Water desorption properties of separated manure solids

Biological Wastes 19 (1987) 107-121

Water Desorption Properties of Separated Manure Solids* David R. B o h n h o f f & James C. Converse Agricultural Engineering Department, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA (Received 14 October 1985; accepted 31 March 1986)

ABSTRACT Separated manure solids were collectedfrom three dairy farms with different solid-liquid manure separators. Desorption isotherms were obtained for water desorption equilibria at five temperature levels. Three isotherm models were fitted to the data. Equations for estimating the isosterie and integral heats of desorption were also developed.

INTRODUCTION Commercially available solid-liquid manure separators are an integral part of a number of large manure handling systems. The solid fraction or separated manure solids (SMS) produced during the separation process consists mainly of fibrous particles of hay, grain, silage and bedding materials. Research has shown that several practical and profitable alternatives exist for the utilization of this material. However, for most of these applications, reduction in the moisture content of the solids is desirable. A number of methods and processes exist for the removal of moisture from a material. In order to evaluate and optimize the performance of a particular system, an engineer must be able to predict the changes in the performance of the system due to variations in operating procedures and * Research supported by the College o.f Agricultural and Life Sciences, University of Wisconsin-Madison. 107 Biological Wastes 0269-7483/87/$03.50 O Elsevier Applied Science Publishers Ltd, England, 1987. Printed in Great Britain

108

David R. Bohnhoff, James C. Converse

modifications to the design of the system. With the aid of a computer, such predictions can be made quickly and accurately using a finite difference or finite element program which properly models the process. Mathematical models used to simulate drying systems are based on properties of the material, equations of continuity, and the conservation of energy and mass. Two important properties of a material are the equilibrium moisture content and the heat of desorption. The equilibrium moisture content establishes a lower limit to which the material can be dried and therefore has a major influence on the drying rate of the material. The heat of desorption is the quantity of energy required to evaporate moisture from the surface of the material and therefore is a significant variable in heat balance equations. The objectives of this study were: (1), to determine equilibrium moisture contents and heats of desorption of separated manure solids from water desorption data; (2), to express the equilibrium moisture content of the material as a function of relative humidity and temperature using previously published sorption isotherm models; and (3), to develop expressions relating the isosteric and integral heats of desorption to the moisture content and temperature of the SMS.

REVIEW OF L I T E R A T U R E

Equilibrium moisture content When a hygroscopic material such as SMS is placed in a moist environment, it will gain (adsorption) or lose (desorption) a quantity of moisture until a state of equilibrium is reached. The moisture content of the material at equilibrium is referred to as the equilibrium moisture content (EMC). Likewise, the relative humidity of the air above the material at equilibrium is referred to as the equilibrium relative humidity (ERH). A graphical representation of EMC plotted against E R H for a particular temperature is referred to as a sorption isotherm. Depending upon the approach taken to reach the equilibrium state, the curve is either an adsorption or a desorption isotherm. For a given material at a particular temperature these two isotherms seldom coincide due to hysteresis effects. Several methods have been used by researchers to determine EMC data. All methods are a variation of one of two basic techniques; either (1), the material is subjected to a constant humidity environment and the moisture content of the material is measured after equilibrium between the sample and the environment is reached; or (2) the vapor pressure above a sample of known moisture content is measured. The first technique has been used by

Water desorption of manure solids

109

several investigators working with cereal grains. The material is placed in a temperature-controlled chamber. The vapor pressure or humidity in this chamber is normally regulated with acid or salt solutions. In order to construct an entire isotherm, several experimental runs must be made using different saturated salt-solutions or by varying the concentration of the acid solutions. To speed up the process, air can be mechanically circulated within the chamber or the chamber can be evacuated to increase the mass transfer of water molecules. Several empirical, semi-empirical and theoretical equations have been developed over the years in an effort to predict moisture contents. Most of these models are capable of reproducing EMC data for a wide range in relative humidities; however, only a few of them are also able to adequately describe the temperature dependency of the isotherms. Five sorption models capable of describing the temperature dependency of isotherms were compared by Pfost et al. (1976). They concluded that the Henderson equation (as modified by Thompson) and the Chung-Pfost equation, both three parameter models, were as adequate in predicting sorption phenomena as any of the four parameter models they examined. The modified Henderson equation can be expressed as: RH = 1 . 0 - e x p ( - K ( T k + C)(Mab,%)N)

