- Email: [email protected]
A mathematical model of a pig slurry treatment system
J.agric. Engng Res.(1977)22,421-437
A Mathematical
Model
of a Pig Slurry
Treatment
System
E. AUDSLEY; D. S. BOYCE; J. A. WHEELER; A. G. DUMONT* Mathematical models have been developed of a pig slurry treatment system which includes mechanical separation of the fibre from the raw slurry, treatment of the defibred slurry in a biological filtration tower and then a further separation of sludge. Both the fibre and sludge are handled as stackable solids. Evaporation is considered to take place from the slurry within the pig house, within the filtration tower and from the defibred slurry which is being desludged. The models are suitable for considering both steady and variable inputs of raw slurry and evaporation. This study indicates many of the problems likely to be encountered when designing and operating such a system. In particular it has been shown that only small reductions in the dry matter content of the raw slurry can result in very large increases in the amount of liquid to be handled. 1.
Introduction
Systems of treating animal manures with the object of reducing their pollution potential and facilitating their economic utilization have been the subject of research and development in the last few years. This has become increasingly important with the advent of large production units handling manure as slurry in quantities which may exceed the chemical and or hydraulic capacity of the available land. Systems for treating animal slurries are relatively simple in concept; however, as all the inputs, internal flows, suspended solid contents and outputs are inter-related their operation can be complicated. It is likely that they can only be understood and the effect of changes in their operation determined by developing appropriate mathematical models. Such models will also aid the design of systems to be operated under specific sets of conditions and the long term operation of a system in different weather conditions and with different inputs can be examined. 2.
Pig slurry treatment systems
Systems of treating pig slurries with the objective of simplifying their subsequent storage, handling and disposal have been proposed in recent years. ’ A feature of some of these systems is that the slurry is separated into a liquid and solid fraction. The amount of liquid to be handled is reduced as much as possible by encouraging evaporation and by incorporating as much liquid with the solids as is compatible with them remaining stackable. The N.I.A.E. have developed an integrated separation, aerobic treatment and sludge dewatering system2-4 the general features of which are shown diagrammatically in Fig. 1. While the mathematical model which has been developed is based on this configuration it can be easily modified. The slurry is collected in a dunging channel and pumped to a separator. The separator removes the more fibrous fraction of the suspended solid matter, subsequently referred to as the fibrous solid. It can be adjusted to give different moisture contents in the fibrous solid. The object is to produce a solid that is stackable with little seepage of liquid. The removal of the fibrous material is necessary for the operation of the next part of the treatment system in which the separated liquid is pumped up into a biological filtration tower. This reduces the BOD (biological oxygen demand), removes some of the unpleasant odours and some moisture is evaporated. There is a settlement tank below the tower. The overflow from the settlement tank is returned to the dunging channel to flush it out. At intervals, sludge is removed from the bottom of the settlement tank, mixed with a chemical flocculant and pumped to porous containers where the sludge is dewatered by gravity. The filtrate drains to a tank from which some is returned to the system to ‘Systems
Department,
Received
16 June
1976;
N.I.A.E., accepted
Wrest
Park,
in revised
Silsoe,
form
Bedford
3 July
1977
421
422
PIG
SLURRY
TREATMEN
r SYST1.M
maintain it in a suitable operating condition while any excess must eventually be disposed Evaporation occurs from the dunging channel, the filtration tower and the dewatering area. may be possible to increase the evaporation in the tower by siting it in the piggery so that warm passes up the tower. While the concept of this system for treating pig slurry is simple, its design and operation different conditions is not. A suitable mathematical model will produce information on performance over long periods of time with different inputs relatively quickly and cheaply.
Ambient
I
OCR
for its
Raw Slurry
1
-
Pig house ventllotlng olr
of. It air
-
3
from dunging channel
e
sludge
-
System
-
Internal -
-
-
Fig. I. Schematic
3.
boundary
Inputs
e -
removed
flows
Mo~siure evaporated Solids and the system
from the system
hqutds removed for dlsposol
from
diagram of a pig slurry treatment
system
Model of a pig slurry treatment system
The slurry input to a treatment system is a function of the number of pigs, their diet and age. It will alter as the pigs mature. It is also likely to alter over a 24-h period as the pigs become active, feed and rest. This latter may be important when designing and operating a system. It is also important when sampling a system to determine its likely mean condition during a 24-h period. The condition of the ambient air, which determines evaporation, will vary over a 24-h period and seasonally. A model is developed (Appendix A) to provide information on the flows of material in the system and to calculate the output of fibrous solid, sludge and filtrate in terms of the raw slurry input, the volume input to the tower, the volume desludged, the evaporation and the system parameters. A dynamic model is developed where the input slurry and evaporation can be varied for different periods within 24 h. This model is simplified if the rate of slurry input and evaporation are constant and is referred to as a steady-state model.
E.
AUDSLEY
42.3
ETAL.
It has already been stated that air evaporates moisture from different parts of the treatment system. Seasonal effects and the variation from year to year can be investigated using the steadystate model with mean daily weather data recorded over many years. The relationship of the weather variables to evaporation from different parts of the system is considered in Appendix R. Pig slurry is a mixture of solids and liquids. The solids consist of a soluble and suspended fraction, A slurry treatment system is basically concerned with the suspended fraction. When evaporation of a liquid occurs the concentration of the soluble material increases. This concentration could perhaps reach a level where bacterial activity would be inhibited. While it is beyond the scope of this study to determine what concentration of soluble solids will inhibit bacterial activity, a relatively simple analysis (Appendix C) indicates the soluble solids concentration within the system knowing the initial concentration of soluble solids, the liquid throughput and evaporation rate. The analysis shows that the concentration does not increase without bound as long as there is some input to the system, irrespective of any output. As the soluble solids do not affect the operation of the system, they will be neglected in all further calculations and only suspended solids considered. The soluble solid content of pig slurry is approximately l-50/;;. The dry matter content which is the figure usually quoted is the sum of the suspended solids and soluble solid contents. 4.
Information provided by the model
Some examples are given of the type of information which can be provided how it can be used for designing and operating a system. The requirements operating system are also considered.
4.1.1.
by the model and for sampling an
4.1. Steady-state conditions Analysis of the treatment system
The solution of the steady-state model described in Appendix A provides an analysis of the system. The weight and solids content of the outputs from the system, the fibrous solid (W,-,,D,& the de-watered sludge ( Wso,Ds,,) and the filtrate (WE F,D E F) are independent of the volume of liquid input to the tower (B) and volume of sludge de-watered (C) and also independent of the volumes of the tanks in the system. Analysis of WEF, the excess filtrate, shows that this surplus is reduced if: (i) the separator efficiency, p, decreases provided the sludge solids content is less than the fibrous solids content; (ii) the raw slurry solids content, a, increases; (iii) the fibrous solids content, m, decreases; (iv) the sludge solids content, s, decreases; (v) the evaporation, E, increases; (vi) the filtrate solids content, b, decreases. 4.1.2. Examples of solution Typical inputs, parameters and evaporations for a slurry treatment system for 500 pigs are given in Table I. These are used with appropriate alterations for the different examples which are considered. As the density of the slurry and the liquid in the system is approximately one, volume and weight can be used interchangeably. The steady-state model can be used to determine the flows in the different parts of a system for any given set of conditions. Using the input data, Table I, the steady-state results for a 24-h period are (the symbols are defined in Appendix A): D RS ~-- 184 kg suspended solids added in raw slurry D SP = 320 kg suspended solids input to separator
424
weight of suspended weight of suspended weight of suspended suspended weight of suspended suspended weight of weight of weight of weight of
PIG
SLURRY
TREATMI-NT
SYSTEM
W SP 8790 D FS 85 W,, 513 D LO 235 W LO 8277 D 237 0;:’ ~~ 136
kg kg kg kg kg kg kg 6650 kg w,, D 102 kg 99 kg D::, W SD ll66kg W DW -: 2734 kg 2523 kg W,, W,, 210 kg
slurry input to separator solids in fibrous output from separator fibrous output from separator solids in separated liquid separated liquid produced solids input to tower solids overflow from settlement tank overflow from settlement tank solids in sludge from settlement tank solids in de-watered sludge de-watered sludge produced filtrate produced filtrate returned excess filtrate produced
Then : suspended
solids content
of (a) (b) $1 (e)
dunging channel separated liquid tower input channel circulant sludge from settlement
s DC S LO s S;; S,,
tank
0.036 0.028 = 0.022 0.020 0.026 =
If the inputs occur at an uneven rate the suspended solids at any given time are not likely to be those indicated; however, the total flow over a 24-h period would be the same. The steady-state solution is suitable for long-term planning. For instance, using the input data in Table I and assuming that the winter period is 180 days, the excess filtrate, which is a function of the mean total daily evaporation is: Winter
Total evaporation, kg/d Excess filtrate, kg/d
IX8 435
Summc~r 455 165
If it is assumed that no filtrate can be applied to the land for 180 days during the winter, the total filtrate to be stored would be 78,300 kg so at least 78.3 m3 of storage must be provided. The steady-state model can be used to provide information on how the system must be operated to meet some specific requirement. For example, it is probably desirable to control the suspended solids content of the slurry being treated in the tower to prevent a build-up of material in it. This is controlled by the amount of sludge periodically removed for de-watering from the settlement tank. This is shown graphically in Fig. 2. The amount of sludge, C, to be de-watered is plotted against the suspended solids content, S, w of the slurry entering the filtration tower for different values of 4, the settlement ratio. Evaporation is neglected as it is small in comparison with the volume of liquid within the system. From this example if 4000 kg/d are de-watered and y =- 0.8, the solids content STW of the input to the tower will be 2.2% (equivalent to 3.7 “/g d.m.). If, however, it is necessary to reduce S,,, to 1.5% (equivalent to 3.0% d.m.), the volume of sludge to be de-watered must be 6300 kg/d. Outputs from the system are independent of the volume de-watered but the above steady-state results will alter thus: suspended solids input to separator weight input to separator suspended solids in separated liquid
D
-=~ 242 kg
W:‘, D LO
~~ 6490 kg -~
157 kg
E.
