A Giraud

I Sevostianov

F Chen

D Grgic

Effective thermal conductivity of oolitic rocks using the Maxwell homogenization method

Keywords: effective thermal conductivity, Maxwell homogenization method, oolitic limestone, two-scale porosity, concave pore

). At the mesoscale, porous oolitic inclusions are quasi spherical whereas two families of mesopores are considered according to analysis of photomicrographs: (1) randomly oriented oblate spheroidal pores and (2) concave pores. The proposed model is compared to a simplified one when all the pores are of ellipsoidal shape. The relevancy of the ellipsoidal approximation is then evaluated. In particular, the influence of the shape of the mesopores on the overall thermal conductivity is discussed. Comparisons between multi-scale model based on Maxwell homogenization method and experimental data show that effects of porosity and saturating fluids on overall conductivity are correctly predicted when concave pores are taken into account.

Introduction

The present work focuses on the determination of overall thermal conductivity of oolitic limestone that is modeled as a heterogeneous material composed by an assemblage of quasi-spherical porous grains (oolites, o), mesopores (b) and solid matrix (sparitic cement c) (see [START_REF] Giraud | Effective poroelastic coefficients of isotropic oolitic rocks with micro and meso porosities[END_REF], [START_REF] Grgic | The influence of CO 2 on the long-term chemo-mechanical behavior of an oolitic limestone[END_REF], [START_REF] Nguyen | A composite sphere assemblage model for porous oolitic rocks[END_REF], [START_REF] Ghabezloo | Effective stress law for the permeability of a limestone[END_REF]). For this goal, we use recently reformulated Maxwell's homogenization method for elastic composites [START_REF] Sevostianov | Generalization of Maxwell homogenization scheme for elastic material containing inhomogeneities of diverse shape[END_REF] which was successfully applied to the estimate of effective elastic constants of oolitic. This method has also been explored in ( [START_REF] Levin | Generalized Maxwell's scheme for homogenization of poroelastic composites[END_REF], [START_REF] Sevostianov | On the shape of effective inclusion in the Maxwell homogenization scheme for anisotropic elastic composites[END_REF] , [START_REF] Sevostianov | Effective properties of linear viscoelastic microcracked materials: Application of Maxwell homogenization scheme[END_REF]) for mechanical properties and in ( [START_REF] Kushch | Effective conductivity of composite with imperfect contact between elliptic fibers and matrix: Maxwells homogenization scheme[END_REF], [START_REF] Sevostianov | Effective thermal conductivity of a composite with thermo-sensitive constituents and related problems[END_REF]) for conductivity. It must be emphasized that Maxwell's homogenization model has been presented in [START_REF] Zimmerman | Thermal conductivity of fluid-saturated rocks[END_REF] for the prediction of the thermal conductivity of fluid-saturated rocks. In particular, it has been shown in [START_REF] Zimmerman | Thermal conductivity of fluid-saturated rocks[END_REF] that this model allows to predict overall thermal conductivity in a wide range of rock-microstructure type of sedimentary or cristalline rocks, by considering randomly distributed spheroidal pores. One specific point related to the microstructure of heterogeneous oolitic porous rocks is the multiscale structure of pore space. The complex realistic pore structure can be simplified and the total porosity can be decomposed into two scale separated classes of pores: intra oolitic pores or micropores, at the micro scale, and inter oolitic pores or mesopores at the mesoscale. The microstructural model presented in [START_REF] Giraud | Micromechanical modeling of the effective elastic properties of oolitic limestone[END_REF] is adopted in this paper. The novelty of the model consists in the account for concave pores modelled by superspherical ones. Reformulation of Maxwell's homogenization method in terms of the resistivity contribution tensors allows accounting for nonellipsoidal shape of such pores using the numerically evaluated contribution tensors (see [START_REF] Chen | Evaluation of the effective elastic and conductive properties of materials containing concave pores[END_REF]) when no analytical solution can be obtained. This model is then compared to a simple one in which the concave pores are replaced by the best ellipsoidal approximates. Extensive study of the effective properties of carbonate rocks taking into account a multi-scale description, with applications to elasticity, electrical conductivity, thermal conductivity and permeability in the context of a cross property analysis have been presented by M. Markov and coauthors ( [START_REF] Kazatchenko | Simulation of acoustic velocities, electrical and thermal conductivities using unified pore-structure model of double-porosity carbonate rocks[END_REF], [START_REF] Kazatchenko | Joint inversion of conventional well logs for evaluation of double-porosity carbonate formations[END_REF], [START_REF] Markov | Conductivity of carbonate formations with microfracture systems[END_REF], [START_REF] Markov | Determination of electrical conductivity of double-porosity formations by using generalized differential effective medium approximation[END_REF], [START_REF] Aquino-López | Modeling and inversion of elastic wave velocities and electrical conductivity in clastic formations with structural and dispersed shales[END_REF]). In these works, two distinct classes of pores are considered: primary small scale pores and secondary mesoscopic pores. Small scale pores are similar to intra oolitic pores of oolitic rocks, and secondary pores similar to inter oolitic pores. A very complete description of the secondary (large scale) porosity is presented in [START_REF] Kazatchenko | Simulation of acoustic velocities, electrical and thermal conductivities using unified pore-structure model of double-porosity carbonate rocks[END_REF] by introducing four types of pores: vugs (quasi-spherical inclusions), quasi vugs (oblate ellipsoids), channels (prolate ellipsoids), and cracks (strongly oblate inclusions). The presence of an interphase coating oolites, an Interfacial Transition Zone (ITZ ), is not taken into account in this paper but it is certainly important in porous oolitic rocks similarly to the cement based material (see for example [START_REF] Lutz | Effect of an inhomogeneous interphase zone on the bulk modulus and conductivity of a particulate composite[END_REF] for a study of the influence of Interfacial Transition Zone on effective conductivity). Among many papers related to characterization of thermal conductivity of porous heterogeneous rocks, [START_REF] Alishaev | Effective thermal conductivity of fluid-saturated rocks: Experiment and modeling[END_REF] present an experimental characterization including a large sensitive study of physical parameters, in a wide temperature range. An extensive literature review on thermal conductivity measurements in carbonate rocks may be found in [START_REF] Thomasjr | Thermal conductivity of carbonate rocks[END_REF]. Importantly, overall isotropy of thermal conductivity is observed in most cases. The authors pointed out that anisotropic single crystals, including calcite, show directional differences in thermal conductivity, but randomly oriented polycrystalline aggregates produce an overall isotropic thermal effective conductivity. This result is consistent with the developed approach in the present paper. Random distribution of calcite phase mineral is accounted through averaging of the calcite mineral thermal conductivity (see [START_REF] Suquet | Homogénéisation en mécanique des matériaux 2. Comportements non linéaires et problèmes ouverts[END_REF]) and by using equivalent isotropic conductivity. A detailed review of thermal conductivity data sets for geomaterials made of natural soil particles, crushed rock particles and sedimentary rock including analysis of influence of particle shape, grains pore-size distributions, fluid saturated (air and liquid water) is given in [START_REF] Côté | Assessment of structure effects on the thermal conductivity of two-phase porous geomaterials[END_REF]. It may be noticed that [START_REF] Markov | Effective thermal conductivity of inhomogeneous medium containing gas-filled inclusions[END_REF] have recently studied thermal conductivity of gas saturated porous materials taking into account methods of statistical physics and rarefied gas dynamics. They have shown that in the slip flow regime corresponding to low Knudsen number, it is necessary to use the method of rarefied gas dynamics to correctly predict the effective thermal conductivity. These phenomena may be of major importance in nano-porous materials and porous rocks such as gas shales. In the present study we focused on the micro and meso porosities of oolitic limestones, respective pore size correspond to the standard hydrodynamic regime and these phenomena have been neglected.

