is calculated from external heat and
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mass transfer considerations, and a new Krischer curve is produced by scaling up the batch drying curve. By taking the inverse of the drying rate, a moisture–time curve for the new conditions can be generated, and the required time to dry from the initial moisture content to the desired final moisture can be read off from the graph. In general, it is found that the moisture–time plot is smoother than the ratetime plot. Even if the moisture curve is fairly smooth, the rate curve obtained by differentiation will usually have a significant amount of random noise (see the experimental plots later in this paper). It is often desirable to smooth the data to make the rate curve less jagged. If the original moisture–time plot is not smooth (because it consists of a small number of samples), it will be essential to perform some sort of smoothing in order to obtain any meaningful rate curve at all. The signal-to-noise ratio becomes worse towards the tail of the drying curve (low moisture content and drying rate, long drying times) and, in the Krischer curve in particular, the data points at low rate and low moisture content are very close together. This makes it dangerous to back-calculate estimated drying times from this part of the curve, as it involves dividing by a small number (i.e., the drying rate) and the possible absolute error is large. For example, Fyhr and Kemp (9) used a simple power-law characteristic drying curve to approximate a complex rate-moisture curve obtained from an advanced model, and then back-calculated the moisture–time curve. The results are shown in Figure 2. Over most of the range, the approximation is indistinguishable from the original curve; if a drying time were read from either curve, the values would be within 2% of each other. However, at the bottom end, the curves diverge sharply; the time to dry to X = 0.02 would be read as 110 s from the characteristic curve but is 200 s in reality, which would lead to a seriously undersized dryer. The error becomes even worse at lower moisture contents. This is not because the characteristic curve model is faulty, but because the fit to the data at the bottom end was poor. If the data below φ = 0.1 were refitted with a further power law curve, the CDC result would again become very close to the results from the advanced model.
Figure 2. Effect of an approximate data fit on rate-moisture and moisture–time curves.
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PROCESSING OF WEIGHT-LOSS AND MOISTURE–TIME DATA Possible methods for dealing with a moisture–time curve include the following: a. Use the raw data directly. This is helpful if one has only a few data points, e.g., after an oven test with limited and infrequent sampling so that there are only 5 to 10 data points. This method can also be used if an accurate weighing method has been used on a reasonably sized sample or over a very long period of time, so that there is little or no random scatter. b. Use the raw data, but remove outlying points, which are likely to be spurious. c. Use the raw data, remove outliers, and also any points whose moisture content is greater than for the previous point. This is needed to eliminate possible multiple solutions in computer algorithms looking for a drying time for a given moisture content. d. Use a simple averaging method over a number of adjacent points to produce a piecewise curve. e. Use the averaging method, produce the piecewise curve, and then refine by removing any outlying points which lie too far from the curve. f. Smooth the curve using a cubic spline fit over a number of adjacent data points. A number of alternative spline fits may be tried, based on different numbers of points. The best fit is most easily found by taking the differential (gradient) of the curve, as discontinuities in the gradient show up much more clearly than poor fits on the moisture-content points. This also guarantees that the derived rate-time curve will be smooth. g. Smooth the curve using a second degree polynomial on successive points (five is a typical value). This is similar to the above method but with a different curve form; adjusted values for moisture content X of the median point and derivative dX/dt are computed for each experimental point (special treatment is used for the first and last points). h. Fit the curve to an equation of a likely theoretical form. For example, a linear fall followed by a falling exponential, or a double exponential (product of two exponentials), has been used, but with only limited success (this form of equation implicitly assumes a first-order falling rate period). A further section is needed at the start for the induction period. i. Use a conventional curve-fitting program to fit a variety of possible curves to the drying curve and choose the best-fit shape. This will often be a polynomial or rational fraction. Data may be smoothed first using
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programs such as TableCurve and MS-Excel’s Trendline function. There will be no real theoretical basis for such a fit; it is simply a correlation. j. Develop a drying model for the particular material (which may include allowances for NTUs, etc.), and fit the data to adjustable parameters in the model. This is particularly effective for families of materials that can be expected to fit a given model, e.g., various foods. The drying rate-time and rate-moisture curves must now be derived from the moisture–time curve. This is usually done by numerical differentiation e.g., by a finite-difference method. The rate curves are often much more jagged than the moisture–time curve, and it may be useful to resmooth to give an acceptablelooking curve. Figure 3 shows a drying curve for silica gel, obtained using a thin-layer kinetics test. It has been successfully smoothed using a cubic spline. The derivative of the curve has also been calculated, and this indicates the shape of the drying rate curve. There is some noise, especially at the lower end, but the curve is smooth and the fit is good. In contrast, Figure 4 shows a curve that has been undersmoothed (the rate curve is still jagged) and one that has been oversmoothed (the rate curve is very smooth, but the fit to the original moisture content curve is now poor). In practice, it is often best to smooth the rate–time curve separately, addressing only the areas where there is a clear deviation (e.g., beyond about 40 s in the curves in Figs. 3 and 4). Figure 5 illustrates the effect of attempting to fit the curve to
Figure 3. Moisture–time curve smoothed by cubic spline fit.