AUDSLEY
weight of suspended suspended suspended weight of weight of weight of suspended
125
DAL.
separated liquid produced solids input to tower solids overflow from settlement tank solids in sludge from settlement tank overflow from settlemant tank filtrate produced filtrate returned solids content of (a) dunging channel (b) separated liquid (c) tower input (d) channel circulant (e) sludge from settlement
W LQ D TW D cc D SL W cc W,, WFR
S DC S LQ S TW S cc S SL
tank
5977 kg 162kg ~~ 58 kg 104 kg -~:= 4350 kg == 5034 kg = 4823 kg 0.036 0.026 0.015 = 0,013 0.017 -=
kg kg kg kg kg
Assumptions lkgQ4 hl 8=10,800 kg input to tower, A = 23CQlq raw slurry input, E. = 160 kg of moisture ewporoted fmm the &qing channel, ETW= 150 kq of moisture wapomted fmn Me beer
3
If 4OOOk@d are de-watered, fk soI& ccntent is 2.2% idry matter ccm+en+ appoximotely 37%. If the solids content is to be kn than I.%, more than 6300 kg/d must be de-watered
8000
E
2mJl
I.00
I.50
I 2a
I
I 2.50
I 3.00
1
Tower input solids content P&J
Fig. 2. -Relationship between weight to be de-watered and tower input solids conterrt
4.2. Variable inputs The model can be used to show how the slurry treatment system operates when the inputs vary. There are likely to be three circumstances as follows. (i) Changes in the slurry and weather inputs over a 24-h period. (ii) Changes as the animal matures. This will result in a general increase in food intake with a corresponding increase in slurry. (iii) Change due to seasonal weather. This will affect the evaporation of moisture and the ventilation requirements. This study has only been concerned with 24-h weather and slurry changes and the effect of seasonal weather. It is unlikely that changes in slurry output with pig maturity is important in terms of treatment system design and operation. 4.2.1. Variable inputs-24 h period If the rate of input of slurry to the system varies over a day the suspended solid contents within the system will change. A mathematical model was developed to simulate the performance of the system when the slurry input and evaporation varied over 24 h (Appendix A). The efficiency of the separation of the fibrous solids is calculated from the following expression derived from data provided by the Farm Buildings Department of N.T.A.E. :
PIG
126
SLURRY
TRL:ATMFN~I‘
SYSTEM
y := 0.443L2.2 D,,/l+',,-0.345nz. The data used in the following example is the same, except where noted, as in Table I. input of raw slurry A is still 2300 kg/d, but for this example the day was divided into periods. The variation in the production of raw slurry by pigs over a 24-h period does to be known so the input of raw slurry and the evaporation for each period was taken
The total four 6-h not seem to be:
Period I
2
3
4
900 164
1000 205
350 41
50 0
--__
Raw slurry, kg/6 h
Evaporation, kg/6 h
Table II, part A, shows for comparison the flows and the suspended solids contents if the slurry input and evaporation are constant over a 24-h period. Table II, part B, shows the system flows and the solid contents for one set of channel, separator reservoir and settlement tank capacities. Over the 24-h period the solid content of the input to the slurry separator, S, P, ranges from 3 “/,,to 4 “/;I,input to the tower, Ss ,+ from 1.9 % to 2.5 %, and of the filtrate, S,,, from 2.5 “:, to 2.6 “I,;,.The daily outputs, however, are little altered. TABLE
Input data-model
I
studies of a pig slurry system for 500 pigs
Inputs
A, raw slurry B, tower C, liquid to be de-watered
I 2300 kg/d 10800 kg/d 4000 kg/d
Parameters (i)
Suspended solids content (I, raw slurry b, filtrate HI, fibrous solids s, de-watered sludge
(ii) Others p, fibre separator efficiency y, settlement ratio Evaporation E Dc, dunging channel E TW, filtration tower E DW, de-watering
0.080 0.001
0,165 0.085 0.46 0.80
160 kg/d 150 kg/d 100 kg/d
Table II, part C, shows the results obtained when the volume of the dunging channel, VDc is reduced from 2300 1 to 1000 1 and the separator reservoir from 643 I to 100 1. This reduction in buffering only increases the range of solids contents a little. There is very little change in the solids content of the de-watered slurry because this is buffered by the large volume of the settlement tank which has remained unaltered. These results indicate the following: (i) Since the rate of slurry output from pigs is likely to vary over 24 h, in as yet some unmeasured way, samples taken from a slurry treatment system during any one period of the day could be misleading. Samples should therefore be taken throughout the 24-h period.
E.
AUDSLEY
427
ET,~L.
TABLE
II
Simulation model results showing the effect of dunging channel and separator reservoir volume on the system operation over 24 h with constant and variable production of raw slurry
Volume afdunging channel: Separator reservoir. Settlement tank:
Volume of dungingchunnel: Separator reservoir. Setrlement tank:
2300 I 643 l 7000 I
IO00 I 100 I 7000 I
1 period 24 h
A Flow rates (kg/period) 2300 8845 519 8327 I0800 6665 4000 1155 2699 2472
Raw slurry Input to separator Fibrous solid Output from separator Input to tower Channel circulant Sludge for de-watering De-watered sludge Filtrate Filtrate returned Suspended
,I_
Four periods-6
I
/
I
2
I
h
3
I
4
B
295 646 331
350 1972 79 1893 2700 1673 1000 293 678 806
50 1723 II 1712 2700 1700 1000 280 720 988
3.99 2.78 2.45 2.06 2.58
3-60 3.06 2.17 2.05 2.56
3.01 2.92 1.89 I ,96 2.45
900 2552 203 2349 2700 1646 1000 283 659 351
1000 2598 230 2369 2700 1646
3.60 2.49 2.18
1000
If
900 2552 204 2348 2700 1646 1000 286 655 352
2598 231 2367 2700 1646 1000 303 638 333
350 1972 78 I894 2700 I673 1000 295 676 806
50 1723 II 1712 2700 1700 1000 273 727 988
3.70 2.59 2.27 I .97 2.46
4.18 2.97 2.62 2.10 2.62
3.51 2.97 2.11 2.06 2.58
2.70 2.61 I .69 I .92 2.40
1000
solids confent
%
3.60 2.80 2.18 2.02 2.52
Input to separator Output from separator Input to tower Channel circulant Sludge for de-watering
1.98 2.47
-
It is also likely that the difference between samples will be in part due to experimental error and part due to variation in the input of raw slurry. The average of measurements taken over a 24-h period is, however, likely to provide an estimate of the mean value of the suspended solids over a 24-h period. which will be helpful in the design of slurry (ii) This model can be used to provide information treatment systems. For example : (a) if the maximum level of suspended solids which can be handled by the filtration tower or any other part of the system has been established, the volume to be desludged and the buffering required by providing reservoirs of sufficient capacity can be determined; (b) the minimum storage required for the excess filtrate can be determined for different sets of conditions. inputs-seasons and years 4.2.2. Variable The most important effect of weather on the operation of a slurry treatment system is likely to be the effect of evaporation from various parts of the system on the amount of excess filtrate which must be disposed of. The model calculates the seasonal production of solid and filtrate for disposal and the expected annual variation. Fig. 3 shows the mean and maximum amount of filtrate produced over a IO-year period under the weather conditions prevailing at Rothamsted Experimental Station, Harpenden, Hertfordshire, 1959-68. Four levels of slurry dry matter content which indicate either changes in the
PIG
428
Max 1968 MI!- 1967
500 t
Max 1968 Min 1958
Max 1965 Min 1959
SLURRY
TREATMENl-
SYSTEM
Max 1962 Mln 1959
mrter 4
1
Mean
and range
0
Slurry dm = 4%
0
Slurry dm ; 6%
m
Slurry d m = 8%
m
Slurry d m = 10%
Fig. 3. The mean und range of seasonal production of excess filtrure, 1959-68, from a piggery housing 500 5O-kg meal-ftid pigs, for slurry d.m.s of 4%, 6%, S”,: and 100,:. The wet area for evaporation inside the pighouse was 280 m2 ; sepnrntor eficiency = 50 % I_fibrous solids d.m. = 22 %; de- wutered sludge d.m. 7 I I a’;; excess filtrate d.m. = I.75 06. Each quarter is 91 du,>.y
ration dry matter to water ratio, or that water has leaked into the system are considered. There are small differences between the amount of filtrate produced from year to year and from season to season. In contrast, changes of a few percent in the dry matter content of the raw slurry will This highlights the importance of have a very large effect on the amount of excess filtrate. ensuring that pigs are not allowed diets with unnecessary water content and that every effort be made to prevent extraneous water from getting into the raw slurry treatment system. Table III shows mean values for the weather parameters for 3 widely dispersed sites in England. There is little difference between the mean annual evaporation and mean daily dry bulb temperature; however, the annual rainfall at Ellbridge, Cornwall, is nearly double that of Cawood, Yorkshire. Fig. 4 shows the mean annual accummulated filtrate for disposal from January to December, for 1959-1968. As expected from the evaporation values given in Table III there is little difference in the annual quantities of excess filtrate from each site. If the hydraulic loading of the soil is likely to be a limiting factor, rainfall may be an important factor in planning a land spreading programme.
Mean weather conditions at 3 sites, 1959-1968
Mean duil) dry bulb temperature, ‘C
Cawood, Yorkshire Rothamsted, Hertfordshire Ellbridge, Cornwall
Mean rainfall, mmjveur
8.9 9.1
600 723
IO.1
1159
Mean absolute evaporation from a free wufet surface, mm/yea! 155 720 142
E.
AUDSLEY
429
ET AL.
