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Bulk density and porosity distributions in a compost pile

J.T. VAN GINKEL1, P.A.C. RAATS1,2,* AND I.A. VAN HANEGHEM3

1Research Institute for Agrobiology and Soil Fertility Research (AB-DLO), P.O.Box 14,

NL-6700 AA Wageningen, The Netherlands

2Wageningen Agricultural University, Department of Agricultural, Environmental and

Systems Technology, Dreijenlaan 4, NL-6703 HA Wageningen, The Netherlands

3Wageningen Agricultural University, Department of Agricultural, Environmental and

Systems Technology, Bomenweg 4, 6703 HD Wageningen, The Netherlands

* Corresponding author

Received 18 May 1998; accepted 17 June 1999

Abstract

This paper mainly deals with the description of the initial distribution of bulk density and

porosity at the moment a compost pile is built or rebuilt. A relationship between bulk density

and vertical position in a pile is deduced from theoretical and empirical considerations. For-

mulae to calculate the air filled volume fraction and the true densities of the solid phase and

of the organic matter are also derived. The true density of dry matter is used in the computa-

tion of porosity distributions. The relationships between bulk density and height and be-

tween air-filled volume fraction and height are shown to be valid for composting material

consisting of chopped wheat straw and chicken manure. The check of this validity is limited

to total bulk density values ranging from 150 to 950 kg m– 3, with values of dry matter con-

tent varying between 18 and 28% (w.b.). Moreover, the gravimetric dry matter content must

be constant throughout the total cross section of the pile. The error in the calculated bulk

densities and air-filled volume fractions was found to be 12% at a reliability level of 95%. It

seems likely that the presented equations will give reasonable results for other values of dry

matter content and other kinds of chopped fibrous materials as long as the gravimetric dry

matter content remains independent of height.

Keywords: compost, settlement, decomposition, transport processes

Introduction

Transport of mass and heat in a compost pile is significantly affected by the geome-

try and size distribution of the pores and the composition of the composting materi-

al. Therefore it is at least necessary to have information about the spatial distribution

of porosity. Porosity can be calculated from dry matter content, true density of dry

matter and total bulk density. Dry matter content and true density of dry matter are

easily measured in the laboratory. To describe the bulk density distribution, distinc-

tion is made between time dependent and time independent processes.

Netherlands Journal of Agricultural Science 47 (1999) 105-121

Netherlands Journal of Agricultural Science 47 (1999)

105

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The time independent process results from the compressibility of composting ma-

terial (Randle and Flegg, 1985). Compressibility is defined as the reciprocal of the

resistance of the material against mechanical deformation, or more precisely, as the

ratio between deformation and stress. Due to this property the bulk density is a func-

tion of the local pressure and therefore depends on the position in the pile.

The time dependent process is illustrated by the results of Lopez-Real (1990), who

examined the material losses of a seaweed/straw mixture after 28 days of composting

in a forced aeration system with turning. He found a total weight reduction of 50%, a

volume reduction of 77%, and a bulk density increase from 310 to 670 kg m– 3, indi-

cating that settlement occurred. Settlement is defined as the increase of mechanical

deformation as a function of time under constant pressure conditions. When a com-

post pile is built, the initial bulk density distribution is only determined by the com-

pressibility of the composting material. However, during the process bulk density

and porosity are also influenced by the combined effects of subsidence, loss of or-

ganic matter due to biological degradation processes and change of water content

due to transport processes.

In this paper we mainly describe the initial distribution of bulk density and porosi-

ty at the moment the pile is built or rebuilt. For composting material, no detailed dis-

cussion of the relation between bulk density and position was found in the literature.

In section 2 we deduce such a relation from theoretical and empirical considerations.

We also derive formulae to calculate the air filled volume fraction and the true den-

sities of the solid phase and the organic matter. The true density of dry matter is used

in the computation of porosity distributions. In section 3 the design of the experi-

ments is described. The results are presented in section 4. A discussion of the results

is given in section 5. Unless otherwise stated, the errors of experimentally deter-

mined quantities are expressed as standard error of the mean (Lyons, 1991).

This paper is based on the PhD thesis of the senior author (Van Ginkel, 1996). In

the thesis a wide range of other physical, biochemical, and calorimetric aspects are

dealt with.

Modeling composition and compression of compost

Description of the composition of compost

Compost can be regarded as a mixture of a solid phase s, a liquid phase l and a

gaseous phase g, with each of these phases themselves being mixtures of numerous

constituents (cf. Raats, 1984). The volume fractions θi= (θs, θl, θg) of the phases are

subject to the constraint

∑

(1)

The true densities γi= (γs, γl, γg) of the phases are defined as masses per unit volume

of the phase i. We prefer to take the volume fractions, with the constraint defined by

equation (1), and the true densities of the phases as the basic compositional vari-

J.T. VAN GINKEL, P.A.C. RAATS AND I.A. VAN HANEGHEM

106

Netherlands Journal of Agricultural Science 47 (1999)

θθθθ

gisl

=++=

1.

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ables. All other compositional variables are logically deduced from these basic vari-

ables. This way we avoid giving ad hoc, unrelated definitions of terms.