(1)

or as:

Mdb,% =

In ( 1 - RH) -] ,/N Z / ~ ( ~ TC)A

(2)

The Chung-Pfost equation can be expressed as:

RH:exp[(T-k~A-c)eXp(--BMdb,%)l

(3)

Mdb.% = E -- Fln ((Tk + C)in (RH))

(4)

or as:

where E = In (A)/B and F = I/B; A, B, C, K, N are constants; RH, is relative humidity, decimal; Tk is temperature, K; and Mdb,% is moisture content, dry basis, percent. Constants obtained for the above equations for some common grains are summarized in ASAE Data (1983).

Heat of desorption The heat of desorption is the amount of energy required to vaporize water from the surface of the particles. For biological materials with a moisture

110

David R. Bohnhoff, James C. Converse

content greater than 30% dry basis, the heat of desorption is roughly equivalent to the heat of vaporization of unbound water. As the moisture content falls below 30% and approaches zero, intermolecular forces of attraction between the water molecules and the solid surface become more and more significant and the water becomes increasingly more difficult to remove. Because of this phenomenon, the heat of desorption is not constant but steadily increases as the moisture content decreases below 30%. The amount of energy required to remove the water at a specific moisture content is termed the isosteric (constant moisture) heat of desorption (AHd). This quantity is normally expressed in units of kJ per kg of water removed. The total amount of energy required to reduce the moisture content of the material from one level to another is referred to as the integral heat of desorption (Qd). It is found by integrating the isosteric heat of desorption over the range of moisture contents in question. In equation form it is defined as:

Qd =

AHddM

(5)

1

where M2, M t are moisture contents, dry basis, decimal; AHd is isosteric heat of desorption, kJ per kg of water; and Qd is integral heat of desorption, kJ per kg of dry solid. Methods used to determine the isosteric heat of desorption are based on the Clausius-Clapeyron equation which is given as: dP PAH dT TER - -

-

-

-

(6)

or as:

d(ln(P)) _ d(1/r)

AH R

(7)

where T is absolute temperature, K; R is universal gas constant, 8.315 kJ (kgmol)-1 K-1; p is absolute vapor pressure, Pa; AH is isosteric heat of sorption, kJ (kg mol)-I(AH = AHd for desorption). If AH is independent of temperature, a plot of ln(P) vs 1/T for a particular moisture content will yield a straight line with a slope of AH/R. However, this is not the case, and for large temperature differences the variation in AH should not be disregarded. For example, at 0°C the heat of vaporization of unbound water, 2, is 2501 kJkg -1. At 70°C the heat of vaporization is 2334 kJ kg-1 (a 7% decrease). This is due to the fact that a rise in temperature will increase the translational and rotational energies of the molecules and they will have a greater tendency to escape into the vapor phase (Stamm, 1964).

Water desorption of manure solids

111

Othmer (1940) developed an alternate method for determining the isosteric heat of sorption. He realized after rearranging the ClausiusClapeyron equation in the form, dP PAH-

dT T2R

(8)

that for any two ideal gases maintained at the same temperature, the values of dP/P A H would have to be equivalent. Equating these values for the two gases and rearranging, Othmer developed the following relationship: dP/P AH d(ln (P)) dU/P' - AH' - d(ln (P'))

(9)

If one of the gases is water in a saturated vapor state, this equation can be written as, AH _ d(ln (Pv)) 2 d(ln (Pv,))