0
5
IO
15
20
25
30
35
40
45
50
Week number
Fig. 4. Accumulatedfiltrate for disposal, January to December, mean of IO years 1959W58, Cawood (C), Ellbridge (E) and Rothamsted (R) from a piggery having 500 50-kg pigs for a slurry d.m. of IO’%. The wet area for evaporation inside the pighouse was 280 m2; separator ejjiciency SOaL; fibrous solids d.m. = 20%; de-watered sludge d.m. = 10%;
exressfiltrate
5.
d.m. =
1.75%
Conclusions
A mathematical model study of a pig slurry treatment system which separates the slurry into a solid and liquid fraction has been used to provide information on how it operates under various conditions. While the model can be modified to represent different system configurations the following general conclusions apply to this type of system. (9 The soluble solids concentration does not increase without bound as long as there is some input to the system, irrespective of any output. (ii) The excess filtrate is reduced if the moisture content of the fibrous solid and de-watered sludge is increased, though they must still remain stackable. It is also reduced if the separator efficiency is reduced, however, the separator must remove sufficient fibrous solids to allow the remainder of the treatment system to operate effectively. (iii) The variation in the production of raw slurry by pigs over a 24-h period affects the suspended solids contents in the different parts of the system. Variability in slurry production may be important if a system is to be sampled in order to estimate its mean state over 24 h. It may also be important when designing a treatment system, to provide sufficient buffering capacity so that the suspended solids content does not increase in any part of the system to a level which could interfere with its operation, for instance, the input to the filtration tower. (iv) Using 1959-68 weather data, there were only small changes in the amount of filtrate produced from year to year due to variations in natural evaporation. (v) The amount of filtrate produced by the treatment system using ten years of weather data from three widely separated sites in England varied little. There was little difference in the natural evaporation between these sites. There was, however, a considerable difference in rainfall between sites which could influence a land spreading programme. (vi) The factor which had the largest influence on the amount of filtrate was the dry matter content of the raw slurry. For one set of conditions and 500 pigs a decrease in the dry matter content of the raw slurry from 10 o/1to 6 7; increased the production of filtrate from 60 t to 225 t (IO-year average). The output solids cannot hold any more water so all the extra water goes through the system to become filtrate. Similarly any extra evaporation would directly affect the filtrate produced. This indicates the importance, if the quantity of liquid to be handled is to be minimized, of not feeding unnecessary water and preventing leakages of water into the slurry.
430
PIG
SLURRY
TREATMI-NT
SYSTEM
REFERENCES
Osborne, L. E. The efficient use of slurry. J. Proc. lnstn agric. Engrs, 1975 30 40-43 2 Osborne, L. E.; Hepherd, R. Q.; Sneath, R. W. An integrated separation, aerobic treatment and siudgc de-watering system for pig slurry. J. agric. Engng Res., 1976 21 2 ’ Hope, H. “Clean” the slurry and “wash” the air. Fmrs’ Wkly, 1977 86 83, 85, 87 4 Ockwell, T. New building willgive waste the@/ treatment. Br. Fmr Stockbr. Muck ‘77 supplement. ’
26 March 1977 ’ O’Callaghan, J. R.; Pollock, K. A.; Dodd, V. A. Land spreading qf’manure .fkoln anin?al production units. J. agric. Engng Res., 1971 16 3 ’ Randall, J. M.; Carpenter, G. A.; Hawkins, J. 0. Air distribrttion in a fkN scale section Q/a livrstoch building--Part I. Dep. Note DN/FB/319/3020, natn. Inst. agric. Engrs, Silsoe (unpubl.). 1975 ’ Owen, J. E.; Carpenter, G. A.; Randall, J. M. A simulatedpigjbr use in ventilation studies. Dep. Note DN/FB/168/3020, natn. Inst. agric. Engng, Silsoe (unpubl.), 1971 ’ Treybal, R. E. Mass Transfer Operation, 2nd Edition. Tokyo, Japan : McGraw-Hill I968 177. 2 I7 ’ Potential Transpirationfor Use in Irrigation and Hydrology in the U.K. and Republic of Ireland. M AFF Technical Bulletin No. 16, 1967 ” Penman, H. L. Natural evaporation fLonl open water, bare soil and grass. Proc. R. SOC., Lond. A. 1948 120-45 ” Carpenter, G. A.; Randall, J. M. Private communication Appendix Mathematical
A
model of slurr!, treatment system
A.1. Dynamic model The dynamic model of the slurry treatment system is described by the 26 equations shown in Fig. 5 where a prime denotes a variable changing from an old value to a new value, lower case letters represent parameters of the system. The amount of raw slurry can be altered by changing the number of pigs or their food. The input to the tower and volume desludged, controlled by pumps, can be set, within reason, to any desired value. All other flows within the system are fixed by these and can thus be calculated from them. As the density of the slurry and the liquid in the system is approximately one, volume and weight will be used interchangeably. The evaporation from the system can be calculated from past weather data (Appendix B) and in this case is assumed to be known. A.1 .l. Steady-state mode/. Assuming the system is operating in a steady state, that is, that all the volumes and suspended solids contents within the system remain the same from day to day, these equations can be solved in terms of the volume of raw slurry (A), the volume input to the tower (B), the volume removed for de-watering (C), the evaporations (E,.) and the system parameters: D RS -~~aA
DS, m,here
. ..(Al)
= aA $4 (B-C-E,,)
(A/I +h (C
EDr / ETW))/C
. ..(A2)
/I
- a-ap-&hap/m
. ..(A31
w,,
=- A -{-B-C-ETw-E,r
. ..(A4)
D FS W,, D
LQ
apA,
. ..(A5)
:= apA/m,
. ..(A6)
:
a (1 -P>
W LQ - (l-up/m) D Tb D,,.
A +q
(B-C--ET,)
(AB
+~ h (C
7 EDc
A$-B-C-E,.,-EE,,,
(1 m’q (B-CC--E,,M’)(4-t m=q (B-CC--ETw)
(A/l+b
+B,,))lC,
. ..(A7) . ..(A8)
b CC Em:-E,,)), (C1~E,,~I
E,,)),‘C.
. ..(A9) . ..(AIO)
NOTATION
USED IN THE APPENDICES
. indicates where two capital letters will be used as subscripts to denote the part of the system referred to. A a B b
c Cj
D.. d E..
Ej .ell
F fj
GS HB
HP K,
k LJ
MP m
N P P
QJ 4
R, r S.. s Y d
weight of raw slurry suspended solids content of raw slurry weight input to the tower suspended solids content of filtrate weight removed for de-watering soluble solids concentration of liquid removed from the system on dayj weight of suspended solids soluble solids concentration of liquid added to the system weight of evaporated water weight of water evaporated on day j saturated vapour pressure at Tj, mm Hg mean vapour pressure, mm Hg volume of ventilating air through the piggery, m3/h liquid removed from system during dayj dry air mass flow rate of the ventilating air through the piggery, kglh heat loss from building, kJ/h sensible heat output of a pig to the air, kJ/h volumetric mass transfer coefficient, kg h-l mm3 per unit change in log humidity gradient suspended solids content of input to tower liquid in the system at the end of day j moisture loss from a pig to the air, kgih suspended solids content of fibrous solids number of pigs volume of tower packing, m3 efficiency of removal of suspended solids in raw slurry by separator total soluble solids in system on day j settlement ratio (solids content in recirculant : solids content in sludge removed for dewatering) total radiation from the sun, mm water equivalent ratio of weight of sludge for de-watering to weight recirculated suspended solids content suspended solids content of solid sludge maximum possible hours of sunshine/ day (24 h) actual hours of sunshine/day
mean ambient temperature, F temperature inside piggery, C temperature outside piggery, C liquid added to the system during lj day j uz run of wind at 2 m height, mile/d capacity of reservoir V.. daily evaporation from the dunging *‘DC. channel, kg/m* weight of water evaporated from the VTW tower, kg/h expected evaporation from site, mm/d VDW VWS evaporation from an open water surface, mm/d W.. weight of liquid weight of pig, kg W absolute humidity of inlet air, kg VI water vapour/kg dry air absolute humidity of outlet air, kg Y2 water vapour/kg dry air average absolute humidity in piggery Yi kg water vapour/kg dry air absolute humidity outside piggery, kg Yt water vapour/kg dry air YS absolute humidity at the adiabatic saturation temperature of the inlet air, kg water vapour/kg dry air 0 Stefan’s constant T, T, To
Two capital letters will be added at as subscripts to denote the part of the system referred to : cc overflow from settlement tank to dunging channel dunging channel DC DW from de-watering area excess filtrate disposed of EF returned to separator reservoir from FR filtrate tank fibrous solid from separator FS in the filtrate tank FT from separator to separator reservoir LQ raw slurry added to dunging channel RS de-watered sludge SD from settlement tank for de-watering SL input to separator from dunging SP channel separator reservoir SR settlement tank ST tower TW Thus for instance: =weight of water evaporated from the de-watering area WFT -weight of liquid in the filtrate tank
ED,
432
PIG
SLURRY
TREATMENT
SYSTEM
. ..(A1 1) . ..(Al2) . ..(Al3)
Sepamtor Fibre sqmded DFS
sdlds
m. efflclency P
= ~0~s
- (6)
W FS = D&m
- I71
WLQ = WSP -Wm
94s - (8) “‘FS
D LQ = DSP -DFS
- (9)
‘+&a
DLQ
resermir
Sepwotor Capacity
>
V,, - (IO)
w;,
= w,+w,,tw,,-w,
DSR
= OS,+
I
+ DFR - DTW
- (150)
= WSL / WCC
D,,/W,
= (rt
I) &,I
f+,/W,=q(rtll
fJsr/
W&
= w,,t
w,-
‘ST
= OS,+
DT,-ax
DSD t
w,+
wsr
-(I51
Irtq)
W,
-(I61
Em
DDW 0,
-
- (18)
DSL
solids 5, sOlIds b = WSL
-
(19)
= DSL
-
(20)
-
-4,
-
(231
D;,:
-DE,
-
(24)
D,,
D~+DDW-DFR = bWm
Op. =bWn,
WSD
(22)
w;, = wFT+ w,, -wFu
Fig. 5. Flow chr~ OJ’N pig slurq~ ttwtment
940
_
- (25) -
F EDW. 0
- (21)
= SW,
DDI=bWDl
Wm. Dr.
-wsL-(171
-0s~
po I lets
Sludge suspended filtmR smpmded t
(r+ql
Ew-W,
W,L t-k-nvterlng
w,
(III (12) (13)
tank
setllemmt
WCC. “cc
D,,
-
wan* ‘,F
126)
system
,
E.
AUDSLEY
433
ETAL.
WSD = A/W--b)+b
. ..(A14)
(E,,-t-E,,+E,,)/(s--h),
WDW= C-AB/(s-h)-sE~w/(s-h)-h W,R = C-(l-up/m)
(ED, I E,,)/(s--h),
. ..(Al5) . ..(Al6)
A+E,,+6Tw,
and W EF = A (s--a--s~plm+ap)/(s--b&-s
. ..(Al7)
(E,,+E’,,+E,,)l(s--).
