J. agric. Engng Res. (1991) 50, 209-218

Modelling Gas Flow in a Silage Clamp After Opening

D. J. PARSONS

AFRC Institute of Engineering Research, Silsoe, Bedford MK45 4HS, UK

(Received 19 November 1990; accepted in revised form 17 March 1991)

A mathematical model has been developed of the flow of gas in a bunker silo after opening the front face. It assumes that the driving force is the difference in density between the air outside and the carbon dioxide-rich gas inside the clamp. Darcy's law for fluid flow in a porous medium is used to calculate the gas flux.

The model has been solved using a computational fluid dynamics program. It shows that the density differences generate a generally semi-circular flow pattern: air enters at the top of the front face and leaves at the bottom. As a result, the penetration of oxygen is much more rapid near the top of the clamp. This agrees qualitatively with the results from experimental silos in which oxygen was found to spread from the top of the open face. In the model, with inert silage, after 7 days the oxygen concentration reached 1% at a depth of 4 m from the face at the top, but only 1 m at the bottom.

To explore the effects of biological activity on the gas transport model a simple microbial growth model using Monod kinetics with oxygen as the sole substrate was included. It had a large effect on the flow pattern: initial penetration was similar to that in the inert silage, but the population was able within a few days to consume most of the oxygen within 1 m of the face. Thus oxygen penetration over 7 days was substantially reduced. The microbial population was highest near the top of the open face, where most oxygen was available, corresponding with the pattern of heating found in the experimental silos.

1. Introduction

When a silage clamp is opened to allow the silage to be fed to livestock, oxygen is allowed in, and microbial activity starts, causing available carbohydrates to be consumed. In order to maximize the feeding value of the silage it is necessary to minimize the microbial activity, by minimizing the ingress of oxygen. Standard advice is based on at tempting to remove silage from the face of the clamp faster than oxygen can penetra te , but there is presently no way to predict the penetrat ion rate.

Experimental w o r k b y Rees etal . 1~ has measured some physical propert ies of silage which are expected to affect penetra t ion (porosity, diffusion coefficient) and the effects on these of density, chop length and moisture content. The physical and biological processes involved are only partially unders tood however, and the available knowledge is difficult to apply in farm-scale situations. The situation is complicated by the fact that microbes near the face can consume oxygen as it enters, and prevent it penetrat ing the silo as deeply as a purely physical model would predict. This has been the case with pilot-scale silos constructed at the A F R C Institute of Engineering Research, where oxygen was found close to the open face only, with the highest concentrat ion near the top. a Heat ing, indicating microbial activity, also occurred mainly at the top near the face.

In order to make the best use of available information and to test hypotheses about the processes involved, a mathematical model of the changes during feeding out is being developed. This is required to simulate both the physical processes causing gas movemen t within the silo, and the biological processes which cause oxygen to be consumed and carbon dioxide to be produced. There have been several a t tempts to model the

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© 1991 Silsoe Research Institute"

210 G A S F L O W IN A S I L A G E C L A M P

Notation

Notation for physical model x distance from face, m z height above ground, m

Cx mole fraction of component x # dynamic viscosity of air, Pa s c" rate of production of component x, s -1 p density of gas in silo, kg/m 3

p~ initial density of gas in silo, kg/m 3 g gravity vector, m s -2 Po density of air, kg/m 3 g magnitude of g q~ porosity of silage

H height of silo, m K permeability, m 2 The subscripts used for gas components

Mx molar mass of component x, kg are p pressure, Pa c carbon dioxide

Pi initial pressure, Pa n nitrogen Po standard pressure, Pa 0 oxygen

t time, s u velocity component in x direction, Notation for microbia lmodel

m/s K m Monod half-rate constant v superficial velocity, m/s Y yield of carbon dioxide from

Vm volume of one mole of gas at microbes STP, m 3 /) maximum specific growth rate,

on velocity component normal to s- boundary, m/s 0 measure of microbial population,

- 3 w velocity component in z direction, m m/s

fermentation stage, for example Neal and Thornley, 4 and Muck et al. S and also the effects of leakage of small quantities of oxygen during storage, for example Pitt. 6 Buckmaster et al. 7 include a simple diffusion model of the feed-out phase within a more general model. The present model appears to be the first to concentrate on the feed-out period. This paper describes a model of gas movement . A simple model of microbial development is included to illustrate the effect of respiration on the flow patterns.