Background results

Hereafter we define some notations and recall some results which are needed later. Upper case boldsymbols P , Λ, I refer to second order tensors, lower case boldsymbols, as a, ε, σ, refer to first order tensors. I represents the second-order, identity tensor (δ ij denotes Kronecker delta symbol, δ ij = 1 if i = j, δ ij = 0 otherwise). For the sake of simplicity only the polarisation tensors related to spheroidal inclusions are recalled. The general case of the 3D ellipsoid could be also considered in what follows. Oblate spheroïd (0 < γ < 1) and prolate spheroïd (1 < γ), with symmetry axis 3 are described by equation

z ∈ Ω I ⇔ z 2 1 a 2 + z 2 2 a 2 + z 2 3 a 2 γ 2 ≤ 1 , 0 ≤ γ ≤ 1 a 1 = a 2 = a , a 3 = aγ (1)
Hill Polarisation tensor of a spheroidal inclusion in an infinite isotropic elastic medium (λ denotes the conductivity of the infinite isotropic medium surrounding the spherical inclusion) is a transversely isotropic second order tensor

P = Q(γ) λ I T + 1 -2Q(γ) λ I N (2)
I N = e 3 ⊗ e 3 , I T = e 1 ⊗ e 1 + e 2 ⊗ e 2 , I = I N + I T (3)
with (see [START_REF] Torquato | Random Heterogenous Materials. Microstructure and Macroscopic Properties[END_REF] p. 441, or [START_REF] Carslaw | Conduction of Heat in Solids[END_REF] p. 406, among many others)

Q(γ) =                      1 2 1 + 1 u 1 - γ √ v arctan √ v γ if γ < 1 1 3 if γ = 1 1 2 1 + 1 u 1 - γ 2 √ u ln γ + √ u γ - √ u if γ > 1 v = 1 -γ 2 , u = γ 2 -1 (4)
Hill Polarisation tensor of a spherical inclusion (γ = 1 and Q = 1/3)

P = 1 3 λ I (5)
Q tensor (see [START_REF] Sevostianov | Generalization of Maxwell homogenization scheme for elastic material containing inhomogeneities of diverse shape[END_REF] equation 2.9) for Maxwell homogenization scheme

Q = Λ. (I -P .Λ) (6)
In the case of a sphere (using 5 and Λ = λI)

Q = 2 3 λI (7)
Conductivity contribution tensor (see [START_REF] Sevostianov | Effective thermal conductivity of a composite with thermo-sensitive constituents and related problems[END_REF])

N i = P + (Λ i -Λ) -1 -1 (8)
Resistivity contribution tensor (see [START_REF] Sevostianov | Effective thermal conductivity of a composite with thermo-sensitive constituents and related problems[END_REF])

H i = -Λ -1 .N i .Λ -1 (9)
Dilute concentration tensor

A i = [I + P . (Λ i -Λ)] -1 (10)
In this paper, the reformulation of the Maxwell homogenization scheme in terms of resistivity contribution tensor (9) will be used. For a spherical inclusion i (λ i ) embedded in an infinite isotropic matrix

N i = N i I , H i = H i I , A i = A i I (11)
A i = 3λ 2λ + λ i (12)
and

H i = λ -λ i λ 2 A i , N i = -(λ -λ i ) A i (13)
In the case of an isotropic ellipsoidal inclusion with conductivity tensor Λ i = λ i I surrounded by an infinite isotropic matrix with conductivity tensor Λ = λI (1) relation [START_REF] Ghabezloo | Effective stress law for the permeability of a limestone[END_REF] gives

A i = λ 1 λ (1 -Q(γ)) + λ i Q(γ) I T + 1 2λQ(γ) + λ i (1 -2Q(γ)) I N (14)
Orientational average (case of a random orientation distribution)

a = 1 3 T r (a) I (15)
One obtains spherical (isotropic) second order tensors

A i = A i I , H i = H i I (16)
with

g (λ, λ i , γ) = λ 3 2 λ (1 -Q(γ)) + λ i Q(γ) + 1 2λQ(γ) + λ i (1 -2Q(γ)) (17)
A i = g (λ, λ i , γ) (18)
One verifies relations

H i = λ -λ i λ 2 A i (19)

Microstructure of a reference porous oolitic limestone

One presents in this section some microstructural observations of a reference porous oolitic rock chosen for this work, an oolitic limestone from Lavoux (West of France, see [START_REF] Sterpenich | Experimental ageing of oolitic limestones under CO2 storage conditions. Petrographical and chemical evidence[END_REF]) whose microstructure has been detailed [START_REF] Giraud | Micromechanical modeling of the effective elastic properties of oolitic limestone[END_REF]. One may also refers to [START_REF] Nguyen | A composite sphere assemblage model for porous oolitic rocks[END_REF], [START_REF] Giraud | Effective poroelastic coefficients of isotropic oolitic rocks with micro and meso porosities[END_REF], for details. Oolites are quasi spherical grains constituted by concentric porous layers. The oolite microstructure are constituted by an assemblage of calcite grains (micrite, solid grains with diameter range 1µm -5µm) and micropores. More precisely oolites contain quasi spherical grains composed of concentric layers, diameter range 100µm -1mm, the layers are composed by an assemblage of micropores and micrite grains. Micrite or microcristalline calcite is composed spherical grains constituting solid oolitic phase, diameter range 1µm -5µm. Sparitic calcite cement or sparite, spar calcite, diameter range 20µm -100µm, it corresponds to the solid phase at the mesoscale. Solid phase of Lavoux limestone, i.e. micritic grains inside oolites and sparitic cement between oolites, is a quasi mono-mineral material constituted of pure calcite (solid volume fraction of calcite, f s calcite = Ω calcite /Ω s ≈ 0.98). The total pore volume fraction of Lavoux limestone varies from 0.15 to 0.30, it is decomposed into two classes of pores: inter oolitic pores(mesopores) and intra oolitic pores (micropores) of approximately equal partial porosities [START_REF] Giraud | Effective poroelastic coefficients of isotropic oolitic rocks with micro and meso porosities[END_REF]. As in [START_REF] Giraud | Micromechanical modeling of the effective elastic properties of oolitic limestone[END_REF], a sensitive study is performed in this paper on a relatively wide range of porosity. Mesoscopic pores are divided into two types of pores: oblate spheroidal pores of aspect ratio γ = 0.2 (index b1 in what follows) and ellipsoidal pores (index b2) replacing superspherical concave pores taken into account in [START_REF] Giraud | Micromechanical modeling of the effective elastic properties of oolitic limestone[END_REF]. Two cases are considered, flat pores similar to cracks are represented by oblate spheroidal pores of aspect ratio γ = 0.05, and elongated pores cracks are represented by prolate spheroidal pores of aspect ratio γ = 20. The partial porosities of the two kind of pores are assumed equal. Flat and elongated pores may respectively correspond to particular cases of secondary pores of carbonate rocks described in [START_REF] Kazatchenko | Simulation of acoustic velocities, electrical and thermal conductivities using unified pore-structure model of double-porosity carbonate rocks[END_REF]: channels (prolate ellipsoids, as elongated pores), and cracks (flat oblate ellipsoids). At the macroscopic level, experimental characterizations of the Lavoux limestone show that the overall elastic behaviour is not far from isotropy. It results from an isotropic or random distribution of constituents: oolites, sparitic cement and mesopores. Thermal conductivity needs to be measured on this reference material (and experimental study is currently performed and results will be presented in a next paper), and it is assumed that the overall conductivity is also isotropic. See [START_REF] Thomasjr | Thermal conductivity of carbonate rocks[END_REF] for an extensive review on thermal conductivity of carbonate rocks which confirms reasonably overall isotropy in most cases. The thermal conductivity of the pure calcite mineral will be assumed equal to λ c = 3.3 W m -1 K -1 (according to [START_REF] Vasseur | Thermal conductivity estimation in sedimentary bassins[END_REF] and [START_REF] Guéguen | Microstructures, percolation thresholds, and rock physical properties[END_REF]). The numerical values of thermal conductivities for liquid and air are respectively λ = 0.5984 W K -1 m -1 and λ g = 0.0255 W K -1 m -1 (according to [START_REF] Clauser | Thermal conductivity of rocks and minerals[END_REF]).

Volume fractions and constituents

As in [START_REF] Giraud | Effective poroelastic coefficients of isotropic oolitic rocks with micro and meso porosities[END_REF]- [START_REF] Giraud | Micromechanical modeling of the effective elastic properties of oolitic limestone[END_REF] three different scales may be identified. First the smallest scale, referred as microscopic scale, corresponds to the intra granular or intra oolitic level. Second the intermediate scale, referred as as mesoscopic scale, corresponds to the scale of oolite grains, syntaxial calcite grains (referred as sparitic calcite cement, and inter oolitic pores. Third the largest scale, referred as macroscopic scale corresponds to a large representative volume elements compared to the oolite size, interoolitic pores and syntaxial calcite grains. At the meso scale, one considers a four phase composite material composed of poroelastic oolites (o) (constituted by solid grains and intra oolitic pores, or micro pores), inter oolitic meso pores divided into two families b1 and b2, and sparitic cement (or syntaxial calcite) constituted by pure calcite grains (index c). A two scale porosity is considered as two population of voids may be identified. Intra oolitic voids of spherical or ellipsoidal shape, with average diameter of 0.1 µm, referred as micropores in what follows, with index a. Inter oolitic voids of ellipsoidal shape, with average diameter approximately of 10 µm, referred as mesopores b, divided into two families of equal volume fraction, indexes b1 and b2. The total volumes occupied by the phases write

Ω = Ω o + Ω b + Ω c ( 20
)
with

Ω b = Ω b1 + Ω b2 (21)
one have

Ω = Ω o + Ω b1 + Ω b2 + Ω c (22)
with corresponding volume fractions

f o = Ω o Ω , f b1 = Ω b1 Ω , f b2 = Ω b2 Ω , f c = Ω c Ω f o + f b1 + f b2 + f c = 1 (23)
One defines the total volume of intra oolitic pores

Ω o = Ω a + Ω s o (24)
and the porosity of the oolite phase at the mesoscopic scale

f a = Ω a Ω o (25)
The total pore volume can be expressed as

Ω p = Ω a + Ω b1 + Ω b2 (26)
and the total porosity

f p = Ω a Ω + Ω b1 Ω + Ω b2 Ω = f a f o + f b1 + f b2 (27)
Representative data for the reference material studied in this paper are close to f p = 0.26, f o = 0.74, f a f o = 0.14 , f a = 0.19 , f b = 0.12 (see [START_REF] Giraud | Effective poroelastic coefficients of isotropic oolitic rocks with micro and meso porosities[END_REF]) but a sensitivity study will be performed on the volume fractions of the different phases.