The suspended solids content of the different parts of the system are given by:
s DC
=
D,s+Dcc
=
QA+#----ET,)
(A~+h(C+EDC+ETW))/C~
A+B-C-E,,
A+WCC
SLQ
=
D,,l
..(A18) . ..(A19)
WLQ,
S TW = &WI&
. ..(A20)
s cc
= dAb+&c+E,c+-&w))/c
. ..(A21)
S SL
=
and . ..(A22)
[AP+~(C+EDC+~~W)I/C~
A.l.2. Input to tower The solids content of the input to the tower must be kept sufficiently low for the bacteria to operate properly but the amount of input is fixed by the need to keep the surfaces wet so that the only control of the solids content is by varying the weight of liquid removed for de-watering (C). Suppose we wish the input to the tower to have solids content k. The amount that needs to be desludged, C, can be found by solving: STW = k, . ..(A23)
(1 +q(B--C--E,w)/C)AB+b(C+ED,+E,w)=kB, m,C2+m2Ctm,
= 0
where ml =
W-_q),
‘% =
(1-q)
m3 =
O--ET
(AP+b(E,,+E,,)+bq(B-ET,))-kB
and W)
(AB+HEDC
This is shown diagrammatically
-t&
~1).
in Fig. 2. Appendix B
Evaporation from a pig slurry treatment
system
B.l. Pig house ventilation This analysis is based on a 500-pig unit. The heat output of a pig is in two parts: sensible heat, to the surrounding air, and latent heat, corresponding to a quantity of moisture given up by the pig to the air; either in the breath or from the skin. Some moisture is also given to the air by evaporation of the urine. For sensible heat losses the heat balance equation is:
PIG
434
the moisture
balance
equation
TREATMtNT
sensible heat output of pigsE heat losses from the building.
sensible heat removed by ventilating air Similarly,
SLURRY
. ..(BI)
is:
moisture loss from pigs I moisture given to ventilating air rX evaporation from manure. The heat loss from the building N.I.A.E.6 is given by:
based on data from the Farm
H,
=
SYSTEM
2.0(7.-T,,)
(1.66N
Buildings
. ..(B2) Department
of the . ..(B3)
50).
This assumes a side wall and roof area of 1.66 m”/pig, end wall area of 50 rn’ and an overall heat transfer coefficient of 2.0 kJrnm2”C-~ ’h- *. The moisture output of pigs, including evaporation from urine, and sensible heat output of pigs from 50-100 kg weight were fitted approximately by a linear relationship also based on data from the Farm Buildings Department of the N.T.A.E. M,
= 0.00367Ti
‘-m
;q 0.028 IO.05
x’ 677-T,(7.427
+
The sensible heat output of the pigs results in an increase the water vapour in the air. That is: G,x w here
1.00(7’-T,){-G,x
l.88( YiTi-
1.88 -- specific heat of water vapour, ??
X 16.135). in the heat content
.(B5) of the dry air and . ..(B6)
Y,,T,,) = H,N-HHB
kJ kg--’ “C-l :
I.00 ~- specific heat of dry air, kJ kg-r ‘C-l. ??
The moisture ventilating air:
output
from
the pigs results
in an increase
in the absolute
humidity
. ..(B7)
Yi : Y,,$-N.M,/G,s. Substituting
of the
for Yi in Eqn (B6): G,(T,-T,)
(I-1-1.88
Y,,)i 1.88 Ti M,N
=: H,N-H,.
Since I.88 Y, is usually much less than 1.0, that is, the heat increase of the water vapour is negligible compared to the increase in heat to the dry air, this equation gives: Gs = [(HP-- l-88 TiM,)N-
H,]/(T,-T,,)
. ..(BX) in the air . ..(Bo)
A constraint is placed on the air flow rate which must be high enough to prevent accumulation of toxic odours and low enough to prevent excess draught for the pigs. The limits’ were set at 0.2 m3/h and 2 m3/h per kg of pig, which, assuming a 75kg pig, means a minimum flow rate of 7500 kg dry air/h and a maximum of 75 000 kg/h for a 500-pig unit. Where the flow rates go beyond these limits the rate is fixed at the appropriate value and the temperature in the house allowed to change. B.2. Evaporation from ajiltration
tower
The theory used to describe the effect of blowing air through the filtration tower was that given by Treybal* for a recycling liquid, gas humidification process. Jn this process, in the steady state, with an inlet gas at constant temperature and humidity the recycled liquid approaches the
E.
AUDSLEY
ETAL.
435
adiabatic saturation temperature (wet bulb) of the inlet gas. The gas is humidified and cooled along the constant heat line corresponding to the inlet conditions of the gas. Although heat is produced in a biological filtration tower as a bi-product of the bacterial degradation of the slurry, in the absence of data to the contrary, this heat was neglected in comparison with the amount of heat exchange between air and liquid. Using this theory the relation between mass airflow and inlet and outlet humidities is given by: ,n
( K- Y,) __W’ (Ys- Yz> Gs
Re-arranging Eqn (BIO) gives an expression for a given air flow rate: V TW
=
G,( Y2-
for the quantity
Ys-
Y,)=G,(
. ..(BlO) of water evaporated
Yl)
from the tower
. ..(Bl I)
Since Y, is the absolute humidity of the air ventilating the piggery, this equals Yi. The prototype filtration tower used by Farm Buildings Department. N.I.A.E., was ventilated at 30°C. Measurements on the inlet and outlet air for the tower were taken sporadically to compare with the theoretical values. The results were inconclusive both in predicting the value of the heat and mass transfer characteristics and also in comparing the actual behaviour of the tower with the theoretical. The results for the volumetric mass transfer coefficient, K,, were between 50 and 200 kg h-l mW3 for the “Flocor” packed tower, and asimilar range forthe heat transfer coefficient. The variation is probably explained by the fact that the system is never in a completely steady state because of the variation in ambient humidities. A value of 100 was taken as an estimate of the mass transfer coefficient, and it is thought that the error in this value is at the most 50 “/,. The results using this value indicated that using such a rough estimate was justified in this study. B.3. Evaporation from site The area for evaporation from the site was made up of three parts: the exposed area of the de-watering pallets; the area below and around these pallets; and any other site area liable to be continually wet. This included drainage channels and open tanks. In the results given, 7 pallet boxes were assumed to be draining at any one time, each being 1.2x 1.06x0.76 m high. Because of their construction only half the side area plus the base and top surface were available for evaporation and over the 7 days’ draining they were assumed to be 80% full on average. This gives an area for evaporation of: 0.8 x (0.76 x 1*06+0.76x
1*2+2x
1.2 x 1.06) m2/pallet.
Using 7 pallet boxes a base area of 10 m2 and other site area of 20 m2 were Penman’s formula9 for a permanently-saturated soil surface was used to evaporation from the surface of the settlement tank, concrete drainage area It was assumed these areas were exposed to sun and wind for evaporation, The formula gives for evaporation from an open water surface:
HA/y+
vws = A/y+-1 where:
y A H=
=
E,
assumed. estimate the potential and the stacked solid. but not to rain.
..(B12)
0.27 mm/OF,
de = dT T, I
=
slope of the saturated ambient temperature,
0.75 Rr--aTa4
c, = O-35 (ell-Zd)
(0.47W.O75e,) (0*5+U,/lOO)
vapour
(0.17+0.83
pressure-temperature d/y),
curve at the mean . ..(B13) . ..(Bl4)
436
PIG
SLURRY
TREATMINT
SYS-TFM
and R, -m=R, (0.16+0.62 For a saturated
. ..(Bl5)
d/Y).
soil surface the evaporation V DW
=
is estimated
as: . ..(Bl6)
0.8 x vws.
B.4. Evaporation from dunging channel Evaporation of moisture within the pighouse occurs from the wetted surface of the slats and the slurry channel. The evaporation was calculated using an exponential form of Penman’s evaporation from an open water surface.’ O V DC
=
. ..(Bl7)
0.033 U, o,68 (e,-2,).
Since U?, the mean wind speed, has not been measured within a pig house. estimates were made. Carpenter and Randall” of the N.I.A.E. Farm Buildings Department state that the air speeds over the slatted area would be within the range 0.1-1.1 m/s. The air-flow volume is dependent on weather conditions, but it is estimated that if the air speed is to be within the range specified then the effective cross-section area through which it flows will be about 16 m2. The evaporation equation becomes : V DC --
2.87
IO--’ < F o.68x (e,--
x
This was reduced by a factor of O-9 in accordance rather than an open water surface.
J.
. ..(Bl8)
with Penman’s
formula
for a wet soil surface,
Appendix C The concentration of soluble solids The soluble solids are not known to have any effect on the operation of a slurry treatment system, nor are they considered in the mathematical models of the system which have been developed. A simple analysis has, however, been carried out to determine how the soluble solid content varies with evaporation. The concentration of soluble solids will increase with evaporation of water and it was thought that they might build up with time eventually becoming sufficiently high to inhibit the growth of bacteria. The concentration of the soluble solids and the liquid movements within a day are calculated as follows :
Lj+l = Ljmj-tj-fj-Ej,
. ..(Cl)
Qj+,
. ..(C2)
=
_ ‘3+1 -
cjLj+dtj-(;lfj,
QjAl
---z Lj .1
(c,Lj-t-dtj_cjSj) .(C3) (Lj-i
tj-,f,-Ej)
’
We wish to examine the conditions under which the concentration decreases from one day to the next, cj+,:scj or
within the system
increases
or
E. AUDSLEY
ETAL.
337
Dropping the subscript and re-arranging: . ..(C4a)
E> [(c-d)t]/c
or equivalently : c
(if r>E).
.( C4b)
These can be interpreted as follows. If the system concentration is less than the input concentration (cd), the system concentration will increase if the evaporation, E, is more than (c-#/c, otherwise it will decrease. For any given amount of evaporation E, there is an equilibrium value to which the concentration will tend which is independent of the output from the system: (‘E I dt/(t-E).
. ..((I)
If the evaporation is E every day, the system concentration will get closer and closer to cE. If the system concentration is more than cE it will decrease. If it is less it will increase no further than cE. This means that the concentration does not increase without bound as long as there is some input to the system. For large evaporation, the equilibrium concentration can become quite high which may inhibit bacterial growth. For example: if the daily input t = 2000, and the input soluble solids concentration, d = 0.015, and if we let the evaporation E = 200,400,700,1000 kg/d, which covers the range to be expected in Britain, then the equilibrium concentration cE = 0.017, 0.020, O-023, 0.030, so that even if 50% of the input is evaporated the soluble solids concentration is only doubled.