The bulk densities ρi= (ρs, ρl, ρg) of the phases are defined by:

(2)

Solving (2) for θigives:

(3)

Introducing (3) in the constraint (1) gives:

∑

(4)

The wetness w is defined as:

(5)

The total bulk density ρ is defined as the sum of the bulk densities of the phases:

∑

(6)

Introducing (2) in (6) results in:

∑

(7)

The dry matter content dsis defined as:

(8)

Next we show that the total bulk density ρ and the dry matter content dscan be

used to derive convenient expressions for the volume fraction θgof the gaseous

phase and the true density γsof the solid phase.

First we consider the volume fraction θg of the gaseous phase. Solving the con-

straint (1) for θggives:

(9)

Introducing (3) in (9) results in:

(10)

After solving (6) for ρland substituting the result in (10), it follows that:

(

(11)

BULK DENSITY AND POROSITY DISTRIBUTIONS IN A COMPOST PILE

Netherlands Journal of Agricultural Science 47 (1999)

107

ρ θ γ

iii

=

.

θ ρ γ

iii

=

/

.

ρ γ ρ γ

s

/

=

ρ γ

l

ργ

iislgg

///

++=

1.

w

ls

= ρρ

/

.

ρρρρρ

==++

islg.

ρ θ γ

i i

θ γ

s s

θ γ

l l

θ γ

g

==++

g.

dss

= ρρ

/ .

θθθ

gsl

= −

1

−

.

θ ρ γ

s

/

ρ γ

lgsl

= −

1

−

/

.

θ ρ γ

s

/

ρρργ

gssgl

= −

1

−−−

)

/

.

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Making use of the fact that ρg<< ρs, solving (8) for ρs, and substituting the resulting

expression in (11) gives:

(

(12)

or

(13)

Equations (12) and (13) show that the volume fraction of the gaseous phase θgcan be

calculated from the total bulk density ρ, the dry matter content ds, and the true densi-

ties γsand γl.

Next we consider the true density γsof the solid phase. Solving (4) for γsgives:

(

(14)

Expressing, as above, the bulk density of the water ρlsin terms of the total density ρ

and the dry matter content ds, and further replacing ρg/ γgby θgand ρsby ρdsit fol-

lows that:

=(

(15)

Equation (15) shows that the true density of the solid phase γscan be calculated from

the total bulk density ρ, the dry matter content ds, the true density of the liquid phase

γl, and the volume fraction of the gaseous phase θg.

Generally the solid phase of compost is itself a mixture of numerous compounds.

For our purposes it is sufficient to distinguish the organic subphase o and inorganic

(‘ash’) subphase a, each characterized, respectively, by their individual volume frac-

tions θoand θa, true densities γoand γa, and bulk densities ρoand ρa, such that:

(16)

and

(17)

Summation of (16) and (17) gives equation (2) for s:

(18)

with θsgiven by:

(19)

J.T. VAN GINKEL, P.A.C. RAATS AND I.A. VAN HANEGHEM

108

Netherlands Journal of Agricultural Science 47 (1999)

θγ γ ρ

l

]

gsss

dd

= −

1

+−

)

[

1

//

,

θγγγρ

)

glsssl

dd

= −

1

+−

(

1///

.

γρ ρ γ

l

ργ

sslgg

=−−

)

///

1.

γρ ρ γ

)

θ

ssslg

dd

)

−−

(

−

[]

//

11.

ρ θ γ

ooo

=

,

ρ θ γ

aaa

=

.

ρ θ γ

sss

=

,

θθθ

soa

=+

.

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Equation (19) is a necessary consequence of splitting the solid phase in an organic

subphase and an inorganic (‘ash’) subphase. From the equality of the right hand side

of (18) to the sum of the right hand sides of (16) and (17), it follows that the true

density of the organic subphase is given by:

(

(20)

An alternative form of (20) can be obtained by defining the concentrations coand ca

of, respectively, the organic and inorganic (‘ash’) subphases:

(21)

(22)

Clearly the sum of these two concentrations is unity:

(23)

Dividing in (20) the numerator and the denominator by ρsand making use of (21),

(22) and (23), it follows:

(

(24)

Equation (24) shows that the true density γoof the organic subphase can be calculat-

ed from the true densities γsand γa, and the concentration caof the inorganic (‘ash’)

subphase.

Compression of compost

The total equilibrium force balance in three dimensions xi= (x1, x2, x3) can be written

as:

∂

∂

i

(25)

where Tijis the stress tensor, whose 3×3 matrix of components describes the normal

and shear stresses in the compost, and gjthe gravitational force per unit mass. We

simplify the force balance by means of three assumptions:

1.The vertical direction z (positive upward) is a principal direction and the principal

stress in that direction is σ [N m]:

∂

∂

z

(26)

Equation (26), which may be regarded as the vertical force balance of an infinitesi-

BULK DENSITY AND POROSITY DISTRIBUTIONS IN A COMPOST PILE

Netherlands Journal of Agricultural Science 47 (1999)

109

γρ ρ γ

s

ργ

oosaa

=−

)

///

.

co

ca

os

= ρρ

/

,

as

= ρρ

/

.

cc

oa

+= 1.

γγγ

oasaa

cc

=−

)

−

()

11

/ //

.

ρ

xT

g

ijj

+= 0.

σρ

g

+= 0.