In sensitive study, as in [START_REF] Giraud | Micromechanical modeling of the effective elastic properties of oolitic limestone[END_REF] we will consider

f b1 = f b2 = f b /2 4.
A two-scale porosity model for effective thermal conductivity of isotropic porous oolitic rocks 4.1. First step: homogenization of micropores and solid grains inside oolites The first step represents the transition from the microscopic scale to the mesoscopic scale. Oolite pores are homogenized and the result of the first step is the porous oolite.

As previously indicated, the granular and random microstructure of oolites conduces to choose the self consistent approximation, originally due to [START_REF] Bruggeman | Berechnung verschiedner Physicalischer Konstanten von heterogenen Subztanzen. I. Dielektrizitätskonstanten und Leitfähigkeiten der Mischkörper aus isotropen Substanzen[END_REF], for the step I. By respectively denoting λ I o , λ a , λ o conductivity of the oolite at the mesoscale, conductivity of the intra oolitic porous phase, conductivity of micritic solid grains (λ o = λ c ), the well known self consistent approximations for a two phase material with spherical particles is the positive root of the quadratic equation (see [START_REF] Torquato | Random Heterogenous Materials. Microstructure and Macroscopic Properties[END_REF] formula 18.13 p. 463)

f a λ a λ a + 2λ I o + (1 -f a ) λ o λ o + 2λ I o - 1 3 = 0 (28)
It's well known solution writes (see [START_REF] Torquato | Random Heterogenous Materials. Microstructure and Macroscopic Properties[END_REF] formula 18.14 p. 463, with d = 3,

f 2 = 1 -f 1 ) h(λ 1 , λ 2 , f 1 ) = 1 4 α 12 + α 2 12 + 8λ 1 λ 2 (29)
α 12 = λ 1 (3f 1 -1) + λ 2 (2 -3f 1 ) (30)
and then self consistent approximation writes

λ I o = h(λ a , λ o , f a ) (31)
It may be noticed that, in the tested range of microporosity f a < 0.2, as we consider spherical particles, numerical differences between Self Consistent approximation, and other approximations such as Maxwell or Mori Tanaka would not be very significant. In the present model, the impact on overall thermal conductivity is limited when compared to the second homogenization step which corresponds to the mesoscopic scale. This comment is restricted to the tested range of microporosity and it would be irrelevant for a wider range.

4.2. Second step: transition from the mesoscopic scale to the macroscopic scale with ellipsoidal pores At the mesoscale one considers a four phase phase heterogeneous medium, which is composed of porous oolites, nearly spherical and randomly distributed, it is the main phase (f o ≈ 0.74 in the reference case), pure solid calcite referred as sparitic cement (index c), meso pores modelled as two distinct families of ellipsoids randomly distributed in orientation. Reformulation of Maxwell homogenization scheme recently by I. Sevostianov and coauthors in the context of elasticity and conductivity problems (see [START_REF] Sevostianov | Generalization of Maxwell homogenization scheme for elastic material containing inhomogeneities of diverse shape[END_REF], [START_REF] Giraud | Micromechanical modeling of the effective elastic properties of oolitic limestone[END_REF], [START_REF] Sevostianov | On the shape of effective inclusion in the Maxwell homogenization scheme for anisotropic elastic composites[END_REF] , [START_REF] Sevostianov | Effective properties of linear viscoelastic microcracked materials: Application of Maxwell homogenization scheme[END_REF] , [START_REF] Kushch | Effective conductivity of composite with imperfect contact between elliptic fibers and matrix: Maxwells homogenization scheme[END_REF], [START_REF] Sevostianov | Effective thermal conductivity of a composite with thermo-sensitive constituents and related problems[END_REF]) is then used for the transition from the mesoscopic scale to the macroscopic scale. More precisely reformulation of Maxwell homogenization scheme in terms of resistivity contribution tensor provides (see [START_REF] Giraud | Micromechanical modeling of the effective elastic properties of oolitic limestone[END_REF] relation 10 using compliance contribution tensor) the simple scalar relation established under assumption of macro isotropy

λ eff MX = 1 λ c + f b1 H b1 + f b2 H b2 + f o H o -1 - 2 3 λ c -1 -1 (32)
with H b1 , H b2 and H o respectively given by formula (19-13)

H b1 = λ c -λ b λ 2 c g (λ c , λ b , γ b1 ) , H b2 = λ c -λ b λ 2 c g (λ c , λ b , γ b2 ) (33)
H o = 3 λ c -λ I o λ c (2λ c + λ I o ) (34)
From relation [START_REF] Clauser | Thermal conductivity of rocks and minerals[END_REF] one may easily deduce an explicit formula for the effective thermal conductivity

λ eff MX = λ c 3 -2λ c f b1 H b1 + f b2 H b2 + f o H o 3 + λ c f b1 H b1 + f b2 H b2 + f o H o (35)
It should be emphasized that a more complex description of the mesoscale porosity could be easily introduced in the reformulation of Maxwell homogenization scheme in terms of resistivity contribution. As an example, the fourth types of secondary pores distinguished in [START_REF] Kazatchenko | Simulation of acoustic velocities, electrical and thermal conductivities using unified pore-structure model of double-porosity carbonate rocks[END_REF] for carbonate rocks could be introduced as randomly oriented spheroids are considered and relation (32) would be replaced by

λ eff MX = 1 λ c + f b1 H b1 + f b2 H b2 + f b3 H b3 + f b4 H b4 + f o H o -1 - 2 3 λ c -1 -1 (36)
f bi and H bi respectively denoting volume fraction and resistivity contribution tensor of the mesoscale pore bi. As oolites are not perfectly spherical, a random distribution of the best ellipsoidal approximation of oolites (oblate spheroids with aspect ratio close to γ = 0.7) could be also used and relation [START_REF] Clauser | Thermal conductivity of rocks and minerals[END_REF] would be replaced by

λ eff MX = 1 λ c + f b1 H b1 + f b2 H b2 + f o H o -1 - 2 3 λ c -1 -1 (37)
with H o given by a relation similar to [START_REF] Bruggeman | Berechnung verschiedner Physicalischer Konstanten von heterogenen Subztanzen. I. Dielektrizitätskonstanten und Leitfähigkeiten der Mischkörper aus isotropen Substanzen[END_REF]. In further works we will also take into account more realistic shapes such as concave shapes (see recent paper [START_REF] Chen | Evaluation of the effective elastic and conductive properties of materials containing concave pores[END_REF]). As previously indicated, ellipsoidal shape is adopted for simplicity and in this case the best ellipsoidal approximation of more complex shapes needs to be used. It may be noticed that relations (32-36-32) are very similar to relation 4.9 of paper [START_REF] Sevostianov | Generalization of Maxwell homogenization scheme for elastic material containing inhomogeneities of diverse shape[END_REF], and relations 13 -17 of paper [START_REF] Giraud | Micromechanical modeling of the effective elastic properties of oolitic limestone[END_REF], which have been obtained in elasticity.

Second step: transition from the mesoscopic scale to the macroscopic scale with concave pores

As in [START_REF] Giraud | Micromechanical modeling of the effective elastic properties of oolitic limestone[END_REF], concave pores (b2) are approximated by superspheres

(|x|) 2p + (|y|) 2p + (|z|) 2p = 1 (38)
of concavity factor p = 0.35 (see figure 4) For pores of the shape of supersphere of concavity factor p, approximate expressions for components of the resistivity contribution tensor have recently be obtained by [START_REF] Chen | Evaluation of the effective elastic and conductive properties of materials containing concave pores[END_REF] (see [START_REF] Chen | Numerical evaluation of the Eshelby tensor for a concave superspherical inclusion[END_REF] for the elasticity problem) thanks to a numerical method (Finite Element Method). As this tensor is spherical (hydrostatic) one have

H b2 = H b2 (39)
Numerical values of the resistivity contribution tensors are given in the next section, as they depend on the thermal conductivity of the surrounding matrix (λ c ) and the inclusion (liquid water and air will be considered).