The driving force in the model is the difference in density caused by the high carbon dioxide concentrations in the silo, and the pressure gradients induced as a result. Experiments by Parsons and Hoxey 8 have shown that small pressure gradients can produce flow rates sufficient to allow deep penetration into silage clamps over the time scales involved. Experiments by H. Honig of FAL, Germany (personal communication) have shown that carbon dioxide-rich gas mixtures will travel downwards through silage at similar rates. The flow rates involved are at least an order of magnitude greater than those produced by diffusion in the work of Rees et al. 2 Models based on diffusion also fail to predict the strong vertical variation in oxygen concentration found in the pilot experiments.

2. Description of the model

2.1. Geometry

The type of silo being considered here (Fig. 1) is a clamp or bunker, which is approximately a rectangular parallelepiped, typically about 2 m high (z), 4 m wide and 15 m long (x). For the purposes of the model, it is reduced to two dimensions by assuming

D. J. PARSONS 211

that all properties are uniform across the width of the clamp. The origin is taken to be at the base of the open face, with the x axis horizontal and the z axis vertical. The x component of velocity is denoted by u and z component by w. Fig. 1 shows a longitudinal section through the silo. This view is used in all subsequent figures, but they are truncated about 6 m from the face, because no significant effects are observed beyond this depth during the simulations described.

2.2. Gas f low

The empirical equation usually used to describe fluid flow in porous media is known as Darcy's Law. a In three dimensions it takes the form

v = - (K/u) (V p - pg)

The permeability, K, is a scalar, corresponding to the assumption that the medium is isotropic (has the same permeability in all directions). In practice silage is probably anisotropic, due to the generally horizontal orientation of the grass particles within the clamp. For full generality, an anisotropic medium must be described by a second order tensor, though it may be adequate simply to use different values of permeability in the coordinate directions, corresponding to a diagonal tensor. At present there are insufficient data to resolve this question. A method of measuring the permeability of silage was described by Parsons and Hoxeyfl

The constituent equation allows the density, p, to be calculated for any given gas mixture and pressure. Treating air as a mixture of nitrogen, oxygen and carbon dioxide with mole concentrations c,, co, c¢ and molar masses Mo, Mo, Me respectively,

p = (p/po)(c .Mo + coMo + ccMc)/Vm

where Po is standard pressure and Vm is the molar volume at standard temperature and pressure (STP). Temperature effects are ignored in the present model.

A continuity equation applies to each component of the gas mixture in the usual form:

8c /8 t = V . (c v) + c'/dp

where c' is a source term due to microbical activity, which will be described later. In many applications of Darcy's law to gaseous flows the main driving force is pressure,

and gravity is ignored, unless heating leads to buoyancy effects. In a clamp immediately after opening, the temperature is fairly uniform and the pressure is close to atmospheric. In this situation the gravitational effects due to the different densities of different gas mixtures become important.

The initial state for the model is the equilibrium condition reached before opening the face. The gas is a mixture of approximately 80% nitrogen and 20% carbon dioxide. The pressure is uniform horizontally, but a hydrostatic pressure gradient exists in the vertical direction. Assuming perfect sealing, the gradient over a small distance, such as the height

Closed top

Open face

Closed base

Closed back

Fig. 1. Longitudinal section through silo showing coordinate system

212 GAS FLOW IN A SILAGE :CLAMP

Of the e I~p : , is approximately linear Of magnitude gPi, Where: p:~ is the initial density of the ~ m r e , The pressure is assumed to be po at the vertical midpoint, so

p =po + ( H / 2 - z lgp i ;(t = O)

The :back, top and bottom faces of the clamp are assumed to: be impermeable, so the conditions at these boundaries are:

1Jn=O

where vn is the component of; v :normal to the boundary. The front face is open to the atmosphere, in which there is again a vertical hydrostatic

pressure gradient, with the pressure assumed equal to P o at the midpoint of the clamp, The air is treated as 80% nitrogen and 20% oxygen, with density Po, so the gradient is gpo. The height at which the pressureS inside and outside are equal has ) e w little effect on the final results.