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Figure 4. Undersmoothed and oversmoothed drying curves.
equations with a falling exponential tail (corresponding to first-order kinetics). The equations fail totally to allow for the induction period, but are also a poor fit generally, despite their reasonable theoretical basis. The more irregular the moisture–time curve, the more smoothing is necessary before trying to calculate drying rates. Figure 6 shows data obtained from a
Figure 5. Drying curve fitted to theoretical equation forms.
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Figure 6. Smoothing of direct weighing data from drying tunnel experiment.
direct-weighing experiment of a small mass of particles in a drying tunnel. The signal-to-noise ratio is low and there is some evidence of a regular periodic oscillation. However, this data has again been successfully smoothed by a spline fit. This was helped by removing obviously erroneous outlying points from the data before performing the final fit. Figure 7 shows a drying curve for paddy rice, obtained from a thin layer drying experiment with periodic direct weighing of the entire sample and temporary deviation of the drying air. It has been successfully smoothed using a sliding polynomial, and the rate-time curve has been derived at each point from the corresponding polynomial. There is some noise in the rate-time curve due to the very low drying rate, but the moisture content at each point is very close to the raw experimental one. Case Study on Curve Smoothing The following example, illustrating the difference between the results obtained by handling the same data by different smoothing techniques, was developed by the University of Pau. Figure 8 shows a drying curve obtained by a continuous weighing technique. The moisture–time curve appears smooth. However, on differentiating the curve to give the rate-time plot and the Krischer rate–moisture plot (Fig. 9), it is clear that there is some scatter on the
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Figure 7. Drying curve for paddy rice smoothed by second order polynomial.
Figure 8. Experimentally recorded moisture–time curve.
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Figure 9. Drying rate data obtained by differentiation, unsmoothed.
data. There are significant random variations near the moisture peak and the bottom part of the curve shows a good deal of noise. The latter problem occurs because the very low drying rates involved give small changes in recorded weight and moisture content, which are of the same order of magnitude as the noise from vibration of the weighing device. Hence, some smoothing is desirable. The data has been processed in two ways in Figure 10. The first is to draw a line through all the points with a small degree of smoothing by averaging between successive points, also removing any clearly spurious outlying points. This removes the worst of the noise at the bottom end of the Krischer plot. However, there are still substantial variations elsewhere; the line could not be described as smooth. The second method is to fit the line to a suitable equation. In this case, an eighth-order polynomial has been used. This smoothes out both the lower end of the curve and the substantial peaks and troughs at the top end. The question arises, however, whether these peaks and troughs are due to experimental error or are a genuine phenomenon (e.g., due to shrinkage or a change in internal moisture movement mechanism). If the latter is the case, use of the smoothed curve will conceal valuable information. A third method which could be tried is to make use of drying theory and to plot the section between X = 2.5 and X = 3.3 as a horizontal line (a constant rate period), then fitting one or more polynomials to the remainder of the curve (falling rate period). In this case, it is very difficult to fit a curve effectively to the sharp dip around X = 2.2. Figure 11 shows the effect of fitting a simple straight line for the falling rate period (first-order kinetics or drying coefficient analysis)
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Figure 10. Rate data smoothed by piecewise approximation and polynomial fit.
and a characteristic curve (approximated in this case by two power-law sections with smooth transitions). An alternative method is to fit the data to an equation. The following equation has been proposed as appropriate for this system:
Figure 11. Rate data fitted as constant rate and falling rate sections.