Numerical results

Experimental data

We present in this section a comparison of the developed micro-macro model with experimental results for relatively pure calcitic limestones presented in [START_REF] Robertson | Thermal properties of rocks[END_REF]. Oolitic limestones studied in this paper belong to this type of limestone. Intra oolite solid grains and inter oolite sparitic cement are composed of calcite. Extensive bibliographical review and data relative to thermal conductivity of limestones may be found in [START_REF] Alishaev | Effective thermal conductivity of fluid-saturated rocks: Experiment and modeling[END_REF], [START_REF] Popov | Interrelations Between Thermal Conductivity and Other Physical Properties of Rocks: Experimental Data[END_REF], and in [START_REF] Zimmerman | Thermal conductivity of fluid-saturated rocks[END_REF] for porous rocks more generally. Experimental results are presented in figures [START_REF] Ghabezloo | Effective stress law for the permeability of a limestone[END_REF][START_REF] Levin | Generalized Maxwell's scheme for homogenization of poroelastic composites[END_REF] and they cover a wide range of porosity (upper porosity is close to 0.7 which corresponds to highly porous rocks). In this paper, we restrict the study to the range 0 ≤ f b ≤ 0.3 which is relatively large for oolitic limestones. Upper value of thermal conductivity is given by the conductivity of the calcitic solid phase and it corresponds to the case of zero porosity. As expected, as conductivities of air and liquid water are lower than that of solid, effective thermal conductivity decreases with increasing values of porosity. In both cases, pore space respectively fully saturated by air or liquid water, effective thermal conductivity -porosity curve may be accurately fitted by a linear function of porosity (see figures [START_REF] Ghabezloo | Effective stress law for the permeability of a limestone[END_REF][START_REF] Levin | Generalized Maxwell's scheme for homogenization of poroelastic composites[END_REF]. As experimental data collected in bibliographical review are not restricted to the detailed investigated microstructure type (oolitic limestone rocks with two-scale porosity), the aim of the comparison is not to very accurately fit the data but mainly to recover qualitative results, in particular effects of porosity and saturating fluid on overall thermal conductivity.

Simplified model based on ellipsoidal approximation for all pore families

The sensitive study is similar to the one presented in [START_REF] Giraud | Micromechanical modeling of the effective elastic properties of oolitic limestone[END_REF]. For the simplified model based on ellipsoidal approximation, mesopore family b2 is modelled by flat oblate pores close to cracks (γ = 0.05) or elongated prolate pores (γ = 20) instead of concave pores of superspherical shape. Two cases are considered: porosity fully saturated with liquid water (λ = 0.5984 W m -1 K -1 ), wet case, and porosity fully saturated with air (λ a = 0.0255 W m -1 K -1 ), dry case. Figures (7-8-9-10) illustrate dependence of the effective thermal conductivity on the mesoporosity (assuming that b1 and b2 pore families have the same volume fractions) at different levels of the volume fraction of oolites (f o = 0.4 -0.5 -0.6 -0.7).

As it has been observed in elasticity [START_REF] Giraud | Micromechanical modeling of the effective elastic properties of oolitic limestone[END_REF], distribution of the volume concentration between spar calcite and porous oolitic grains plays minor role as compare to volume fraction of pores. As expected, to the higher conductivity contrast between solid calcite mineral and air:

λ c λ g ≈ 129.4 (40)
compared to the corresponding ratio between solid calcite and liquid water

λ c λ ≈ 5.5 (41)
the higher impact of the porosity on the overall thermal conductivity is observed in the dry case. Due to this higher contrast, the case of the air saturated porosity the most interesting for a micro-macro characterization because it is more sensitive to pore shape than the case of water liquid saturated (air saturated porosity is similar to an insulating phase). Comparisons between model and experiments show that flat oblate spheroidal pores (γ = 0.05) overestimate the effect of porosity on the overall in the case of air saturated pores. This overestimate is less pronounced in the case of liquid saturated pores. In both cases, liquid and air, prediction of model are more accurate with prolate spheroidal elongated pores (γ = 20) than crack similar oblate pores.

Model including concave pores family

One only replaces ellipsoidal pore family b2 by superspheres of concavity factor p = 0.35 and the same sentivity study is performed. Preceding values of resistivity contribution tensor (formula 33) needs to be replaced by the following numerical values (see [START_REF] Chen | Evaluation of the effective elastic and conductive properties of materials containing concave pores[END_REF] for details on calculation of resistivity contribution tensors).

H supersph b2 (λ c , λ ) = 0.447518 (42)
H supersph b2 (λ c , λ g ) = 0.528849 (43)
and relation ( 35) can be used. Figures [START_REF] Zimmerman | Thermal conductivity of fluid-saturated rocks[END_REF][START_REF] Giraud | Micromechanical modeling of the effective elastic properties of oolitic limestone[END_REF] illustrate dependence of the effective thermal conductivity on the mesoporosity at different levels of the volume fraction of oolites. Comparison with experimental data show that the model accurately predicts effect of porosity and effect of saturating fluid.

Similarly to the model with prolate elongated pores, variations of effective thermal conductivity with porosity in the most sensitive case of air saturated porosity are correctly reproduced. Microstructural observations (see figure 4) show that concave pore shapes are more relevant than elongated pore shapes to describe the mesopores filling the space between spherical oolites. Experimental data correspond to purely calcitic limestones, and it is not restricted to oolitic limestones. A more accurate validation of the model by comparison with experimental data specific to oolitic limestone will be necessary. Experimental study of effective thermal conductivity of Lavoux oolitic limestone is in progress and experimental results will be presented in a next paper. On the basis of the preceding results, a best ellipsoidal approximation can be proposed for this material by minimising the difference between the numerical values of the resistivity contribution tensor respectively obtained for the supersphere (43-42) and for the spheroids [START_REF] Bruggeman | Berechnung verschiedner Physicalischer Konstanten von heterogenen Subztanzen. I. Dielektrizitätskonstanten und Leitfähigkeiten der Mischkörper aus isotropen Substanzen[END_REF], for the two cases (air saturated and water liquid saturated)

γ Air-min b2 ≈ 0.31 (44) γ Lq-min b2 ≈ 0.11 (45)
Resistivity contribution tensor of a superspherical inclusion depends on the shape parameter (concavity parameter p) and on the contrast between respective thermal conductivities of inclusion and matrix. This contrast is very different in the two extreme cases investigated (see 40-41). As a consequence, the best ellipsoidal approximation depends on the conductivities of constituents, and it yields different aspect ratii in the two cases

Conclusion

The main factor affecting elastic properties of oolitic limestone is the pore space geometry. As identified in [START_REF] Giraud | Micromechanical modeling of the effective elastic properties of oolitic limestone[END_REF] some mesopores are concave and may be approximated by superspherical shape (see [START_REF] Chen | Numerical evaluation of the Eshelby tensor for a concave superspherical inclusion[END_REF], [START_REF] Chen | Evaluation of the effective elastic and conductive properties of materials containing concave pores[END_REF]). A simplified model is presented by using ellipsoidal approximation for all the pores. This model could be used as a first approach for estimating overall thermal conductivity, its advantage being the simplicity of the corresponding homogenization model. Numerical results confirms the potential importance of the shape of mesopores for the conductivity problem (see [START_REF] Giraud | Micromechanical modeling of the effective elastic properties of oolitic limestone[END_REF]). In the two particular cases presented: air saturated and liquid water saturated pores, the comparison between resistivity contribution tensors of spheroids allows to define, in each case the best ellipsoidal approximation for a given superspherical shape. Comparison between multi-scale model based on Maxwell homogenization method and experimental data show that it correctly predicts effects of porosity and saturating fluid on overall thermal conductivity, when taking into account concave pore of superspherical shape. These results are interesting in relation to cross property analysis between elastic coefficients and thermal conductivity. It confirms previous results obtained with a similar upscaling model for the same material, for the prediction of elastic coefficients [START_REF] Giraud | Micromechanical modeling of the effective elastic properties of oolitic limestone[END_REF]. Experimental characterization of the thermal conductivity of such oolitic limestones, at different saturation ratios is also in progress and comparison with numerical results needs to be performed. Step II : Maxwell homogenization scheme sparite c meso pores (b2) (randomly oriented)

1 Figure 1 :Figure 2 :

 112 Figure 1: Scanning Electron Microscopy (SEM) images of Lavoux limestone (see [29]) 20

Figure 3 :

 3 Figure 3: Second homogenization step: transition from mesoscale to macroscale with Maxwell homogenization method, case of simplified model (ellipsoidal approximation for all the pores)

Figure 4 :

 4 Figure 4: Mesoporosity: ellipsoidal pores (b1) and concave pores (b2) (see [29])

Figure 5 :Figure 6 :

 56 Figure5: Pores saturated with air: experimental thermal conductivity as a function of porosity, for pure calcitic limestones[START_REF] Robertson | Thermal properties of rocks[END_REF]

Figure 7 :Figure 8 :