P =Po + (H/2 - z ) gPo

~ i s system of equations, initial conditions and boundary conditions describes the gas flow model.

2.3. Microbial reactions

A complete model of the changes in a sil0 after ,opening will require a sub-model representing the major microbial reactions taking place i:n the deteriorating silage. Courtin and Spoelstra !° describe a model of microbial activity with an abundant oxygen supply. This requires validation for British grass silages and the inclusion of oxygen ~ t a t i o n of growth to be useful,

In order to investigate the effect of incorporating such a model, a very simple, single population model using Monod kinetics was devised. Oxygen is treated ,as the Sole Substrate, with .carbon dioxide being produced, This approach was chosen, rather than Courtin and Spoelstra!s model,: because it was impo~ant that the growth rate depended on o~gen concentration, Co, Microbial growth is described by

dO/dt = ftOco/(K m +co)

where 0 is a measure of the microbial population, The rates :of consumption of oxygen and the rate o f production o f carbon dioxide are

then

c" = - Y dO/dt

t Co= Y dO /d t

Fig, 2. FlOw: pattern in inert silage o f density 600 kg/m a after 4d, ~ = lOOmm[h

D. J. PARSONS 213

This mode l was first tested as a simple simulation and c o m p a r e d with exper iments at A F R C Inst i tute of Engineer ing Research on control led infusion of oxygen into silage. It was then built into the comple te gas exchange model . The pa rame te r values used were /~ = 0 - 1 s -1, Km = 0 - 0 2 , Y = 2 0 0 0 0 .

3 . R e s u l t s

The mode l was solved using the P H O E N I C S computa t iona l fluid dynamics package f rom C H A M Ltd. A full descript ion o f the p rogram is given in Parsons. 11 The model was

17 13 9 5 1 Time. d

I7 13 9 5 1

17 13 t~ 5 I

17 13 L~ 5 I

Fig. 3. Oxygen penetration (%) into inert silage of density 600 kg/m 3

214 G A S F L O W IN A S I L A G E C L A M P

run with K = 60/am z, which is typical of the 800 kg/m 3 silages tested by Parsons and Hoxey; 8 and K = 210 # m z for 600 kg/m 3 silages. Figs 2 and 3 show the results of running the model before the microbial activity was added. Fig. 2 is a vector plot of the flow pattern after 4 days in a 600 kg/m 3 silage, in which the direction of each arrow shows the direction of flow, and its length is proportional to the magnitude. It shows flow into the clamp through the upper part of the face, and a strong flow out at the bottom. The contour plots in Fig. 3 show the oxygen penetrat ion into 600 kg/m 3 silage at intervals of 1 days for 4 days. A steady penetration is seen, faster at the top of the clamp, with oxygen

17 13 9 5 1 Timc, d

5 3 135 5 3 I

(7

Fig. 4. Oxygen penetration (%) into active silage of density 600 kg/m 3

D. J. PARSONS 215

4 3 ,.'~ 1

Fig. 5. Microbial population [log (no~m3)] in active silage of density 600 kg/m 3, after 2 d

detected approximately 3.7 m into the clamp after 4 days. The pattern in 800 kg/m 3 silage is similar, but oxygen penetrates only three-quarters of the distance in the same time.

Fig. 4 shows the corresponding oxygen profiles when the microbial activity is included. After 1 day the profile is similar to Fig. 2, but thereafter the microbes begin to grow and consume the oxygen more rapidly. After 2 days, traces of oxygen only are found beyond the front layer. After that oxygen is consumed almost as quickly as it enters the clamp, and never penetrates more than 0.5 m from the face. Contour plots of the microbial population are shown in Fig. 5, with contours at 10, 100, 103 and 104 units. The maximum population at each stage, which is found at the top front corner, is given in Table 1. It can be seen that there is a very rapid initial multiplication, slowing down as the populat ion becomes so large that the oxygen supply is limiting. The results for 800 kg/m~silage are again similar but with slightly slower penetration.