A Mathematical
Model
of a Pig Slurry
Treatment
System
E. AUDSLEY; D. S. BOYCE; J. A. WHEELER; A. G. DUMONT* Mathematical models have been developed of a pig slurry treatment system which includes mechanical separation of the fibre from the raw slurry, treatment of the defibred slurry in a biological filtration tower and then a further separation of sludge. Both the fibre and sludge are handled as stackable solids. Evaporation is considered to take place from the slurry within the pig house, within the filtration tower and from the defibred slurry which is being desludged. The models are suitable for considering both steady and variable inputs of raw slurry and evaporation. This study indicates many of the problems likely to be encountered when designing and operating such a system. In particular it has been shown that only small reductions in the dry matter content of the raw slurry can result in very large increases in the amount of liquid to be handled. 1.
Introduction
Systems of treating animal manures with the object of reducing their pollution potential and facilitating their economic utilization have been the subject of research and development in the last few years. This has become increasingly important with the advent of large production units handling manure as slurry in quantities which may exceed the chemical and or hydraulic capacity of the available land. Systems for treating animal slurries are relatively simple in concept; however, as all the inputs, internal flows, suspended solid contents and outputs are inter-related their operation can be complicated. It is likely that they can only be understood and the effect of changes in their operation determined by developing appropriate mathematical models. Such models will also aid the design of systems to be operated under specific sets of conditions and the long term operation of a system in different weather conditions and with different inputs can be examined. 2.
Pig slurry treatment systems
Systems of treating pig slurries with the objective of simplifying their subsequent storage, handling and disposal have been proposed in recent years. ’ A feature of some of these systems is that the slurry is separated into a liquid and solid fraction. The amount of liquid to be handled is reduced as much as possible by encouraging evaporation and by incorporating as much liquid with the solids as is compatible with them remaining stackable. The N.I.A.E. have developed an integrated separation, aerobic treatment and sludge dewatering system2-4 the general features of which are shown diagrammatically in Fig. 1. While the mathematical model which has been developed is based on this configuration it can be easily modified. The slurry is collected in a dunging channel and pumped to a separator. The separator removes the more fibrous fraction of the suspended solid matter, subsequently referred to as the fibrous solid. It can be adjusted to give different moisture contents in the fibrous solid. The object is to produce a solid that is stackable with little seepage of liquid. The removal of the fibrous material is necessary for the operation of the next part of the treatment system in which the separated liquid is pumped up into a biological filtration tower. This reduces the BOD (biological oxygen demand), removes some of the unpleasant odours and some moisture is evaporated. There is a settlement tank below the tower. The overflow from the settlement tank is returned to the dunging channel to flush it out. At intervals, sludge is removed from the bottom of the settlement tank, mixed with a chemical flocculant and pumped to porous containers where the sludge is dewatered by gravity. The filtrate drains to a tank from which some is returned to the system to ‘Systems
Department,
Received
16 June
1976;
N.I.A.E., accepted
Wrest
Park,
in revised
Silsoe,
form
Bedford
3 July
1977
421
422
PIG
SLURRY
TREATMEN
r SYST1.M
maintain it in a suitable operating condition while any excess must eventually be disposed Evaporation occurs from the dunging channel, the filtration tower and the dewatering area. may be possible to increase the evaporation in the tower by siting it in the piggery so that warm passes up the tower. While the concept of this system for treating pig slurry is simple, its design and operation different conditions is not. A suitable mathematical model will produce information on performance over long periods of time with different inputs relatively quickly and cheaply.
Ambient
I
OCR
for its
Raw Slurry
1
-
Pig house ventllotlng olr
of. It air
-
3
from dunging channel
e
sludge
-
System
-
Internal -
-
-
Fig. I. Schematic
3.
boundary
Inputs
e -
removed
flows
Mo~siure evaporated Solids and the system
from the system
hqutds removed for dlsposol
from
diagram of a pig slurry treatment
system
Model of a pig slurry treatment system
The slurry input to a treatment system is a function of the number of pigs, their diet and age. It will alter as the pigs mature. It is also likely to alter over a 24-h period as the pigs become active, feed and rest. This latter may be important when designing and operating a system. It is also important when sampling a system to determine its likely mean condition during a 24-h period. The condition of the ambient air, which determines evaporation, will vary over a 24-h period and seasonally. A model is developed (Appendix A) to provide information on the flows of material in the system and to calculate the output of fibrous solid, sludge and filtrate in terms of the raw slurry input, the volume input to the tower, the volume desludged, the evaporation and the system parameters. A dynamic model is developed where the input slurry and evaporation can be varied for different periods within 24 h. This model is simplified if the rate of slurry input and evaporation are constant and is referred to as a steady-state model.
E.
AUDSLEY
42.3
ETAL.
It has already been stated that air evaporates moisture from different parts of the treatment system. Seasonal effects and the variation from year to year can be investigated using the steadystate model with mean daily weather data recorded over many years. The relationship of the weather variables to evaporation from different parts of the system is considered in Appendix R. Pig slurry is a mixture of solids and liquids. The solids consist of a soluble and suspended fraction, A slurry treatment system is basically concerned with the suspended fraction. When evaporation of a liquid occurs the concentration of the soluble material increases. This concentration could perhaps reach a level where bacterial activity would be inhibited. While it is beyond the scope of this study to determine what concentration of soluble solids will inhibit bacterial activity, a relatively simple analysis (Appendix C) indicates the soluble solids concentration within the system knowing the initial concentration of soluble solids, the liquid throughput and evaporation rate. The analysis shows that the concentration does not increase without bound as long as there is some input to the system, irrespective of any output. As the soluble solids do not affect the operation of the system, they will be neglected in all further calculations and only suspended solids considered. The soluble solid content of pig slurry is approximately l-50/;;. The dry matter content which is the figure usually quoted is the sum of the suspended solids and soluble solid contents. 4.
Information provided by the model
Some examples are given of the type of information which can be provided how it can be used for designing and operating a system. The requirements operating system are also considered.
4.1.1.
by the model and for sampling an
4.1. Steady-state conditions Analysis of the treatment system
The solution of the steady-state model described in Appendix A provides an analysis of the system. The weight and solids content of the outputs from the system, the fibrous solid (W,-,,D,& the de-watered sludge ( Wso,Ds,,) and the filtrate (WE F,D E F) are independent of the volume of liquid input to the tower (B) and volume of sludge de-watered (C) and also independent of the volumes of the tanks in the system. Analysis of WEF, the excess filtrate, shows that this surplus is reduced if: (i) the separator efficiency, p, decreases provided the sludge solids content is less than the fibrous solids content; (ii) the raw slurry solids content, a, increases; (iii) the fibrous solids content, m, decreases; (iv) the sludge solids content, s, decreases; (v) the evaporation, E, increases; (vi) the filtrate solids content, b, decreases. 4.1.2. Examples of solution Typical inputs, parameters and evaporations for a slurry treatment system for 500 pigs are given in Table I. These are used with appropriate alterations for the different examples which are considered. As the density of the slurry and the liquid in the system is approximately one, volume and weight can be used interchangeably. The steady-state model can be used to determine the flows in the different parts of a system for any given set of conditions. Using the input data, Table I, the steady-state results for a 24-h period are (the symbols are defined in Appendix A): D RS ~-- 184 kg suspended solids added in raw slurry D SP = 320 kg suspended solids input to separator
424
weight of suspended weight of suspended weight of suspended suspended weight of suspended suspended weight of weight of weight of weight of
PIG
SLURRY
TREATMI-NT
SYSTEM
W SP 8790 D FS 85 W,, 513 D LO 235 W LO 8277 D 237 0;:’ ~~ 136
kg kg kg kg kg kg kg 6650 kg w,, D 102 kg 99 kg D::, W SD ll66kg W DW -: 2734 kg 2523 kg W,, W,, 210 kg
slurry input to separator solids in fibrous output from separator fibrous output from separator solids in separated liquid separated liquid produced solids input to tower solids overflow from settlement tank overflow from settlement tank solids in sludge from settlement tank solids in de-watered sludge de-watered sludge produced filtrate produced filtrate returned excess filtrate produced
Then : suspended
solids content
of (a) (b) $1 (e)
dunging channel separated liquid tower input channel circulant sludge from settlement
s DC S LO s S;; S,,
tank
0.036 0.028 = 0.022 0.020 0.026 =
If the inputs occur at an uneven rate the suspended solids at any given time are not likely to be those indicated; however, the total flow over a 24-h period would be the same. The steady-state solution is suitable for long-term planning. For instance, using the input data in Table I and assuming that the winter period is 180 days, the excess filtrate, which is a function of the mean total daily evaporation is: Winter
Total evaporation, kg/d Excess filtrate, kg/d
IX8 435
Summc~r 455 165
If it is assumed that no filtrate can be applied to the land for 180 days during the winter, the total filtrate to be stored would be 78,300 kg so at least 78.3 m3 of storage must be provided. The steady-state model can be used to provide information on how the system must be operated to meet some specific requirement. For example, it is probably desirable to control the suspended solids content of the slurry being treated in the tower to prevent a build-up of material in it. This is controlled by the amount of sludge periodically removed for de-watering from the settlement tank. This is shown graphically in Fig. 2. The amount of sludge, C, to be de-watered is plotted against the suspended solids content, S, w of the slurry entering the filtration tower for different values of 4, the settlement ratio. Evaporation is neglected as it is small in comparison with the volume of liquid within the system. From this example if 4000 kg/d are de-watered and y =- 0.8, the solids content STW of the input to the tower will be 2.2% (equivalent to 3.7 “/g d.m.). If, however, it is necessary to reduce S,,, to 1.5% (equivalent to 3.0% d.m.), the volume of sludge to be de-watered must be 6300 kg/d. Outputs from the system are independent of the volume de-watered but the above steady-state results will alter thus: suspended solids input to separator weight input to separator suspended solids in separated liquid
D
-=~ 242 kg
W:‘, D LO
~~ 6490 kg -~
157 kg
E.