 78 Figure 7: Pores saturated with air : effective thermal conductivity as a function of mesoporosity with b2 = random distribution of cracks (oblate γ = 0.05)-blue : f o = 0.4f o = 0.5 -green : f o = 0.6 -red : f o = 0.7, experimental data taken from[START_REF] Robertson | Thermal properties of rocks[END_REF]

Figure 9 :Figure 10 :

 910 Figure 9: Pores saturated with liquid water : effective thermal conductivity as a function of mesoporosity with b2 = random distribution of cracks (oblate γ = 0.05)-blue : f o = 0.4 f o = 0.5 -green : f o = 0.6 red : f o = 0.7, experimental data taken from[START_REF] Robertson | Thermal properties of rocks[END_REF]

Figure 11 : 35 Figure 12 :Figure 13 :

 11351213 Figure 11: Pores saturated with air : effective thermal conductivity as a function of mesoporosity with b2 = random distribution of superspheres (p = 0.35) -blue : f o = 0.4 f o = 0.5 -green : f o = 0.6 -red : f o = 0.7, experimental data taken from[START_REF] Robertson | Thermal properties of rocks[END_REF]

Figure 14 :

 14 Figure 14: Pores saturated with liquid water : Resistivity contribution tensor of spheroid as a function of pore aspect ratio γ, comparison with supersphere (p = 0.35, , H SP-lq b2 = 0.448)

Acknowledgement

Financial support from the from TAMER European project(Trans-Atlantic Micromechanics Evolving Research Materials containing inhomogeneities of diverse physical properties, shapes and orientations), FP7 Project TAMER IRSES-GA-2013-610547, New Mexico Space Grant Consortium contained in the NASA Cooperative Agreement NNX13AB19A to New Mexico State University, and NSF grant DMR-1229558 are gratefully acknowledged.


N Bulle

Ralph K Rosenbaum

Assumpció Anton

Xavier Bengoa

Anders Bjørn

Richard Brain

Cécile Bulle

Nuno Cosme

Teunis J Dijkman

Peter Fantke

Mwema Felix

Trudyanne S Geoghegan

Bernhard Gottesbüren

Carolyn Hammer

Sebastien Humbert

Olivier Jolliet

Ronnie Juraske

Fraser Lewis

Dominique Maxime

Thomas Nemecek

Jérôme Payet

Kati Räsänen

Philippe Roux

Erwin M Schau

Sandrine Sourisseau

Rosalie Van Zelm

Bettina Von Streit

Magdalena Wallman

The Glasgow consensus on the delineation between pesticide emission inventory and impact assessment for LCA

Keywords: Pesticides, consensus, life cycle inventory (LCI), life cycle impact assessment (LCIA), spatial boundary, temporal boundary, ecosphere, technosphere

The Glasgow consensus on the delineation between pesticide emission inventory and impact assessment for LCA

Introduction

Pesticides, such as fungicides, herbicides, insecticides, plant growth regulators, and defoliants are applied to agricultural fields in order to optimise crop yield. Agricultural pesticide use is substantial and amounts globally to about 1.2 million metric tons of active ingredients (the biologically active part of a commercial pesticide formulation) per year between 2005and 2010(FAO 2013)). In contrast to regulatory assessments, LCA is not used to analyse (or question) product risk or safety, but instead supports to establish and inform environmental performance profiles aiming to identify the most environmentally sustainable way(s) of providing a product or service between different options. These may, for example, range from various functionally equivalent pesticides applied in conventional agriculture to alternative solutions, such as organic or integrated farming practices. Whatever the choice of alternatives, LCA should be able to reliably identify the trade-offs between alternative solutions.

In practice, this ideal is currently hampered by significant inconsistencies between emission inventory modelling and impact assessment, two distinct phases of an LCA study. Notably, a clear definition of the delineation between the product system model as represented in the Life Cycle Inventory (LCI) (i.e. technosphere) and the natural environment as represented by Life Cycle Impact Assessment (LCIA) characterisation models (i.e. ecosphere) is currently missing [START_REF] Dijkman | PestLCI 2.0: a second generation model for estimating emissions of pesticides from arable land in LCA[END_REF]. The typical difficulty with respect to pesticides is to quantify the proportion emitted to the different media in the ecosphere, while usually only the amount applied to the agricultural field is known. This leads to the core question of considering the field as part of the ecosphere or technosphere, which is also related to different agricultural practices (e.g. organic vs. conventional) and represents a modelling choice that is currently inconsistently handled in LCA practice [START_REF] Hellweg | Life cycle impact assessment of pesticides: When active substances are spread into the environment[END_REF][START_REF] Birkved | PestLCI-A model for estimating field emissions of pesticides in agricultural LCA[END_REF][START_REF] Nemecek | Life Cycle Inventories of Agricultural Production Systems[END_REF][START_REF] Dijkman | PestLCI 2.0: a second generation model for estimating emissions of pesticides from arable land in LCA[END_REF][START_REF] Van Zelm | Bridging the gap between life cycle inventory and impact assessment for toxicological assessments of pesticides used in crop production[END_REF]. As a consequence, several approaches and hypotheses have been proposed and used up to now, which leads to inconsistent results and may not always represent realistic conditions.

In 2003, the (Swiss) Discussion Forum on LCA approached the subject of pesticide emission and impact modelling in LCA, providing an overview of LCIA models for pesticides and showing directions for further development [START_REF] Hellweg | Life cycle impact assessment of pesticides: When active substances are spread into the environment[END_REF]. Although, more than ten years have passed since then, several of their conclusions remain valid, stating e.g. that: 1) "the correlation between spatial variability on the one hand and regionally different crops and agricultural management practices on the other hand is not taken into account in LCA."1 ; and 2) underlying assumptions and the model performances [of LCIA methods] need further validation and verification" p. 312 in [START_REF] Hellweg | Life cycle impact assessment of pesticides: When active substances are spread into the environment[END_REF].

A wealth of information is available in the literature on fate and transport processes of pesticides after application to agricultural fields, such as spray drift including deposition, volatilisation, leaching, runoff, washoff, and plant uptake, as well as influencing factors such as buffer zones, application method, temperature, crop/soil type, and degradation, or special cases such as greenhouses. An overview (nonexhaustive) is given in Table 1.

(table 1 here) These processes and conditions mainly influence how much of a pesticide applied to a field will be transported from the field into different environmental media, which is a first step in the environmental fate modelling of these chemicals. These processes depend on a number of factors and in particular on the active ingredient, the formulation containing it, the application method, weather conditions (before, during, and after application), soil conditions, crop characteristics, and whether and how irrigation is used. This complexity creates a substantial obstacle to a consistent quantification of agricultural emissions to environmental media.

In LCA, environmental fate of a chemical emission to the ecosphere is usually modelled in a generic way during the impact assessment phase. However, given the important influence of local conditions and agricultural practice on the first step of the environmental fate of pesticides (i.e. from field application to transport to off-field air, water, and natural soil), using generic fate factors leads to extremely high uncertainty. For this reason, the field may be considered as being part of the technosphere and the first step of fate modelling is thus considered as part of the inventory modelling. Although, inconsistencies exist between this first step of site specific and agricultural practice specific fate modelling included in the inventory phase and the next steps of generic fate, exposure, and effect modelling of toxic substances included in the impact assessment phase.

With the goal of establishing consensus, a full-day expert workshop was organised in a collaborative effort between the Division for Quantitative Sustainability Assessment of the Technical University of Denmark and Quantis on Saturday 11 th May 2013 in Glasgow, UK, back to back with the 23 rd SETAC Europe meeting. More than 30 specialists, representing industry, government, and academia from 15 countries and four continents participated.

The objective of the workshop was to create consensus and clear guidelines for LCA practitioners, data (base) and characterisation method developers, and decision makers where the boundary between the product system model representing the technosphere (emission inventory) and the environmental characterisation model representing the ecosphere (impact assessment) should be set in all three spatial dimensions and time when considering application of substances to an open agricultural field or in greenhouses, and consequent emissions to the natural environment and their potential impacts. The workshop explicitly excluded discussions on how to quantify emissions or related impacts of pesticides, while focusing on clearly defining what should be quantified in the emission inventory of the product system and what should be quantified by the characterisation factors (CF) from the impact characterisation models, avoiding any overlap or double counting of chemical fate processes to be considered. In setting guidelines and recommendations, the workgroup focused on issues of science and scientific consensus and avoided recommendations that would be dependent on or endorse a specific model.