Figs 6 and 7 show the oxygen penetration in 600 kg/m 3 and 800 kg/m 3 silages respectively when the face is moved back by 1 m each day. This represents what might occur when silage is being fed to cattle. In the 800 kg/m 3 silage the oxygen penetration is stable, with concentrations of up to 3% found in the first 1.5 m from the new face. In the less dense silage, however, much higher concentrations are found and oxygen penetrates up to 2 m from the face. The profile is not stable: each day the concentration I m from the new face is about 2% lower than the previous day. This indicates that oxygen is being consumed by an already active microbial population, leading to high losses of feeding value. This illustrates clearly the benefit of denser silage in slowing down aerobic losses and illustrates the type of quantitative information that the model should provide when fully developed.

The complete model has not yet been validated experimentally, due to the absence of a fully developed microbial model and the scarcity of data. The model shows that the hypothesis that the ingress of oxygen is driven by density variations is sufficient to provide a qualitative explanation of the observations made on pilot scale silos a as described in the introduction.

Table 1, Maximum microbial population in clamp

Population, Time, d 10 3 units

1 1-04 2 59'4 3 134'0 4 209-0 5 284"0

216 G A S F L O W IN A S I L A G E C L A M P

17 1 3 9 5 1 Time. d

9 13 13 9 5 1

5 5 9 9 5 1

5 5 9 9 5 1

Fig. 6. Oxygen penetration (%) into active silage of density 600kg/m 3, moving face

D. J. PARSONS 217

3 1 3 5 3 1 T i m e . d

3 1 3 I

3 1 3 I

3 1 3 I

Fig. 7. Oxygen penetration (%) into active silage of density 800kg/m 3, moving face

218 GAS FLOW IN A SILAGE CLAMP

References

1 Rees, D. V. H.; Audsley, E.; Neale, M. A. Apparatus for obtaining an undisturbed core of silage and for measuring the porosity and gas diffusion in the sample Journal of Agricultural Engineering Research 1983, 28:107-114

z Rees, D. V. H.; Audsley, E.; Neale, M. A. Some physical properties that affect the rate of diffusion of oxygen into silage Journal of Agricultural Science, Cambridge 1983, 100:601-605

3 Billington, R. S.; Hoxey, R. P.; Lowe, J. F. The effect of consolidation on the aerobic deterioration of grass silage. Paper presented at Eighth Silage Conference, AFRC Institute for Grassland and Animal Production, Hurley, 7-10 September 1987 (unpublished)

4 Neal, J. D. StC; Thornley, J. H. M. A model of the anaerobic phase of ensiling. Grass and Forage Science 1983, 38:121-134

5 Muck, R. E.; Leibensperger, R. Y.; Pitt, R. E. Mathematical simulation of silage fermentation. ASAE Paper 83-1530, American Society of Agricultural Engineers, St Joseph, 1983

6 Pitt, R. E. Dry matter losses due to oxygen infiltration in silos Journal of Agricultural Engineering Research 1986, 35(3): 193-206

7 Buckmaster, D. R.; Rotz, C. A.; Muck, R. E. A comprehensive model of forage charges in the silo Transactions of the American Society of Agricultural Engineers 1989, 32(4): 1143-1152

s Parsons, D. J.; Hoxey, R. P. A technique for measuring the permeability of silage at low pressure gradients. Journal of Agricultural Engineering Research 1988, 40:303-307

s Collins, R. E. Flow of fluids through porous materials. Reinhold Publishing Corporation, New York, 1961

lo Courtin, M. G.; Spoelstra, S. F. A simulation model of the microbiological and chemical changes accompanying the initial stage of aerobic deterioration of silage Grass and Forage Science 1990, 45(2): 153-166

1~ Parsons, D. J. Modelling gas exchange in a silage clamp using PHOENICS. Divisional Note DN1552, AFRC Institute of Engineering Research, Silsoe, 1989