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X¯ (t) = a +
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t −c 1+e d
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1 t −c 2 exp (1 − e) 2 d
Figure 12 below shows the data fitted to this equation by a least-squares method. Clearly a smooth curve has been obtained. However, comparison with the original data above shows that the curve is markedly different from the original data and presents a completely misleading impression of the results of the original experiment; important information has been concealed. An important point from all these items taken together is that, if smoothing is applied, the raw data should always be retained in parallel, to use as a cross-check and to ensure that the smoothing has not distorted some important aspect. For practical dryer design, a common method would be to transform these curves back to the moisture–time form, then find the times from the curve corresponding to the inlet and outlet moisture contents. The required drying time would be the difference between these. Figure 2 showed the effects of inaccuracies in fitting the Krischer curve on the back-calculated drying curve. Small differences have little effect, except at extremely low drying rates and moisture contents. On this basis, if the curves above were transformed back to drying curves, the smoothed curve, the eighth-order polynomial and the characteristic curve (after an initial constant rate period) would give excellent fits to the raw data and an estimate of drying time well within 5%, which would give an accurate dryer design. Using first-order kinetics would give a reasonable fit, whereas fitting to the equation would give a
Figure 12. Rate data fitted to correlation equation.
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very poor fit and a major error in estimated size of the resulting dryer, especially in the early stages of drying at high moisture contents. In summary, some smoothing may be useful to eliminate the noise and random variation in the drying curve, but the raw data should always be retained for comparison. Obviously erroneous outlying points should be removed before smoothing. The best general-purpose smoothing method is probably a cubic spline or localized sliding polynomial. However, overall polynomials and constantrate/characteristic curve fits have also been successful. Simple first-order kinetics may be useful if very limited test information is available. The derived drying rate curve will fluctuate more, and it can be smoothed by methods similar to that recommended below for humidity curves, though Hager et al. (10) recommended retaining the raw data for the drying rate and not smoothing at all. In general, fitting the results to an equation of predetermined form is not recommended. However, if the drying process is definitely known to follow a particular form of kinetics, then an equation may be used. This approach has been used successfully by the University of Porto to process drying kinetics for food materials. In contrast, AEA Technology in early versions of their FLUBED fluidized bed-drying software attempted to fit drying curves with either a linear section followed by a falling exponential, or two falling exponentials combined, as shown in Figure 5. (This form of curve would correspond to first-order drying kinetics). It was found that the fit was often poor, even for materials that were quite close to first-order kinetics.
PROCESSING OF HUMIDITY–TIME DATA Plots of humidity against time are obtained from experimental apparatus such as the SPS drying kinetics rig (11,12), which measure the outlet humidity rather than weight loss. An infra-red gas analyser (IRGA) may be used to give a large number of humidity recordings at intervals of 5 s or less. A mass balance converts this directly to the plot of drying rate against time, and this can be integrated to give the moisture–time plot. It is essential to cross-check the calculated moisture content reduction with experimental values of inlet and outlet moisture content obtained by oven tests. The humidity signal often has some scatter on it, and smoothing will be necessary to give a smooth drying rate vs. time curve. Figure 13 shows a typical plot and Figure 14 shows smoothed and unsmoothed drying rate curves. A Fast Fourier transform has been used for the smoothing. Note, however, that when the data is integrated to form the moisture–time graph in Figure 15, it appears perfectly smooth, whether the rate data is in raw or smoothed form. The recommended method for dealing with a humidity–time curve is as follows.
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Figure 13. Experimentally recorded humidity–time plot.
r Smooth the raw humidity–time data (which usually has a lot of random scatter) using a Fast Fourier transform. A separate smoothing is desirable for the induction period, as otherwise the humidity peak tends to be artificially lowered. r Convert the humidity–time data to drying rate–time data based on recorded gas velocity and mass of solids present.
Figure 14. Drying rate data from mass balance, smoothed and unsmoothed.