Methods

Life Cycle Inventory (LCI)

In order to at least provide meaningful emission estimates, LCA practitioners and developers proposed generic assumptions regarding varying percentages of applied active ingredient emitted to environmental media [START_REF] Margni | Life cycle assessment of pesticides on human health and ecosystems[END_REF][START_REF] Audsley | Harmonisation of Environmental Life Cycle Assessment for Agriculture. Author-produced version of the article[END_REF][START_REF] Panichelli | Life cycle assessment of soybean-based biodiesel in Argentina for export[END_REF]) and in greenhouses [START_REF] Antón | Comparison of toxicological impacts of integrated and chemical pest management in Mediterranean greenhouses[END_REF][START_REF] Juraske | Human intake fractions of pesticides via greenhouse tomato consumption: Comparing model estimates with measurements for Captan[END_REF]). Furthermore, a number of very different (i.e. inconsistent) approaches and assumptions are currently applied in quantifying life cycle emission inventories of pesticides in any LCA study involving agricultural systems, for example:

1) The widely used life cycle inventory database Ecoinvent adopted the assumption that the amount of pesticide applied is emitted 100% to agricultural soil [START_REF] Nemecek | Life Cycle Inventories of Agricultural Production Systems[END_REF];

2) In the U.S. Life Cycle Inventory Database (NREL 2012) pesticide emissions are inventoried as emissions to air and water based primarily on leaching and runoff data from (US EPA 1999; [START_REF] Kellogg | Environmental Indicators of Pesticide Leaching and Runoff from Farm Fields[END_REF];

3) The pesticide emissions model PestLCI 2.0 [START_REF] Dijkman | PestLCI 2.0: a second generation model for estimating emissions of pesticides from arable land in LCA[END_REF] USES-LCA differentiate between agricultural and natural soil as environmental media. The USEtox developers included agricultural soil arguing that "using two soil types, agricultural and natural soil, accounts for the fraction of agricultural soil relative to the total soil surface and also allows for specific (e.g. pesticide) emissions occurring on agricultural soil only" [START_REF] Rosenbaum | USEtox -The UNEP/SETAC-consensus model: recommended characterisation factors for human toxicity and freshwater ecotoxicity in Life Cycle Impact Assessment[END_REF]. For ecotoxicity, USEtox only accounts for freshwater ecotoxicity and does currently not provide factors for terrestrial ecotoxicity impacts on (or off) the agricultural field due to missing data and appropriate models that could provide a solid basis for a conensus. Therefore, only impacts outside the agricultural field and its soil (i.e. only effects occurring in the ecosphere) are characterised.

In practice this means that the practitioner has two options at the moment: 1) a pesticide emission model (like PestLCI 2.0) used in combination with CFs for emissions to off-field environmental media (e.g. natural soil, air, freshwater in the case of USEtox), or 2) the amount applied to the agricultural field is used and characterised with a CF for on-field emissions (e.g. to agricultural soil in USEtox -CFs for all other emission media are representing off-field emission media and are thus not applicable). In the absence of widely applicable pesticide emission models at the time, this was considered an approximate solution for pesticide emissions, but many important factors and fate processes such as wind drift, application method, buffer zones, plant deposit etc. are not modelled and a CF for an emission to agricultural soil in USEtox comes with considerable model uncertainty of at least two to three orders of magnitude (excluding uncertainty due to missing transport processes) [START_REF] Rosenbaum | USEtox -The UNEP/SETAC-consensus model: recommended characterisation factors for human toxicity and freshwater ecotoxicity in Life Cycle Impact Assessment[END_REF].

With the inherent assumption of steady-state conditions, the dynamic fate processes taking place between the application and the moment the substance is transported outside the agricultural field are not explicitly modelled in LCIA, and are hence presently expected to be represented by LCI data. An implicit assumption thereby is that the field is part of the technosphere, which means that impacts to the environment/ecosystem on the field are not specifically considered. In consequence, all currently used toxicity LCIA models are incompatible with LCI data representing the amount applied to the field. This is true for ecosystem as well as human health LCIA models, although some exceptions to this general rule exist for specific impact pathway mechanisms. For example the human health characterisation model for pesticide residues in food crops by Fantke et al. (2011b), which requires information on the quantity applied to the field, rather than the consequent environmental emissions.

Workshop resume

In order to preserve consistency with the characterisation of other chemical emissions, there seems to be limited flexibility to adapt LCIA characterisation modelling; hence, the most practical way to improve consideration of pesticide field applications in LCA may be to focus on clearly defining the inventory requirements for pesticide emissions as illustrated in Figure 1. Many definitions of delineations between LCI and LCIA are possible that respect the requirements that all flows between environmental media connect and the mass balance is conserved, but it is essential that all stakeholders (i.e. LCI/LCIA modelers and LCA practitioners) are using a consistent approach. Therefore, a consensus-based definition of a convention and related guidance for LCA practitioners and methodology developers is required and was the main objective of the Glasgow pesticide workshop.

(figure 1 here)

While a brief overview will be given hereafter, the complete minutes, details, and most slides presented during the workshop can be found in the Supporting Information. The workshop started with four presentations providing experiences and perspectives of LCA practitioners, emission inventory practice, and impact assessment developers.

Presenting a practitioner's perspective, Sebastien Humbert (Quantis) pointed out that "Between 1 to 5 hours (max) can be allocated by practitioners to modelling inventory of pesticides for one crop. Therefore, practical and efficient solutions are needed." Current issues encountered when conducting an LCA are: a) media of substance application and related fraction emitted to each medium to be considered; b) missing guidelines for greenhouses (Are they part of the technosphere or the ecosphere?); c) other issues related Examples are pesticide formulation by-products (adjuvants, solvents, etc.), phytohormones used as plant growth regulators, animal manure by-products (livestock antibiotics and hormones), sewage sludge constituents (metals, bacteria, etc.), and degradation products (metabolites). "None of these are covered in current LCIA practice, but can we nevertheless assume the same conditions regarding system boundaries?" He identified open questions regarding consistent system boundaries for LCIA: a) How to address species migrating between technosphere and ecosphere? b) How to address species living from the technosphere (e.g. birds feeding on insects living in agricultural fields)? c) How to consider applied mass for impacts from crop intake? He also named a number of LCIA important principles for pesticides: a) include predominant human exposure pathways: intake of treated crops; b) consider time dimensions for exposure via crop intake; c) allow comparison with exposed population sub-groups (e.g. bystanders, operators, etc.).

Rosalie van Zelm (Radboud University) presented work done in collaboration with Irstea (France) focusing on the boundary of LCI and LCIA so as to frame what modelling should be included in LCI and what in LCIA in order to prevent gaps and overlaps [START_REF] Van Zelm | Bridging the gap between life cycle inventory and impact assessment for toxicological assessments of pesticides used in crop production[END_REF]. She outlined the issues that we further and more thoroughly discussed in the meeting. Finally, a case study on bananas was presented applying the proposed framework. It showed the importance of a good integration of LCI-LCIA methodology allowing to quantify differences between efficient vs inefficient agricultural practices taking into account pre-and posttreatment pesticide flows (e.g. cleaning of equipment), use of buffer zones, and (over)dosing. This work was recently published [START_REF] Van Zelm | Bridging the gap between life cycle inventory and impact assessment for toxicological assessments of pesticides used in crop production[END_REF], proposing a framework to bridge the gap and prevent overlaps between LCI and LCIA for toxicological assessments of pesticides.

With these inputs, the discussion was launched with a number of issues and open questions identified beforehand as starting points for the discussion:

• Is the ecosystem on the agricultural field (e.g. aerial such as insects and pollinators, terrestrial and deep soil ecosystems) part of the area of protection (natural environment) and should thus be addressed in the impact assessment or is it a highly controlled ecosystem anyway and essentially part of the technosphere and then (at least partially) covered in the land use impact category (which inherently includes changes in biodiversity due to pesticide application as part of some land-use types)?;

• Does it lead to double counting if both the inventory model and the impact model involve a fate modelling step or can these be distinguished clearly and consistently across substances and conditions?;

• Spatial dimensions: If the field is considered as part of the technosphere, can we define the agricultural field as a 3-dimensional box by height of air above the field, width and length of the field including buffer zones, and soil depth? Then only the fraction(s) of an applied pesticide leaving this box to various environmental media would be accounted for in the emission inventory;

• Temporal dimensions: Pesticides are typically applied in pulses. Does the assumption of similarity between pulse and continuous emissions in the steady-state model of LCA also hold for such emission dynamics? How can it be determined, when steady-state assumptions are satisfactory and when not? Which periods of time from application to ecosphere emissions need to be taken into account in the emission inventory and in the impact assessment?;

• Mass applied vs. mass emitted -what information does the emission inventory need to provide? Which emission media are relevant to cover: air, surface water, ground water, deeper soil layer(s), others? Intake of pesticide residues in food products may be the dominating human exposure pathway in most cases, but requires the inventory to also report the quantity applied directly to the crop and not just the emission to the environmental media. Therefore, a clear definition of what needs to be reported and how in the life cycle inventory is needed;

• Which impact pathways (e.g. direct and indirect human exposure via food residues, inhalation, drinking water, or terrestrial/aquatic/aerial ecosystems on-/off-field, etc.) and indicators (human toxicity, ecotoxicity, species richness, functional diversity, etc.) should be covered for pesticides?;

• Are different recommendations required for specific cases such as greenhouses, irrigated vs. nonirrigated fields, etc.?