(10)

where AH is heat of sorption at temperature T ( b H = AHa for desorption); 2 is heat of vaporization of pure unbound water at temperature T; P~s is pressure of saturated water vapor at temperature T; and Pv is vapor pressure of water above the sample at temperature T. A plot of the In (P~) versus In (Pv~) at various temperatures for a given EMC should yield a straight line whose slope is equal to AHd/2. The term AHa/2 will remain substantially unchanged (especially for related gases) over a much wider temperature range than either AHa or 2 since the variation of both obey the same law, and the quotient therefore will be comparatively unchanged (Othmer, 1940). In integral from eqn 10 is given as:

In (P~) = b-v-Hln( P J + constant

(11)

A

METHODS Separated manure solids that had been composted for at least a month (generally under aerobic and thermophilic (45°C-70°C) conditions) were collected from three dairy farms (A, B and C) for use in the water desorption experiments. The following solid-liquid manure separators are in operation on these farms: farm A, a perforated drum/compressing roller separator; farm B, a stationary screen separator; and farm C, a centrifugal separator.

112

David R. Bohnhoff, James C. Converse

The static method was employed for obtaining water desorption data (Brooker et al., 1981). SMS samples contained in cylindrical baskets were suspended about 4 cm above salt solutions in wide-mouthed, gallon, glass jars. Solutions were made by adding the salts to jars containing 100 ml of distilled water. Salts were added well in excess of the quantity required for complete saturation to ensure that the solutions remained saturated throughout the duration of the experiment. Six different salts were used in this study; they were selected on the basis of cost, availability and level of relative humidity provided. The jars containing material from farm A were labeled and placed in thermostatically controlled chambers maintained at temperatures of 7"2, 15.5, 33"9, 48"9 and 65"5°C. Separated solids from farms B and C were only used in the experiment conducted at the 15.5°C level. All baskets were removed and weighed twice a week. When the change in weight over a twoweek period was 0.02 grams or less, it was decided that equilibrium had been attained. The moisture content of the material was then determined according to Standard Methods (APHA, 1976). The time required to reach equilibrium was mainly dependent on temperature. While material at 65.5°C only took an average of 4 weeks to reach equilibrium, experiments at 7.2°C lasted an average of 14 weeks.

RESULTS A N D D I S C U S S I O N

Equilibrium moisture content Desorption isotherm curves for SMS collected from farm A are shown in Fig. 1. Each point used to construct the isotherms at 7.2, 33"9, 48"9 and 65.5°C is the average of four values, while each point making up the 15.5°C isotherm is the mean of three values. Using the replicates made at each combination of temperature and relative humidity, a value of 0.36 was calculated for the pure error in experimentally determined values of equilibrium moisture content (percent, dry basis). Data at the highest relative humidity level (K2SO 4 salt solution) was discarded and not used in any calculations since excessive mold growth on the material at this level of humidity (95-97%) resulted in an erratic spread of equilibrium moisture contents. The 7.2 and 15.5°C isotherms shown in Fig. 1 cross at a relative humidity of about 75%. Two possible explanations for this occurrence are; (1), experimental error and (2), differences in the physical and chemical composition of the separated manure solids. Since all experiments at the 7-2, 33"9, 48-9 and 64.5°C temperature level were conducted a full year after

Water desorption of manure solids

113

35 o - 280.4 OK- 7.2 *C 30

~- 288.7 °K" 15.5°C o - 307.0 °K- 33.9°C e - 322.0OK- 48.9oC A- 338.7 ° K- 65.5°C

cn <

m 2.5 >rr a

20 FZ

uJ

15

o u

I0

F-Z

bJ OC

i.-5 O0

I

I0

I

a

20

i

30

40

RELATIVE

Fig. l.

