VERC - A Computation Method to Estimate Moisture Content by Product Weight

- Research Notes -

A Computation Method to Estimate Moisture Content by Product Weight
by
Huai-wen Yang and Matthew Yen

CATI Publication #960901
© copyright September 1996, all rights reserved

I. INTRODUCTION

The accurate measurement of moisture content is crucial for the implementation of any dehydration process. Indeed, it forms the basis for gauging the quality and success of a particular dehydration process (Giese, 1995; Carr-Boin, 1986). Over the years, a large number of instruments and methodologies have emerged for the express purpose of providing an accurate measurement of moisture. One example is the gravimetric method which relies very simply on measuring the weight of a sample both before and after its dehydration, and assigning the difference in weight to moisture content. One of the methods that has been widely used in conjunction with gravimetric methods is oven drying.

Oven drying can be divided into four steps: tare-weighing the drying dish; placing a known amount of sample in the dish; driving the moisture out of the sample and cooling the dish and sample; and finally, determining the moisture content using the difference in weights. Oven drying methods suffer from the disadvantage of being time consuming, which however can be offset by the fact that a large number of samples can be processed simultaneously (Coulate, 1990; Kolar, 1992). Air-oven dryers utilize either air convection or a forced draft of air. The temperature range is from 70 to 155°C, with the exact temperature depending on the test sample. Drying times range from one to six hours, depending on the type of analysis.

Another method applied in gravimetric analysis is the vacuum-oven drying method, which is very useful in the removal of the very last traces of moisture from food material, especially those that are sensitive to high temperatures as is the case for various fruits. The principle behind this method is the lowering of the boiling point - caused by the vacuum - which allows for the elimination of moisture without incurring undue degradation of the sample. It has been shown that the vacuum-oven approach leads to satisfactory and reliable results. Indeed, a 24-hour drying period was deemed adequate under all circumstances for accurate measurement of moisture content (Wilhelm et al.,1 988).

Most of the preceding methods suffer from two disadvantages: They rely on tedious procedure in their implementation; and they are time intensive. To circumvent these problems, a formula has been derived which allows the determination of moisture content in a more facile manner, whereby the only input needed is the initial moisture content in addition to the product weight. Such computation-based approaches can contribute to substantial savings in measurement times in the process of securing reliable moisture content data. This formula has been subjected to experimental evaluation of Grape Puffs^TM from the microwave vacuum process system (MIVAC)

II. ANALYSIS

As mentioned earlier, the initial moisture content (IMC) and the final moisture content (FMC) are important quantities to evaluate in a dehydration process. Determination of moisture content is not only tedious and time consuming, but subject to experimental errors of up to 10 percent. Besides, dehydrated products such as Grape Puffs^TM tend to re-hydrate immediately once they are in contact with the environmental moisture. This may lead overstatements of FMC. Therefore, it is desirable to develop some theoretical values as references. The derivation of such a reference formula is given in the following:

Give a certain sample with initial weight (W_i ) and initial moisture content (IMC), and let it undergo a period of dehydration. The finished sample weight is denoted as W_f and the final moisture content is denoted as FMC. By definition, one may write:
W_i = L_i + S_i and W_f = L_f + S_f (1) and (2) IMC = L_i / W_i and FMC = L_f / W_f (3) and (4)
where L_i is the weight of the liquid or moisture in the initial sample and L_f is the moisture weight of the final product. S_i and S_f are the solid mass weight at the beginning and end, respectively. Applying equation (2), FMC can be expressed as:
FMC = W_f - S_f / W_f or FMC = 1 - S_f / W_f (5)
Assuming that S_i = S_f, that the solid mass weight is a constant throughout the dehydration process, then equation (5) can be re-written as:
FMC = 1 - S_i / W_f (6)
According to equation (1), equation (6) can be expressed as:
FMC = 1 - (W_i - L_i) / W_f (7)
Dividing both the numerator and the denominator of the second term, one obtains the following expression:
FMC = 1 - (W_i /W_i) - (L_i / W_i)/(W_f / W_i)] (8)
Simplifying equation (8) with the aid of equation (3),
FMC = 1 - (W_i W_f)(1 - IMC) (9)
This expression reveals that FMC is a hyperbolic function of the product weight W_f. By setting FMC = 0, this function intercepts the product weight axis and yields
W_f = W_i(1 - IMC) (10)
This is a logical deduction of the assumption, i.e.,
W_f = S_f = S_i

III. RESULTS AND DISCUSSIONS

Experiments were performed to compare the FMC values determined by the vacuum-oven measurement with those computed by equation (9) under three different conditions. The first condition uses seven batches of 2-lb Thompson Seedless grape samples. Each one was dehydrated by the MIVAC system at the power level of 1500 W for periods of 5, 10, 15, 20, 25, 30, and 35 min, respectively. The second condition involves five 1-lb grape samples dehydrated at the power level of 1000 W for periods of 5, 10, 15, 20, and 25 min, respectively. The third condition was four 1-lb grape samples dehydrated at 1500 W for periods of 5, 10, 15, and 20 min, respectively.