AUDSLEY
weight of suspended suspended suspended weight of weight of weight of suspended
125
DAL.
separated liquid produced solids input to tower solids overflow from settlement tank solids in sludge from settlement tank overflow from settlemant tank filtrate produced filtrate returned solids content of (a) dunging channel (b) separated liquid (c) tower input (d) channel circulant (e) sludge from settlement
W LQ D TW D cc D SL W cc W,, WFR
S DC S LQ S TW S cc S SL
tank
5977 kg 162kg ~~ 58 kg 104 kg -~:= 4350 kg == 5034 kg = 4823 kg 0.036 0.026 0.015 = 0,013 0.017 -=
kg kg kg kg kg
Assumptions lkgQ4 hl 8=10,800 kg input to tower, A = 23CQlq raw slurry input, E. = 160 kg of moisture ewporoted fmm the &qing channel, ETW= 150 kq of moisture wapomted fmn Me beer
3
If 4OOOk@d are de-watered, fk soI& ccntent is 2.2% idry matter ccm+en+ appoximotely 37%. If the solids content is to be kn than I.%, more than 6300 kg/d must be de-watered
8000
E
2mJl
I.00
I.50
I 2a
I
I 2.50
I 3.00
1
Tower input solids content P&J
Fig. 2. -Relationship between weight to be de-watered and tower input solids conterrt
4.2. Variable inputs The model can be used to show how the slurry treatment system operates when the inputs vary. There are likely to be three circumstances as follows. (i) Changes in the slurry and weather inputs over a 24-h period. (ii) Changes as the animal matures. This will result in a general increase in food intake with a corresponding increase in slurry. (iii) Change due to seasonal weather. This will affect the evaporation of moisture and the ventilation requirements. This study has only been concerned with 24-h weather and slurry changes and the effect of seasonal weather. It is unlikely that changes in slurry output with pig maturity is important in terms of treatment system design and operation. 4.2.1. Variable inputs-24 h period If the rate of input of slurry to the system varies over a day the suspended solid contents within the system will change. A mathematical model was developed to simulate the performance of the system when the slurry input and evaporation varied over 24 h (Appendix A). The efficiency of the separation of the fibrous solids is calculated from the following expression derived from data provided by the Farm Buildings Department of N.T.A.E. :
PIG
126
SLURRY
TRL:ATMFN~I‘
SYSTEM
y := 0.443L2.2 D,,/l+',,-0.345nz. The data used in the following example is the same, except where noted, as in Table I. input of raw slurry A is still 2300 kg/d, but for this example the day was divided into periods. The variation in the production of raw slurry by pigs over a 24-h period does to be known so the input of raw slurry and the evaporation for each period was taken
The total four 6-h not seem to be:
Period I
2
3
4
900 164
1000 205
350 41
50 0
--__
Raw slurry, kg/6 h
Evaporation, kg/6 h
Table II, part A, shows for comparison the flows and the suspended solids contents if the slurry input and evaporation are constant over a 24-h period. Table II, part B, shows the system flows and the solid contents for one set of channel, separator reservoir and settlement tank capacities. Over the 24-h period the solid content of the input to the slurry separator, S, P, ranges from 3 “/,,to 4 “/;I,input to the tower, Ss ,+ from 1.9 % to 2.5 %, and of the filtrate, S,,, from 2.5 “:, to 2.6 “I,;,.The daily outputs, however, are little altered. TABLE
Input data-model
I
studies of a pig slurry system for 500 pigs
Inputs
A, raw slurry B, tower C, liquid to be de-watered
I 2300 kg/d 10800 kg/d 4000 kg/d
Parameters (i)
Suspended solids content (I, raw slurry b, filtrate HI, fibrous solids s, de-watered sludge
(ii) Others p, fibre separator efficiency y, settlement ratio Evaporation E Dc, dunging channel E TW, filtration tower E DW, de-watering
0.080 0.001
0,165 0.085 0.46 0.80
160 kg/d 150 kg/d 100 kg/d
Table II, part C, shows the results obtained when the volume of the dunging channel, VDc is reduced from 2300 1 to 1000 1 and the separator reservoir from 643 I to 100 1. This reduction in buffering only increases the range of solids contents a little. There is very little change in the solids content of the de-watered slurry because this is buffered by the large volume of the settlement tank which has remained unaltered. These results indicate the following: (i) Since the rate of slurry output from pigs is likely to vary over 24 h, in as yet some unmeasured way, samples taken from a slurry treatment system during any one period of the day could be misleading. Samples should therefore be taken throughout the 24-h period.
E.
AUDSLEY
427
ET,~L.
TABLE
II
Simulation model results showing the effect of dunging channel and separator reservoir volume on the system operation over 24 h with constant and variable production of raw slurry
Volume afdunging channel: Separator reservoir. Settlement tank:
Volume of dungingchunnel: Separator reservoir. Setrlement tank:
2300 I 643 l 7000 I
IO00 I 100 I 7000 I
1 period 24 h
A Flow rates (kg/period) 2300 8845 519 8327 I0800 6665 4000 1155 2699 2472
Raw slurry Input to separator Fibrous solid Output from separator Input to tower Channel circulant Sludge for de-watering De-watered sludge Filtrate Filtrate returned Suspended
,I_
Four periods-6
I
/
I
2
I
h
3
I
4
B
295 646 331
350 1972 79 1893 2700 1673 1000 293 678 806
50 1723 II 1712 2700 1700 1000 280 720 988
3.99 2.78 2.45 2.06 2.58
3-60 3.06 2.17 2.05 2.56
3.01 2.92 1.89 I ,96 2.45
900 2552 203 2349 2700 1646 1000 283 659 351
1000 2598 230 2369 2700 1646
3.60 2.49 2.18
1000
If
900 2552 204 2348 2700 1646 1000 286 655 352
2598 231 2367 2700 1646 1000 303 638 333
350 1972 78 I894 2700 I673 1000 295 676 806
50 1723 II 1712 2700 1700 1000 273 727 988
3.70 2.59 2.27 I .97 2.46
4.18 2.97 2.62 2.10 2.62
3.51 2.97 2.11 2.06 2.58
2.70 2.61 I .69 I .92 2.40
1000
solids confent
%
3.60 2.80 2.18 2.02 2.52
Input to separator Output from separator Input to tower Channel circulant Sludge for de-watering
1.98 2.47
-
It is also likely that the difference between samples will be in part due to experimental error and part due to variation in the input of raw slurry. The average of measurements taken over a 24-h period is, however, likely to provide an estimate of the mean value of the suspended solids over a 24-h period. which will be helpful in the design of slurry (ii) This model can be used to provide information treatment systems. For example : (a) if the maximum level of suspended solids which can be handled by the filtration tower or any other part of the system has been established, the volume to be desludged and the buffering required by providing reservoirs of sufficient capacity can be determined; (b) the minimum storage required for the excess filtrate can be determined for different sets of conditions. inputs-seasons and years 4.2.2. Variable The most important effect of weather on the operation of a slurry treatment system is likely to be the effect of evaporation from various parts of the system on the amount of excess filtrate which must be disposed of. The model calculates the seasonal production of solid and filtrate for disposal and the expected annual variation. Fig. 3 shows the mean and maximum amount of filtrate produced over a IO-year period under the weather conditions prevailing at Rothamsted Experimental Station, Harpenden, Hertfordshire, 1959-68. Four levels of slurry dry matter content which indicate either changes in the
PIG
428
Max 1968 MI!- 1967
500 t
Max 1968 Min 1958
Max 1965 Min 1959
SLURRY
TREATMENl-
SYSTEM
Max 1962 Mln 1959
mrter 4
1
Mean
and range
0
Slurry dm = 4%
0
Slurry dm ; 6%
m
Slurry d m = 8%
m
Slurry d m = 10%
Fig. 3. The mean und range of seasonal production of excess filtrure, 1959-68, from a piggery housing 500 5O-kg meal-ftid pigs, for slurry d.m.s of 4%, 6%, S”,: and 100,:. The wet area for evaporation inside the pighouse was 280 m2 ; sepnrntor eficiency = 50 % I_fibrous solids d.m. = 22 %; de- wutered sludge d.m. 7 I I a’;; excess filtrate d.m. = I.75 06. Each quarter is 91 du,>.y
ration dry matter to water ratio, or that water has leaked into the system are considered. There are small differences between the amount of filtrate produced from year to year and from season to season. In contrast, changes of a few percent in the dry matter content of the raw slurry will This highlights the importance of have a very large effect on the amount of excess filtrate. ensuring that pigs are not allowed diets with unnecessary water content and that every effort be made to prevent extraneous water from getting into the raw slurry treatment system. Table III shows mean values for the weather parameters for 3 widely dispersed sites in England. There is little difference between the mean annual evaporation and mean daily dry bulb temperature; however, the annual rainfall at Ellbridge, Cornwall, is nearly double that of Cawood, Yorkshire. Fig. 4 shows the mean annual accummulated filtrate for disposal from January to December, for 1959-1968. As expected from the evaporation values given in Table III there is little difference in the annual quantities of excess filtrate from each site. If the hydraulic loading of the soil is likely to be a limiting factor, rainfall may be an important factor in planning a land spreading programme.
Mean weather conditions at 3 sites, 1959-1968
Mean duil) dry bulb temperature, ‘C
Cawood, Yorkshire Rothamsted, Hertfordshire Ellbridge, Cornwall
Mean rainfall, mmjveur
8.9 9.1
600 723
IO.1
1159
Mean absolute evaporation from a free wufet surface, mm/yea! 155 720 142
E.
AUDSLEY
429
ET AL.