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Figure 15. Drying curve found by integration, smoothed/unsmoothed.
r Integrate the rate-time data to a moisture content-time curve and crosscheck against initial and final moisture content obtained from oven tests. The two results should agree to within 5%. The moisture–time curve obtained is usually very smooth if enough humidity data points were recorded. r Plot the rate-moisture curve; no further smoothing should be necessary. Derive a characteristic drying curve if desired. Note that small errors in the inlet humidity can lead to big final errors in the final drying curve, as the drying rate is proportional to the difference between inlet and outlet humidity. Ideally, the inlet humidity will be precisely the same throughout the experiment, but in practice fluctuations or drift may occur. At the tail end, where the difference is small, an incorrect inlet humidity value will lead to a finite
Figure 16. Krischer (rate-moisture) curve, smoothed/unsmoothed.
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calculated drying rate, whereas it should be tending to zero. It is often possible to identify this situation by examining the moisture–time curve derived from the rate data; either it continues to descend gradually with a steady gradient at the end of drying instead of levelling off, or it reaches a minimum and then rises again. In both cases, the curves should be recalculated using slightly different values of inlet humidity.
INTERPRETATION OF THE EXPERIMENTAL DATA This is a huge subject in itself and would require a further paper to cover adequately. Some simple points can be made, however. r The existence, or otherwise, of a constant rate drying period will indicate
r r
r
r
whether the material goes through a heat-transfer-controlled phase, or is limited by internal moisture transport throughout (the latter being more common at high drying intensities). The smoothness of the data obviously gives an indication of the quality of the original experiments. Many materials fit reasonably well to a simple first-order kinetics curve (linear fall on the Krischer plot), especially in the final stages of drying. The intercept on the moisture content axis indicates whether there is a significant equilibrium moisture content. There is rarely, if ever, a sharp transition from constant rate drying (external heat and mass transfer control) to falling rate drying (internal mass transfer control). Normally, the critical moisture content has to be obtained by projection of fitted lines for the two periods to a meeting point which lies slightly above the experimental curve. It is important to remember that nearly all drying curves are distorted from their theoretical form by layer effects, because there are finite NTUs in the experiments. This again tends to give gentle curves and smooth transitions rather than sharply defined horizontal and sloping sections. In particular, it may give an apparent constant rate period that is actually due to saturation of the air passing through the bed; the material itself is in falling-rate hindered drying.
CONCLUSIONS r It is important to choose an appropriate form of drying kinetics test. Single-particle kinetics curves are fundamental, but they are hard to
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measure and need to be adjusted to allow for the geometry of the actual drying system to be used. For all methods, scale-up and scale-down may be required to allow for differences such as bed depth between the experiment and the full-scale dryer. Saturation in thick layers must always be checked for. For processing moisture–time data obtained by a weight-loss method, the best general-purpose method appears to be a cubic spline fit. Humidity-time data may be smoothed, converted to drying rate v. time by mass balance, and integrated to give a moisture–time curve. Don’t discard the raw data—retain it throughout. Whatever method is used, smoothing tends to conceal information. The raw data provides a “sanity check” on any smoothed curve, and any related curves derived from it. Dubious points should be removed or adjusted before fitting. This is preferable to fitting to an equation or using standardized smoothing routines. An equation-based method should only be used if one is confident that the system is definitely going to fit that type of model. Otherwise, the fit can be extremely poor. Certain regions of curves derived from others are inherently prone to error, as they are differences of large numbers or reciprocals of small ones. Particular care is needed when deriving time data from the low-moisture region of the Krischer rate-moisture curve. Wrong results may be obtained even with the right method (e.g., cubic splining), by using too strong a smoothing factor, again concealing information. The human eye is often the best means of fitting the data or, at least, of checking a computer-generated fit to make sure that it looks sensible! The rate data usually has more noise than the moisture-content data, and it is often best to do an initial fit on the moisture–time curve using a cubic spline, followed by smoothing the later part of the drying rate curve separately.
ACKNOWLEDGMENTS This work was carried out under the QUID (Quality in Drying) project funded by the CEC under the ‘Training and Mobility of Researchers’ scheme. The project is coordinated by the University of Lund; other participants are the Universities of Eindhoven, Karlsruhe, Magdeburg, Pau and Porto, ENSIA-Massy, and AEA Technology plc.
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