The final sample weight (W_f) of each run was determined by a digital balance immediately after the sample was processed. Three grape berries from each batch were randomly selected for the determination of FMC by vacuum oven drying for 24 hr. The IMC was determined in the same way at the beginning of the tests. The FMC of each sample was also computed by equation (9) (FMCC) with the known values of W_i, W_f, and IMC. Tables 1, 2 and 3 summarize the experimental data for three conditions, i.e.: 2 lbs @ 1500 W, 1 lb @ 1000 W, and 1 lb @ 1500 W, respectively. The columns in tables are dehydration time (min.); final product weight (W_f in lb); initial moisture content (IMC in %); vacuum-oven-determined final moisture content (FMCV in %); and computed final moisture content (FMCC in %).

The same data are also presented in two sets of plots: Figures 1-4 show the final weight and final moisture content as a function of time; and Figures 5-7 show the final moisture content as a function of the final product weights.

It can be seen that the final weight decreases linearly with time till the late stage of drying and then tapers off toward a weight corresponding to zero FMC. These zero FMC weights can be computed from equation (10). They are 0.442 lb, 0.168 lb and 0.164 lb respectively. The linear decrement of product weight indicates that moisture removal is at a nearly constant rate throughout most of the dehydration process.

On the other hand, FMC gradually decreases at the early part of the process and then drops rapidly toward the end. This trend is predicted by equation (9) and demonstrated in Figures 4-6 as a hyperbola which intercepts the weight axes at zero FMC weights, i.e., 0.442 lb, 0.168 lb and 0.162 lb.

Table 2 shows that the prediction is extremely accurate to within 3% throughout the test with 1 lb of grapes @ 1000W. In other cases, the computed FMCC and measured FMCV are in good agreement at the early stage of the process to within 5%. Generally speaking, equation (9) tends to underestimate FMC, or, it predicts a lower value of FMC for a given weight. One possible explanation for such underestimation is that the samples are in a state of non-equilibrium while at low moisture level. Thus, they are likely to re- constitute by absorbing atmospherical moisture. If the moisture tests are not conducted immediately after the treatments, then the vacuum-oven determined FMCV may come to be at some value higher than it should be.

Nonetheless, these results are fairly consistent when considering the fact that each berry in the same group can be quite different because grapes are biological products and the constituents in each berry vary considerably.

Variance analyses were also performed for the difference of FMCV and FMCC. It is denoted as c.v.2. The results are shown in Table 4. Thirteen out of 16 (or 81%) samples have a value of c.v.2 less than 5%. Similar analyses were done for the FMCVs, denoted as c.v1, and also included in Table 4. In this case 9 out of 16 ( or 56%) samples have a value of c.v1 less than 5%. This indicates that the computed variance errors are as good as the experimental variance errors or better. In other words, the experimental errors of the vacuum oven measurements are larger than those of the computed data.

IV. CONCLUSIONS

The development of a theoretical reference for FMC has several advantages: It is a quick and efficient way to obtain the FMC data without a long wait - 24 hours to 36 hours in the vacuum oven drying method. Thus, it could avoid potential risk of sample reconstitution or incurring experimental errors.

The weight-determined FMC formula, equation (9), can be applied to products other than Grape Puffs^TM and extended to other dehydration processes aside from the MIVAC. It may be readily implemented for online monitoring for automated processes.

Nonetheless, the discrepancies between FMCC (%) and FMCV(%) as presented in the above need to be studied closely in the future, especially when FMCs are lower than 30%. In case that FMCC were not reliable, future research should take the following directions: (i) Closely examine the validity of the assumption, S_f = S_i. It is likely that S_f _i, but the relationship needs to be quantified; (ii) It is also recommended to perform some regression analysis to generalize equation (9) by including power levels and product attributes.

AUTHORS' NOTE

This publication contains preliminary results and has not undergone peer review.

REFERENCES

Giese, J. 1995. Measuring Physical properties of Foods. Food Tech. 50:2:54-64.

Coultate, T.P. 1990. Food, The Chemistry of Its Components. 292-312. London.

Carr-Brion, K. 1986. Moisture Sensors in Processing Control. pp65-67. Elsver Applied Science Publishers, New York.

Wilhelm, L.R., Perrin, D.R. and Barber, D.J. 1988. Evaluation of Methods for Moisture Content Determination in Snap Beans. American Society of Agriculture Engineers. 31:3:956-961.

Kolar, K. 1992. Gravimetric Determination of Moisture and Ash in Meat and Meat Products: Interlaboratory Study. Journal of Aoac. International. 75:6:1016-1023.

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CALIFORNIA AGRICULTURAL TECHNOLOGY INSTITUTE - CATI
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California State University, Fresno