The discussions during the workshop were comprehensive, focused, and very productive, resulting in the recommendations presented in the following section.

Results and discussion

A balanced assessment of toxicity effects due to pesticide emissions (i.e. to environmental media, which is not the same as the amount of pesticide used/applied) associated to their agricultural use in the context of life cycle assessment (LCA) is strongly desirable, allowing for consideration of both advantages and disadvantages of using pesticides or choosing an alternative approach instead. Recommended practice should enable the assessment of trade-offs between potential negative biodiversity impacts pesticides may cause on and around the field and positive indirect effects on biodiversity due to increased yield and thus less land-use compared to avoiding pesticide application.

In Table 3, the main results from the discussion around the essential core questions of allocation of the agricultural field to technosphere or ecosphere, as well as its spatial and temporal dimensions are presented. These questions were the starting point of the discussion during the workshop and the initial goal was to arrive at recommendations to answer the questions. However, it became clear that there is a strong dependency on goal and scope of an LCA study and that fixing these would not allow certain assessment goals. Instead, the focus was on defining a clear interface between LCI and LCIA. This should be capable of supporting any goal and scope requirements while avoiding double counting or excluding important emission flows (and their potential impacts). The detailed recommendations are given in the section Conclusions and recommendations.

(table 3 here)

Conclusions and recommendations

The boundary between technosphere/ecosphere and allocation of the agricultural field to either technosphere or ecosphere and its spatial dimension was and should not be fixed on a general level, but depend on the goal and scope of the LCA study. Instead, we recommend a number of emission flows, both on and off the field, that need to be quantified in the LCI in order to characterise specific impacts, which may take place on or off the field.

Author-produced version of the article published in International Journal of Life Cycle Assessment, 2015, N°20(6), p. 765-776

The original publication is available at http://link.springer.com Doi: 10.1007/s11367-015-0871-1

Consensus was reached on distinct sets of recommendations for LCI and LCIA respectively, which are presented hereafter. This establishes a clearly defined interface between LCI and LCIA.

Life cycle inventory recommendations:

• For pesticides application, the LCI should report the following information (per functional unit):

-Pesticide identification (CAS registry numbers and names of active ingredients per applied plant protection product, PPP); -Crop; -Mass applied of each active ingredient; -Application method (foliar spray, soil injection, drip irrigation) or formulation type (soluble concentrate, granule, wettable powder); -Presence of buffer zones (y/n); -Location/country (which identifies a default local scenario/site incl. climate, soil conditions, present environmental media, …); -Application time in days before harvest (for human health impacts) and crop growth stage (for terrestrial/aerial ecosystem impacts) during application; -Adherence with Good Agricultural Practice(s) -GAP, such as discussed and defined by FAO (2003) (with adjustable parameters including pre-and post-treatment pesticide flows, e.g. equipment cleaning, tanks and cans residues, etc.), in order to be able to distinguish different levels of agricultural practice from good (i.e. efficient) to average to inefficient (e.g. overdosing, application during precipitation events, etc.); -The goal and scope section of an LCA should clearly state whether the agricultural field is assumed as part of the technosphere or the ecosphere.

• We recommend the explicit reporting of emission fractions, i.e. fractions of the applied pesticide emitted to environmental media via initial distribution from the applied mass based on models and/or measurements with mass fractions going directly to:

-On-field:

• soil surface (excluding plant deposit);

• paddy water (excluding plant deposit), e.g. for paddy rice;

• plant (plant deposit);

-Off-field:

• air (via volatilization on-field and wind drift, fraction not deposited close to the field);

• surface water (via spray drift deposition, excluding runoff, avoiding double counting with air (of which a fraction eventually redeposits on surface water at long distance); distinguishing fresh and marine water as far as possible and meaningful; • soil (distinguishing types [natural, industrial, agricultural, etc.] if possible);

• The emission fractions to environmental media via initial distribution and the degraded fraction should always sum up to 100% of the quantity applied to the field in order to maintain conservation of mass and to allow for assessment of all potential impacts in the LCIA;

• There should be archetypical/default sets of values for these emission fractions to environmental media via initial distribution depending on conditions of applications that could be replaced if measured or more detailed information is available. These will be quantified and agreed upon in a follow-up workshop in Basel in May 2014;

• As a starting point, default values may correspond to current average agricultural practice that may be spatially differentiated;

• Good practice in greenhouses should lead to minimum emissions, but fractions on greenhouse soil surface (excluding plant deposit), plant, leaching through the top soil layer and emissions to air outside the greenhouse should be quantified;

Author-produced version of the article published in International Journal of Life Cycle Assessment, 2015, N°20(6), p. 765-776

The original publication is available at http://link.springer.com Doi: 10.1007/s11367-015-0871-1

• In case buffer zones are present, they should be considered as part of the crop (production system) and the change in yield per ha and the emission fractions to environmental media via initial distribution to off-field soil/surface water accounted for accordingly. Therefore, no specific CFs are required for buffer zones as these will be treated the same way as the rest of the agricultural field;

-Runoff, accounted for in the impact assessment, would have to be modelled accordingly;

• Care should be taken to avoid double counting between the multimedia transfers of these emission fractions and the impact assessment fate model, thus the decision to only have the emission to environmental media via initial distribution in the inventory and subsequent transfers considered in the impact assessment. This is supported by furthermore distinguishing between initial distribution processes in LCI, where steady state conditions are typically not (yet) reached and a dynamic assessment is required [START_REF] Rein | New concepts for dynamic plant uptake models[END_REF]Fantke et al. 2013), and fate processes in LCIA, for which steady state is typically assumed based on continuous diffusive, advective, and degradation processes.

Life cycle impact assessment recommendations:

• Relevant impact categories (with temporal aspects built-in):

-Land-use biodiversity impact on-field; -Toxicity biodiversity impact off-field (terrestrial, aerial, freshwater, ground-water); -Toxicity human health off-field (including residues in treated crops for subsequent human exposure via crop consumption as a potentially predominant exposure pathway, bystander); -Toxicity human health on-field, e.g. occupational exposure, should be further explored;

• LCIA methods should allow for the flexibility to define the agricultural field as part of the technosphere or the ecosphere in the goal and scope of a study (see Table 3) and CFs should be clearly labelled or documented as representing potential impacts in the ecosphere or the technosphere (e.g. terrestrial ecotoxicity on agricultural soil) if a specific assumption is required;

• Impact assessment should model:

-Fate:

• secondary drainage;

• runoff;

• degradation;

• volatilization;

• transfer (leaching) to ground-water and deeper soil layers on the field;

• residues in entire crop of which some parts might remain on-field after harvest  leading to possible subsequent runoff/leaching and resulting background concentrations, or to exposure via fodder for animals or compost (with pesticide residues);

-Human exposure, eventually including bystanders, applicators, field workers, etc.;

• The plant fraction washed off is not yet considered in impact assessment, only the fraction effectively transferred from root to soil could be added to the primary soil emission until properly modelled.

Whether washoff can/should be included or not is a function of the scenario, i.e. at good or average agricultural practice, washoff is negligible, for application shortly before rain events, washoff may become relevant or even dominant;

• Compatibility between the dynamic fate modelling for the initial emission fractions and the subsequent steady-state fate modelling in LCIA needs to be acquired to avoid double counting or omissions of mass transport processes. This notably involves the consideration of the temporary boundary applied to the dynamic emission model;

• Impact assessment methods should also report which multi-media transfers are considered and recommend how the environmental medium may be linked to the mass applied;

• Open issues:

-What is the influence of irrigation and how should it be modelled?;

Author-produced version of the article published in International Journal of Life Cycle Assessment, 2015, N°20(6), p. 765-776

The original publication is available at http://link.springer.com Doi: 10.1007/s11367-015-0871-1

Tables Table 1: Overview of available literature focusing on fate and transport processes of pesticides after application to agricultural fields