0
5
IO
15
20
25
30
35
40
45
50
Week number
Fig. 4. Accumulatedfiltrate for disposal, January to December, mean of IO years 1959W58, Cawood (C), Ellbridge (E) and Rothamsted (R) from a piggery having 500 50-kg pigs for a slurry d.m. of IO’%. The wet area for evaporation inside the pighouse was 280 m2; separator ejjiciency SOaL; fibrous solids d.m. = 20%; de-watered sludge d.m. = 10%;
exressfiltrate
5.
d.m. =
1.75%
Conclusions
A mathematical model study of a pig slurry treatment system which separates the slurry into a solid and liquid fraction has been used to provide information on how it operates under various conditions. While the model can be modified to represent different system configurations the following general conclusions apply to this type of system. (9 The soluble solids concentration does not increase without bound as long as there is some input to the system, irrespective of any output. (ii) The excess filtrate is reduced if the moisture content of the fibrous solid and de-watered sludge is increased, though they must still remain stackable. It is also reduced if the separator efficiency is reduced, however, the separator must remove sufficient fibrous solids to allow the remainder of the treatment system to operate effectively. (iii) The variation in the production of raw slurry by pigs over a 24-h period affects the suspended solids contents in the different parts of the system. Variability in slurry production may be important if a system is to be sampled in order to estimate its mean state over 24 h. It may also be important when designing a treatment system, to provide sufficient buffering capacity so that the suspended solids content does not increase in any part of the system to a level which could interfere with its operation, for instance, the input to the filtration tower. (iv) Using 1959-68 weather data, there were only small changes in the amount of filtrate produced from year to year due to variations in natural evaporation. (v) The amount of filtrate produced by the treatment system using ten years of weather data from three widely separated sites in England varied little. There was little difference in the natural evaporation between these sites. There was, however, a considerable difference in rainfall between sites which could influence a land spreading programme. (vi) The factor which had the largest influence on the amount of filtrate was the dry matter content of the raw slurry. For one set of conditions and 500 pigs a decrease in the dry matter content of the raw slurry from 10 o/1to 6 7; increased the production of filtrate from 60 t to 225 t (IO-year average). The output solids cannot hold any more water so all the extra water goes through the system to become filtrate. Similarly any extra evaporation would directly affect the filtrate produced. This indicates the importance, if the quantity of liquid to be handled is to be minimized, of not feeding unnecessary water and preventing leakages of water into the slurry.
430
PIG
SLURRY
TREATMI-NT
SYSTEM
REFERENCES
Osborne, L. E. The efficient use of slurry. J. Proc. lnstn agric. Engrs, 1975 30 40-43 2 Osborne, L. E.; Hepherd, R. Q.; Sneath, R. W. An integrated separation, aerobic treatment and siudgc de-watering system for pig slurry. J. agric. Engng Res., 1976 21 2 ’ Hope, H. “Clean” the slurry and “wash” the air. Fmrs’ Wkly, 1977 86 83, 85, 87 4 Ockwell, T. New building willgive waste the@/ treatment. Br. Fmr Stockbr. Muck ‘77 supplement. ’
26 March 1977 ’ O’Callaghan, J. R.; Pollock, K. A.; Dodd, V. A. Land spreading qf’manure .fkoln anin?al production units. J. agric. Engng Res., 1971 16 3 ’ Randall, J. M.; Carpenter, G. A.; Hawkins, J. 0. Air distribrttion in a fkN scale section Q/a livrstoch building--Part I. Dep. Note DN/FB/319/3020, natn. Inst. agric. Engrs, Silsoe (unpubl.). 1975 ’ Owen, J. E.; Carpenter, G. A.; Randall, J. M. A simulatedpigjbr use in ventilation studies. Dep. Note DN/FB/168/3020, natn. Inst. agric. Engng, Silsoe (unpubl.), 1971 ’ Treybal, R. E. Mass Transfer Operation, 2nd Edition. Tokyo, Japan : McGraw-Hill I968 177. 2 I7 ’ Potential Transpirationfor Use in Irrigation and Hydrology in the U.K. and Republic of Ireland. M AFF Technical Bulletin No. 16, 1967 ” Penman, H. L. Natural evaporation fLonl open water, bare soil and grass. Proc. R. SOC., Lond. A. 1948 120-45 ” Carpenter, G. A.; Randall, J. M. Private communication Appendix Mathematical
A
model of slurr!, treatment system
A.1. Dynamic model The dynamic model of the slurry treatment system is described by the 26 equations shown in Fig. 5 where a prime denotes a variable changing from an old value to a new value, lower case letters represent parameters of the system. The amount of raw slurry can be altered by changing the number of pigs or their food. The input to the tower and volume desludged, controlled by pumps, can be set, within reason, to any desired value. All other flows within the system are fixed by these and can thus be calculated from them. As the density of the slurry and the liquid in the system is approximately one, volume and weight will be used interchangeably. The evaporation from the system can be calculated from past weather data (Appendix B) and in this case is assumed to be known. A.1 .l. Steady-state mode/. Assuming the system is operating in a steady state, that is, that all the volumes and suspended solids contents within the system remain the same from day to day, these equations can be solved in terms of the volume of raw slurry (A), the volume input to the tower (B), the volume removed for de-watering (C), the evaporations (E,.) and the system parameters: D RS -~~aA
DS, m,here
. ..(Al)
= aA $4 (B-C-E,,)
(A/I +h (C
EDr / ETW))/C
. ..(A2)
/I
- a-ap-&hap/m
. ..(A31
w,,
=- A -{-B-C-ETw-E,r
. ..(A4)
D FS W,, D
LQ
apA,
. ..(A5)
:= apA/m,
. ..(A6)
:
a (1 -P>
W LQ - (l-up/m) D Tb D,,.
A +q
(B-C--ET,)
(AB
+~ h (C
7 EDc
A$-B-C-E,.,-EE,,,
(1 m’q (B-CC--E,,M’)(4-t m=q (B-CC--ETw)
(A/l+b
+B,,))lC,
. ..(A7) . ..(A8)
b CC Em:-E,,)), (C1~E,,~I
E,,)),‘C.
. ..(A9) . ..(AIO)
NOTATION
USED IN THE APPENDICES
. indicates where two capital letters will be used as subscripts to denote the part of the system referred to. A a B b
c Cj
D.. d E..
Ej .ell
F fj
GS HB
HP K,
k LJ
MP m
N P P
QJ 4
R, r S.. s Y d
weight of raw slurry suspended solids content of raw slurry weight input to the tower suspended solids content of filtrate weight removed for de-watering soluble solids concentration of liquid removed from the system on dayj weight of suspended solids soluble solids concentration of liquid added to the system weight of evaporated water weight of water evaporated on day j saturated vapour pressure at Tj, mm Hg mean vapour pressure, mm Hg volume of ventilating air through the piggery, m3/h liquid removed from system during dayj dry air mass flow rate of the ventilating air through the piggery, kglh heat loss from building, kJ/h sensible heat output of a pig to the air, kJ/h volumetric mass transfer coefficient, kg h-l mm3 per unit change in log humidity gradient suspended solids content of input to tower liquid in the system at the end of day j moisture loss from a pig to the air, kgih suspended solids content of fibrous solids number of pigs volume of tower packing, m3 efficiency of removal of suspended solids in raw slurry by separator total soluble solids in system on day j settlement ratio (solids content in recirculant : solids content in sludge removed for dewatering) total radiation from the sun, mm water equivalent ratio of weight of sludge for de-watering to weight recirculated suspended solids content suspended solids content of solid sludge maximum possible hours of sunshine/ day (24 h) actual hours of sunshine/day
mean ambient temperature, F temperature inside piggery, C temperature outside piggery, C liquid added to the system during lj day j uz run of wind at 2 m height, mile/d capacity of reservoir V.. daily evaporation from the dunging *‘DC. channel, kg/m* weight of water evaporated from the VTW tower, kg/h expected evaporation from site, mm/d VDW VWS evaporation from an open water surface, mm/d W.. weight of liquid weight of pig, kg W absolute humidity of inlet air, kg VI water vapour/kg dry air absolute humidity of outlet air, kg Y2 water vapour/kg dry air average absolute humidity in piggery Yi kg water vapour/kg dry air absolute humidity outside piggery, kg Yt water vapour/kg dry air YS absolute humidity at the adiabatic saturation temperature of the inlet air, kg water vapour/kg dry air 0 Stefan’s constant T, T, To
Two capital letters will be added at as subscripts to denote the part of the system referred to : cc overflow from settlement tank to dunging channel dunging channel DC DW from de-watering area excess filtrate disposed of EF returned to separator reservoir from FR filtrate tank fibrous solid from separator FS in the filtrate tank FT from separator to separator reservoir LQ raw slurry added to dunging channel RS de-watered sludge SD from settlement tank for de-watering SL input to separator from dunging SP channel separator reservoir SR settlement tank ST tower TW Thus for instance: =weight of water evaporated from the de-watering area WFT -weight of liquid in the filtrate tank
ED,
432
PIG
SLURRY
TREATMENT
SYSTEM
. ..(A1 1) . ..(Al2) . ..(Al3)
Sepamtor Fibre sqmded DFS
sdlds
m. efflclency P
= ~0~s
- (6)
W FS = D&m
- I71
WLQ = WSP -Wm
94s - (8) “‘FS
D LQ = DSP -DFS
- (9)
‘+&a
DLQ
resermir
Sepwotor Capacity
>
V,, - (IO)
w;,
= w,+w,,tw,,-w,
DSR
= OS,+
I
+ DFR - DTW
- (150)
= WSL / WCC
D,,/W,
= (rt
I) &,I
f+,/W,=q(rtll
fJsr/
W&
= w,,t
w,-
‘ST
= OS,+
DT,-ax
DSD t
w,+
wsr
-(I51
Irtq)
W,
-(I61
Em
DDW 0,
-
- (18)
DSL
solids 5, sOlIds b = WSL
-
(19)
= DSL
-
(20)
-
-4,
-
(231
D;,:
-DE,
-
(24)
D,,
D~+DDW-DFR = bWm
Op. =bWn,
WSD
(22)
w;, = wFT+ w,, -wFu
Fig. 5. Flow chr~ OJ’N pig slurq~ ttwtment
940
_
- (25) -
F EDW. 0
- (21)
= SW,
DDI=bWDl
Wm. Dr.
-wsL-(171
-0s~
po I lets
Sludge suspended filtmR smpmded t
(r+ql
Ew-W,
W,L t-k-nvterlng
w,
(III (12) (13)
tank
setllemmt
WCC. “cc
D,,
-
wan* ‘,F
126)
system
,
E.
AUDSLEY
433
ETAL.
WSD = A/W--b)+b
. ..(A14)
(E,,-t-E,,+E,,)/(s--h),
WDW= C-AB/(s-h)-sE~w/(s-h)-h W,R = C-(l-up/m)
(ED, I E,,)/(s--h),
. ..(Al5) . ..(Al6)
A+E,,+6Tw,
and W EF = A (s--a--s~plm+ap)/(s--b&-s
. ..(Al7)
(E,,+E’,,+E,,)l(s--).