I

t

50

60

I

i

70

80

I

90

tO0

HUMIDITY,%

D e s o r p t i o n i s o t h e r m s for s e p a r a t e d m a n u r e solids from farm A.

the study at the 15.5°C level had concluded, the SMS used in the experiments at 7.2 and 15.5°C were collected from farm A at different times and therefore, in all probability, differed slightly in composition. The effect of material origin or composition on the equilibrium moisture content is illustrated in Fig. 2. This plot was constructed from data obtained in the experiment at 15"5°C. The 15 data points shown in Fig. 2 were placed into five blocks (one for each level of relative humidity) and an analysis of variance was performed to determine if there was a significant difference in EMC's from farm to farm. The average of the three values comprising each block was used to calculate three treatment deviations for each block. The resulting 15 deviations were squared, added together, and 35

_m 30 rn >.

2.5

• •

FARM FARM

A B

•

FARM

C

20

•

I--

z "'

15

Z

O

• I0

•

hl

~

5

~;

0

0

I

I

I

I

I

I

I

I

I

I0

20

30

40

50

60

70

80

90

RELATIVE

Fig. 2.

I00

HUMIDITY,%

Effect of material origin or composition on the equilibrium moisture content of s e p a r a t e d m a n u r e solids at 15"5°C.

114

David R. Bohnhoff, James C. Converse

divided by 10 (degrees of freedom), yielding a treatment mean square of 1.2814. From repeat observations made at 15.5°C with material from farm A, a pure error mean square (based on 10 degrees of freedom) of 0.4156 was calculated. Since the ratio of these two mean squares, 3.08, is slightly greater than the tabulated F(10, 10, 0-95) = 2.98, it can be concluded that there is a significant difference in E M C values from farm to farm. Since water desorption and adsorption are controlled by complex factors such as the size distribution of micro-pores within the media, the amount of surface area per gram of dry matter available for adsorption, and the relative strength of the bonds between the surface of the solid and the adsorbed molecules of water, it is very difficult to predict the amount or direction of variation in equilibrium moisture content from farm to farm. Suffice it to say that on a macroscopic level, the above factors are influenced by the composition of the slurry being separated and by the type of separator in operation on the particular farm. Variations in composition of the slurry are mainly due to different bedding materials, feed rations and/or types of inorganic material in the slurry. Nonlinear least squares regression was used to fit the modified Henderson and Chung-Pfost equations (eqs 1--4) to the desorption data for material collected from farm A (95 points). Separate analyses were carried out with relative humidity as the dependent variable or with moisture content as the dependent variable. A thorough examination of several residual plots indicated that the models with relative humidity as the dependent variable were just as good in explaining variance as the models with moisture content as the dependent variable. To avoid confusion, only parameter estimates from regressions with RH as the dependent variable are presented here. In addition to the Chung-Pfost and modified Henderson equation, several other sorption models were fitted to the data. In terms of 'best overall fit', the following four parameter equation developed by C h e n & Clayton (1971) was the most attractive: RH = exp ( - g , T~' exp

(--g2Mdb.% T~'-))

(12)

where gl, hi, g2, h2 are constants. In alternate form this equation is given as:

Mab,% =

ln(ln(RH)/-giT2') _g2T~2

(13)

Parameter estimates, residual sum of squares (RSS), and the standard deviations (s) associated with the above two equations and eqns 1-4 are given in Table 1. The deviations of moisture content values from the values predicted by the three equations were 0-94%, 1-24%, and 0"80% dry basis.

Water desorption of manure solids

115

55 o - 280.4 " K - 7.2°C

(n •~cn 30 "~ >" 25 = (:3

//Ill

/ ///I IllJ I

'= - 288.7°K-I 5.5"C a _3070-K-33.9°C • -322.0°K-48.9°C =-3~,7°K-65.5°C RH=EXPr-7158.8T -L322 EXP(-3.657.10-TT2.2659

F- 20 Z LU

RH-DECIMAL

//

~/7/"

T-°K.