The suspended solids content of the different parts of the system are given by:
s DC
=
D,s+Dcc
=
QA+#----ET,)
(A~+h(C+EDC+ETW))/C~
A+B-C-E,,
A+WCC
SLQ
=
D,,l
..(A18) . ..(A19)
WLQ,
S TW = &WI&
. ..(A20)
s cc
= dAb+&c+E,c+-&w))/c
. ..(A21)
S SL
=
and . ..(A22)
[AP+~(C+EDC+~~W)I/C~
A.l.2. Input to tower The solids content of the input to the tower must be kept sufficiently low for the bacteria to operate properly but the amount of input is fixed by the need to keep the surfaces wet so that the only control of the solids content is by varying the weight of liquid removed for de-watering (C). Suppose we wish the input to the tower to have solids content k. The amount that needs to be desludged, C, can be found by solving: STW = k, . ..(A23)
(1 +q(B--C--E,w)/C)AB+b(C+ED,+E,w)=kB, m,C2+m2Ctm,
= 0
where ml =
W-_q),
‘% =
(1-q)
m3 =
O--ET
(AP+b(E,,+E,,)+bq(B-ET,))-kB
and W)
(AB+HEDC
This is shown diagrammatically
-t&
~1).
in Fig. 2. Appendix B
Evaporation from a pig slurry treatment
system
B.l. Pig house ventilation This analysis is based on a 500-pig unit. The heat output of a pig is in two parts: sensible heat, to the surrounding air, and latent heat, corresponding to a quantity of moisture given up by the pig to the air; either in the breath or from the skin. Some moisture is also given to the air by evaporation of the urine. For sensible heat losses the heat balance equation is:
PIG
434
the moisture
balance
equation
TREATMtNT
sensible heat output of pigsE heat losses from the building.
sensible heat removed by ventilating air Similarly,
SLURRY
. ..(BI)
is:
moisture loss from pigs I moisture given to ventilating air rX evaporation from manure. The heat loss from the building N.I.A.E.6 is given by:
based on data from the Farm
H,
=
SYSTEM
2.0(7.-T,,)
(1.66N
Buildings
. ..(B2) Department
of the . ..(B3)
50).
This assumes a side wall and roof area of 1.66 m”/pig, end wall area of 50 rn’ and an overall heat transfer coefficient of 2.0 kJrnm2”C-~ ’h- *. The moisture output of pigs, including evaporation from urine, and sensible heat output of pigs from 50-100 kg weight were fitted approximately by a linear relationship also based on data from the Farm Buildings Department of the N.T.A.E. M,
= 0.00367Ti
‘-m
;q 0.028 IO.05
x’ 677-T,(7.427
+
The sensible heat output of the pigs results in an increase the water vapour in the air. That is: G,x w here
1.00(7’-T,){-G,x
l.88( YiTi-
1.88 -- specific heat of water vapour, ??
X 16.135). in the heat content
.(B5) of the dry air and . ..(B6)
Y,,T,,) = H,N-HHB
kJ kg--’ “C-l :
I.00 ~- specific heat of dry air, kJ kg-r ‘C-l. ??
The moisture ventilating air:
output
from
the pigs results
in an increase
in the absolute
humidity
. ..(B7)
Yi : Y,,$-N.M,/G,s. Substituting
of the
for Yi in Eqn (B6): G,(T,-T,)
(I-1-1.88
Y,,)i 1.88 Ti M,N
=: H,N-H,.
Since I.88 Y, is usually much less than 1.0, that is, the heat increase of the water vapour is negligible compared to the increase in heat to the dry air, this equation gives: Gs = [(HP-- l-88 TiM,)N-
H,]/(T,-T,,)
. ..(BX) in the air . ..(Bo)
A constraint is placed on the air flow rate which must be high enough to prevent accumulation of toxic odours and low enough to prevent excess draught for the pigs. The limits’ were set at 0.2 m3/h and 2 m3/h per kg of pig, which, assuming a 75kg pig, means a minimum flow rate of 7500 kg dry air/h and a maximum of 75 000 kg/h for a 500-pig unit. Where the flow rates go beyond these limits the rate is fixed at the appropriate value and the temperature in the house allowed to change. B.2. Evaporation from ajiltration
tower
The theory used to describe the effect of blowing air through the filtration tower was that given by Treybal* for a recycling liquid, gas humidification process. Jn this process, in the steady state, with an inlet gas at constant temperature and humidity the recycled liquid approaches the
E.
AUDSLEY
ETAL.
435
adiabatic saturation temperature (wet bulb) of the inlet gas. The gas is humidified and cooled along the constant heat line corresponding to the inlet conditions of the gas. Although heat is produced in a biological filtration tower as a bi-product of the bacterial degradation of the slurry, in the absence of data to the contrary, this heat was neglected in comparison with the amount of heat exchange between air and liquid. Using this theory the relation between mass airflow and inlet and outlet humidities is given by: ,n
( K- Y,) __W’ (Ys- Yz> Gs
Re-arranging Eqn (BIO) gives an expression for a given air flow rate: V TW
=
G,( Y2-
for the quantity
Ys-
Y,)=G,(
. ..(BlO) of water evaporated
Yl)
from the tower
. ..(Bl I)
Since Y, is the absolute humidity of the air ventilating the piggery, this equals Yi. The prototype filtration tower used by Farm Buildings Department. N.I.A.E., was ventilated at 30°C. Measurements on the inlet and outlet air for the tower were taken sporadically to compare with the theoretical values. The results were inconclusive both in predicting the value of the heat and mass transfer characteristics and also in comparing the actual behaviour of the tower with the theoretical. The results for the volumetric mass transfer coefficient, K,, were between 50 and 200 kg h-l mW3 for the “Flocor” packed tower, and asimilar range forthe heat transfer coefficient. The variation is probably explained by the fact that the system is never in a completely steady state because of the variation in ambient humidities. A value of 100 was taken as an estimate of the mass transfer coefficient, and it is thought that the error in this value is at the most 50 “/,. The results using this value indicated that using such a rough estimate was justified in this study. B.3. Evaporation from site The area for evaporation from the site was made up of three parts: the exposed area of the de-watering pallets; the area below and around these pallets; and any other site area liable to be continually wet. This included drainage channels and open tanks. In the results given, 7 pallet boxes were assumed to be draining at any one time, each being 1.2x 1.06x0.76 m high. Because of their construction only half the side area plus the base and top surface were available for evaporation and over the 7 days’ draining they were assumed to be 80% full on average. This gives an area for evaporation of: 0.8 x (0.76 x 1*06+0.76x
1*2+2x
1.2 x 1.06) m2/pallet.
Using 7 pallet boxes a base area of 10 m2 and other site area of 20 m2 were Penman’s formula9 for a permanently-saturated soil surface was used to evaporation from the surface of the settlement tank, concrete drainage area It was assumed these areas were exposed to sun and wind for evaporation, The formula gives for evaporation from an open water surface:
HA/y+
vws = A/y+-1 where:
y A H=
=
E,
assumed. estimate the potential and the stacked solid. but not to rain.
..(B12)
0.27 mm/OF,
de = dT T, I
=
slope of the saturated ambient temperature,
0.75 Rr--aTa4
c, = O-35 (ell-Zd)
(0.47W.O75e,) (0*5+U,/lOO)
vapour
(0.17+0.83
pressure-temperature d/y),
curve at the mean . ..(B13) . ..(Bl4)
436
PIG
SLURRY
TREATMINT
SYS-TFM
and R, -m=R, (0.16+0.62 For a saturated
. ..(Bl5)
d/Y).
soil surface the evaporation V DW
=
is estimated
as: . ..(Bl6)
0.8 x vws.
B.4. Evaporation from dunging channel Evaporation of moisture within the pighouse occurs from the wetted surface of the slats and the slurry channel. The evaporation was calculated using an exponential form of Penman’s evaporation from an open water surface.’ O V DC
=
. ..(Bl7)
0.033 U, o,68 (e,-2,).
Since U?, the mean wind speed, has not been measured within a pig house. estimates were made. Carpenter and Randall” of the N.I.A.E. Farm Buildings Department state that the air speeds over the slatted area would be within the range 0.1-1.1 m/s. The air-flow volume is dependent on weather conditions, but it is estimated that if the air speed is to be within the range specified then the effective cross-section area through which it flows will be about 16 m2. The evaporation equation becomes : V DC --
2.87
IO--’ < F o.68x (e,--
x
This was reduced by a factor of O-9 in accordance rather than an open water surface.
J.
. ..(Bl8)
with Penman’s
formula
for a wet soil surface,
Appendix C The concentration of soluble solids The soluble solids are not known to have any effect on the operation of a slurry treatment system, nor are they considered in the mathematical models of the system which have been developed. A simple analysis has, however, been carried out to determine how the soluble solid content varies with evaporation. The concentration of soluble solids will increase with evaporation of water and it was thought that they might build up with time eventually becoming sufficiently high to inhibit the growth of bacteria. The concentration of the soluble solids and the liquid movements within a day are calculated as follows :
Lj+l = Ljmj-tj-fj-Ej,
. ..(Cl)
Qj+,
. ..(C2)
=
_ ‘3+1 -
cjLj+dtj-(;lfj,
QjAl
---z Lj .1
(c,Lj-t-dtj_cjSj) .(C3) (Lj-i
tj-,f,-Ej)
’
We wish to examine the conditions under which the concentration decreases from one day to the next, cj+,:scj or
within the system
increases
or
E. AUDSLEY
ETAL.
337
Dropping the subscript and re-arranging: . ..(C4a)
E> [(c-d)t]/c
or equivalently : c
(if r>E).
.( C4b)
These can be interpreted as follows. If the system concentration is less than the input concentration (c
. ..((I)
If the evaporation is E every day, the system concentration will get closer and closer to cE. If the system concentration is more than cE it will decrease. If it is less it will increase no further than cE. This means that the concentration does not increase without bound as long as there is some input to the system. For large evaporation, the equilibrium concentration can become quite high which may inhibit bacterial growth. For example: if the daily input t = 2000, and the input soluble solids concentration, d = 0.015, and if we let the evaporation E = 200,400,700,1000 kg/d, which covers the range to be expected in Britain, then the equilibrium concentration cE = 0.017, 0.020, O-023, 0.030, so that even if 50% of the input is evaporated the soluble solids concentration is only doubled.