///

///

//

~

o~/t

/

c~_~/

o~-~z 15 ,,, I0 I--

5 0

I~,"- I

0

.lO

i

l

i

i

i

~

I

I

.20

.30

.40

.50

.60

.70

.80

.90

RELATIVE Fig. 3.

t.oo

HUMIDITY

Comparison o f experimental data from farm A with desorption isotherms plotted according to the C h e n - C l a y t o n equation.

These are relatively low considering the amount of experimental error associated with a particular measurement and the wide range in temperature and relative humidities covered by these equations. The lowest standard deviations were associated with the four parameter ChenClayton equation. This equation is shown in Fig. 3 along with the experimentally determined EMC values for material from farm A. Although the parameter estimates in Table 1 were based on data for separated solids collected from farm A, these equations may be just as accurate in their prediction of sorption behavior for SMS collected from other farms. For example, the average deviation of the EMC values for farm B material from the values predicted by the Chen-Clayton equation at 15-5°C was only 1-02%. Likewise, the average deviation of EMC values for farm C material from the values predicted by the Chen-Clayton equation at 15"5°C was only 1.42%. Although experimental accuracy enabled detection of measurable differences in EMC values from farm to farm, the farm to farm differences are not significant when compared to the deviations of 0.94, 1.24 and 0"80% listed in Table 1. While it appears that the parameter estimates in Table 1 can be used to roughly predict sorption behavior for all separated manure solids, the accuracy of such predictions are speculative since it has not been shown experimentally that temperature affects the sorption behavior of all SMS materials in the same way.

Heat of desorption Isosteric heats of desorption were calculated using the method developed by Othmer (1940) and the desorption data for material from farm A. An

exp ( - BMab../,,)

In(ln(RH)/-g~T~') --g2T~ ~

g~ = hi = g2 = h2 =

7158'8 -- 1-322 3"657(10 -7) 2'2659

C= -236"71 E = 35-497 F = 6"4102

B = 0" 1560

N = 1"5592 C= -236'06

K = 2-595(10-'*)

Parameter estimates

57-79

140-64

81"74

RSS

Mab,%

0.80

1"24

0"94

s

0.078

0"175

0"114

RSS

Dependent variable RII

0.029

0"044

0"035

s

Tk, Temperature, K. RH, relative humidity, decimal. Man../,, M o i s t u r e content, dry basis, percent. RSS, Residual sum o f squares, s, s t a n d a r d error o f estimate.

Mab'v*

R H = e x p ( - g ~ T ~ " exp(-g2Mab.%T~2))

C h e n - C l a y t o n equation

Man../. = E - F In ((Tk + C)In (RH))

RH = exp

C h u n g - P f o s t equation

M~.~ = L---K(~ + c)J

l n ( l - - R H ) ],/Iv

R H = I - 0 - e x p ( - K ( T k + C)(Mab.%) N)

Modified H e n d e r s o n equation

Equation

TABLE 1 P a r a m e t e r Estimates for D e s o r p t i o n E q u a t i o n s

"

.x,

~.

o',

Water desorption o f manure solids TEMPERATURE II

I

0 I

I0 I

20 I

30 I

40 I

l 17

*C 50 I

60 I

70 I

80 I/AI

I0

3

6

Fig. 4.

7

8

9 LN ( Pvs,Po)

I0

II

Othmer plot constructed from separated manure solids data.

Othmer plot (In (Pv) versus In (Pv,)) constructed from the data is shown in Fig. 4. The data points were generated by first fitting the Henderson equation to the desorption data at each temperature level. The five sets of parameter estimates were then used to determine the ERH (at all five temperature levels) for moisture contents of 3, 6, 9, 12, 15, 18 and 21% dry basis. The slopes of the seven isosteres in the Othmer plot are equal to values of the ratio AHJ2. These ratios, which were determined by linear least squares regression are shown plotted against moisture content in Fig. 5. It is evident from the plot that the isosteric heat ofdesorption steadily increases as more and more water is removed from the surface of the material. The relationship between moisture content and the dimensionless AHJ2 ratio was found to be best described by the following three parameter equation:

AH.

T

= 0"778 96 (0"103 69 + Mab) -°'27522

(14)

where Mdb is moisture content, dry basis, decimal. The average standard deviation of the seven AHJ2 ratios from the curve

118

David R. Bohnhoff James C. Converse 1.5

I

1

I

I

I

I

I

I

l

i

I

i'

I

I

I

I

I I I I s I l I I I I ,12 .16 .20 .24 .28 .32 CONTENT, DRY BASIS, DECIMAL

I

I ,36

1.4

I

I

522

1.3

I

l.I

~.o ............ .9

I 0

I [ I .04 .08 MOISTURE

_~_H~__,_X ....... I

___-~__,

/

I

Fig. 5. Latent heat ratio as a function of moisture content. defined by this e q u a t i o n was 0-0011. A b o v e a m o i s t u r e c o n t e n t o f 3 0 % d r y basis, this e q u a t i o n predicts values o f A H J 2 that are slightly less t h a n unity. Since the isosteric heat o f d e s o r p t i o n m u s t always be greater or equal to the latent heat o f v a p o r i z a t i o n ( A H d / 2 > 1), use o f eqn 14 s h o u l d be restricted to moisture contents less t h a n 30%. F o r m o i s t u r e contents greater than, or equal to, 30%, the isosteric heat o f d e s o r p t i o n for all practical p u r p o s e s is equivalent to the latent heat o f v a p o r i z a t i o n o f water. W i t h i n the 0 to 65'5°C t e m p e r a t u r e range, the latent heat o f v a p o r i z a t i o n o f water, 2, in kJ k g - 1 is given as ( A S A E D a t a , 1982): 2 = 2 5 0 2 5 3 5 - 2 3 8 5 76(Tc)

(15)

TABLE 2 Isosteric Heats of Desorption for Separated Manure Solids Moisture

Temperature, ° C

content

decimal, dry basis

0

I0

0"00 0"05 0"10 0"15 0"20 0"25 0"30 and higher"

3 637 3264 3021 2843 2 706 2 595 2 503

3 603 3233 2992 2816 2 680 2 570 2 479

20 30 40 50 60 (Isosteric heat of desorption, kJ kg- ~)

3 568 3202 2963 2789 2 654 2 545 2 455

3 533 3 171 2934 2762 2 629 2 521 2 431

3 499 3 140 2905 2735 2 603 2 496 2 407

3 464 3 108 2877 2708 2 577 2 471 2 383

" Isosteric heat of desorption = latent heat of vaporization of water.

3 429 3077 2848 2681 2 551 2 446 2 359

70

3 395 3046 2819 2654 2 525 2 422 2 336

Water desorption o f manure solids

119

i 5600

3400

z

o P-Q.

a: 5 2 0 0 o

5000

2800

oo°c - " - . . . ~ . ~ - -

20"C

3o. c

s o % ~ ~..~..'-~_.._~ u 2600

40"C"--'

~ _ ~ _ ~ _ ~

z4oo 0

I 0

I I0

I

MOISTURE

Fig. 6.

I

I

20

CONTENT %DRY

I 30

I 40

BASIS

[sosteric heat of desorption as a function of moisture content.

Since the isosteric heat of desorption is equal to the product of the AHd/). ratio (eqn 14) and the latent heat of vaporization (eqn 15), it can be calculated at any moisture content less than 30% and for any temperature in the 0 to 65"5°C range using the following equation: AHd = (1949-38 - 1.8584(Tc))(0.1037 + Mdb)-°2752

(16)

A plot of this function is shown in Fig. 6. This equation was also used to generate the values given in Table 2. The integral heat of desorption as defined by eqn 5, is the integral of the isosteric heat of desorption between the limits of M 1 and M 2. If the temperature of the material is assumed to remain constant, this integration yields:

Qd = (2689"61 -- 2.3857(T~))(0.1037 +

Mab)°'72481M2 .%I 1

(17)

Since the isosteric heat of desorption was given in kJ per kg of water, and moisture content in kg of water per kg of dry solid, the value of Qd calculated from this expression will be in units of kJ per kg of dry solid. The same restrictions imposed on the use of eqn 16 (0°C < To< 65°C and Mab < 0-30) also apply to the use of eqn 17. The quantities compiled in Table 3 were generated using this equation. Oven-dried SMS from all three farms were also immersed in water (Bohnhoff, 1985). The quantity of energy released per gram of dry matter (heat of wetting) from the three material types was similar, thereby indicating that the heat of adsorption and desorption were not dependent on material origin. This would suggest that although eqns 16 and 17 were developed using data for material from farm A, they could also be used to predict heats of desorption for other SMS materials.

David R. Bohnhoff, James C. Converse

120

TABLE 3 Integral Heats of Desorption for Separated Manure Solids

Temperature (°C)

0 10 20 30 40 50 60 70

Amount of heat in kJ required per kg of dr)' SMS to reduce the moisture content of the material from 30% dry basis to:

0%

5%

10%

15%

20%

25%

873 866 858 850 842 835 827 819

702 695 689 683 677 670 664 658

545 540 535 530 525 521 516 511

398 395 391 388 384 381 377 374

260 257 255 253 251 248 246 244

127 126 125 124 123 122 121 119

CONCLUSIONS 1.

2.

For a given temperature and relative humidity, there is a measurable difference in the equilibrium moisture content of separated manure solids from farm to farm. The relationship between moisture content, relative humidity and temperature was best described by the four parameter C h e n Clayton equation as: E R H = e x p ( - 7158"8(Tk)- 1-322 exp ( -- 3-657 x 10- 7Mdb.% T2"2659))

3.

For moisture contents (dry basis, decimal) less than 0.30 and temperatures between 0 and 65°C, the isosteric heat o f desorption in kJ kg-1 of water removed can be estimated as; Alia = (1949"38 - 1"8584(Tc))(0"1037 + Mab) -°'2752

Above a moisture content of 0"30 the isosteric heat o f desorption of SMS is equivalent to the latent heat of vaporization of water and therefore can be approximated as: A H a = 2502"535 - 2"385 76(Tc)

REFERENCES A P H A . (1976). Standard methods for the examination o f water and waste water.

(14th ed.) American Public Health Association, Washington DC, USA. ASAE Data. (1982). ASAE D271.2, Psychrometric data. 1982 Agricultural

Water desorption of manure solids

121

engineers yearbook. American Society of Agricultural Engineers, St Joseph, Michigan, USA. ASAE Data. (1983). ASAE D245.4, Moisture relationships of grains. I983 Agricultural engineers yearbook. American Society of Agricultural Engineers, St Joseph, Michigan, USA. Bohnhoff, D. R. (1985). Thermal and physical properties of separated manure solids. Unpublished MS Thesis, University of Wisconsin, Madison, Wisconsin, USA. Brooker, D. B., Bakker-Arkema, F. W. & Hall, C. W. (1981). Drying cerealgrains. The AVI Publishing Company, Inc., Westport, Connecticut, USA. Chen, C. S. & Clayton, J. T. (1971). The effect of temperature on sorption isotherms of biological materials. Transactions of the ASAE, 14(5), 927-929. Othmer, D. F. (1940). Correlating vapor pressure and latent heat data. Industrial and Engineering Chemistry, 32(6), 841-56. Pfost, H. P., Maurer, S. G., Chung, D. S. & Milliken, G. A. (1976). Summarizing and reporting equilibrium moisture data for grains. ASAE paper No. 76-3520. American Society of Agricultural Engineers, St Joseph, Michigan, USA. Stamm, A. J. (1964). Wood and cellulose science. The Ronald Press Company, New York, USA.