Process/factor References

Spray drift including deposition [START_REF] Bilanin | AGDISP: The Aircraft Spray Dispersion Model, Code Development and Experimental Validation[END_REF][START_REF] Ganzelmeier | Studies on the spraydrift of plant protection products[END_REF][START_REF] Holterman | Modelling spray drift from boom sprayers[END_REF][START_REF] Bird | Evaluation of the AgDISP aerial spray algorithms in the AgDRIFT model[END_REF][START_REF] Teske | AgDrift®: A model for estimating nearfield spray drift from aerial applications[END_REF][START_REF] Siebers | Investigation on downwind short-range transport of pesticides after application in agricultural crops[END_REF][START_REF] Gil | Emission of pesticides to the air during sprayer application: A bibliographic review[END_REF][START_REF] Gil | Atmospheric loss of pesticides above an artificial vineyard during air-assisted spraying[END_REF][START_REF] Gil | Influence of micrometeorological factors on pesticide loss to the air during vine spraying: Data analysis with statistical and fuzzy inference models[END_REF][START_REF] Wang | A simple probabilistic estimation of spray drift--factors determining spray drift and development of a model[END_REF][START_REF] Teske | Initial Development and Validation of a Mechanistic Spray Drift Model for Ground Boom Sprayers[END_REF][START_REF] Mc | Bystander exposure to pesticide spray drift: New data for model development and validation[END_REF][START_REF] Larsson | Quantifying interactions between compound properties and macropore flow effects on pesticide leaching[END_REF] Volatilisation [START_REF] Kubiak | Volatilization of Pesticides from Plant and Soil Surfaces-Field Versus Laboratory Experiments[END_REF][START_REF] Rüdel | Volatilisation of pesticides from soil and plant surfaces[END_REF]Bedos et al. 2002a;[START_REF] Scholtz | A pesticide emission model (PEM) Part I: model development[END_REF]Bedos et al. 2002b;[START_REF] Wolters | Pesticide volatilisation from plants: Improvement of the PEARL, PELMO and MACRO Models[END_REF][START_REF] Guth | Volatilisation of crop protection chemicals from crop and soil surfaces under controlled conditionsprediction of volatile losses from physico-chemical properties[END_REF][START_REF] Leistra | Measured and computed volatilisation of the fungicide fenpropimorph from a sugar beet crop[END_REF][START_REF] Van Den Berg | Volatilisation of pesticides computed with the PEARL model for different initial distributions within the crop canopy[END_REF][START_REF] Bedos | Modelling pesticide volatilization after soil application using the mechanistic model Volt'Air[END_REF]Davie-Martin et al. 2013b;Davie-Martin et al. 2013a) Leaching [START_REF] Persicani | Pesticide leaching into field soils: sensitivity analysis of four mathematical models[END_REF][START_REF] Sorensen | Pesticide leaching assessment method for ranking both single substances and scenarios of multiple substance use[END_REF][START_REF] Armstrong | CRACK-NP: a pesticide leaching model for cracking clay soils[END_REF][START_REF] Larsson | Quantifying interactions between compound properties and macropore flow effects on pesticide leaching[END_REF][START_REF] Loll | Stochastic analyses of field-scale pesticide leaching risk as influenced by spatial variability in physical and biochemical parameters[END_REF][START_REF] Harris | Evaluating pesticide leaching models: the Brimstone Farm dataset[END_REF][START_REF] Geisler | Variability assessment of groundwater exposure to pesticides and its consideration in life-cycle assessment[END_REF][START_REF] Kruijne | Pesticide leaching to the groundwater in drinking water abstraction areas[END_REF][START_REF] Leterme | Modeling the width and placement of riparian vegetated buffer strips: a case study on the Chi-Jia-Wang stream, Taiwan[END_REF][START_REF] Rosenbom | Ability of the MACRO Model to Predict Long-Term Leaching of Metribuzin and Diketometribuzin[END_REF][START_REF] Akbar | GIS based ArcPRZM-3 model for bentazon leaching towards groundwater[END_REF][START_REF] Vanderborght | Nation-wide assessment of pesticide leaching to groundwater in Germany : comparison of indicator and metamodel approaches[END_REF][START_REF] Vanderborght | Effect of pesticide fate parameters and their uncertainty on the selection of "worst-case" scenarios of pesticide leaching to groundwater[END_REF] Runoff [START_REF] Huber | Modeling pesticide losses with surface runoff in Germany[END_REF][START_REF] Sexton | Pesticide loss in surface runoff under various tillage and pesticide formulation conditions[END_REF][START_REF] Kellogg | Environmental Indicators of Pesticide Leaching and Runoff from Farm Fields[END_REF][START_REF] Inao | Landscape-scale simulation of pesticide behavior in river basin due to runoff from paddy fields using pesticide paddy field model (PADDY)[END_REF][START_REF] Miao | Simulating pesticide leaching and runoff in rice paddies with the RICEWQ-VADOFT model[END_REF][START_REF] Liu | Phase distribution of synthetic pyrethroids in runoff and stream water[END_REF][START_REF] Berenzen | A comparison of predicted and measured levels of runoff-related pesticide concentrations in small lowland streams on a landscape level[END_REF][START_REF] Numabe | Estimation of pesticide runoff from paddy fields to rural rivers[END_REF][START_REF] Schriever | Estimating pesticide runoff in small streams[END_REF][START_REF] Phong | Exposure risk assessment and evaluation of the best management practice for controlling pesticide runoff from paddy fields. Part 2: Model simulation for the herbicide pretilachlor[END_REF][START_REF] Thuyet | Wash off of imidacloprid and fipronil from turf and concrete surfaces using simulated rainfall[END_REF] Washoff [START_REF] Smith | Foliar washoff of pesticides (FWOP) model: Development and evaluation[END_REF][START_REF] Cohen | Foliar washoff of pesticides by rainfall[END_REF][START_REF] Willis | Azinphosmethyl and fenvalerate washoff from cotton plants as a function of time between application and initial rainfall[END_REF][START_REF] Fisher | S-Tributyl Phosphorotrithioate Washoff and Dissipation of Foliar Residues[END_REF] Plant uptake [START_REF] Trapp | Plant Contamination. Modeling and Simulation of Organic Chemical Processes[END_REF][START_REF] Fryer | Model Intercomparison for the Uptake of Organic Chemicals by Plants[END_REF][START_REF] Antón | Comparison of toxicological impacts of integrated and chemical pest management in Mediterranean greenhouses[END_REF][START_REF] Juraske | Human intake fractions of pesticides via greenhouse tomato consumption: Comparing model estimates with measurements for Captan[END_REF][START_REF] Juraske | Uptake and persistence of pesticides in plants: Measurements and model estimates for imidacloprid after foliar and soil application[END_REF][START_REF] Collins | Plant Uptake of Xenobiotics[END_REF]Fantke et al. 2011a) Buffer zones [START_REF] Snoo | Buffer zones for reducing pesticide drift to ditches and risks to aquatic organisms[END_REF][START_REF] Matthews | Can farmers reduce spray drift?[END_REF][START_REF] Leterme | Modeling the width and placement of riparian vegetated buffer strips: a case study on the Chi-Jia-Wang stream, Taiwan[END_REF][START_REF] Lacas | Using grassed strips to limit pesticide transfer to surface water: a review[END_REF][START_REF] Madrigal | Pesticide degradation in vegetative buffer strips: grassed and tree barriers. Case of isoproturon[END_REF][START_REF] Passeport | Selected pesticides adsorption and desorption in substrates from artificial wetland and forest buffer[END_REF] Application method, temperature, crop/soil type, and degradation [START_REF] González | An analytically solved kinetic model for pesticide degradation in single compartment systems[END_REF][START_REF] Boesten | Guidance Document on Estimating Persistence and Degradation Kinetics from Environmental Fate Studies on Pesticides in EU Registration[END_REF][START_REF] Kah | Factors Influencing Degradation of Pesticides in Soil[END_REF][START_REF] Fantke | Variability of pesticide dissipation half-lives in plants[END_REF][START_REF] Fantke | Estimating Half-Lives for Pesticide Dissipation from Plants[END_REF] Greenhouses [START_REF] Paul | Review: The Management of Pesticide Exposure in Greenhouses[END_REF][START_REF] Antón | Comparison of toxicological impacts of integrated and chemical pest management in Mediterranean greenhouses[END_REF][START_REF] Garratt | Modeling Pesticide Leaching and Dissipation in a Mediterranean Littoral Greenhouse[END_REF]) scope of the LCA, etc. Therefore, the spatial dimensions of the agricultural field should not be fixed, but clearly defined in the study's goal and scope.

an interface, since different actors are involved, which are typically disconnected.

If the LCI requirements are clearly set, the LCIA developers can build on these to represent potential impacts based on available impact pathways and models. See "Emissions in the LCI" for further details on recommendations for a definition of this interface.

Temporal dimensions of the agricultural field

Temporal dimensions are dynamic and may depend on various factors, such as crop and pesticide type and its use, etc. The temporal dimensions of the agricultural field need to be fixed and will be defined in a follow-up workshop dealing with the definition of default emission fractions to environmental media via initial distribution.

The temporal dimensions of the agricultural field need to be fixed in order to enable the dynamic modelling of the initial distribution after application (see also under "Emissions in the LCI").

Greenhouses

Greenhouses are always part of the technosphere and emissions to air or soil outside the greenhouse should be quantified.

A greenhouse is a closed and controlled environment, accessible only to a very limited extent for species from its outside.

Emissions in the LCI LCI emissions represent an initial distribution to environmental media both on and off the field.

Double counting between the fate modelling of on-/off-field emission fractions and the impact assessment fate model has to be avoided. Therefore, the emission to environmental media on-/offfield should be modelled dynamically via an initial distribution in the LCI for a specific time span after application (where steady state conditions are typically not (yet) reached and a dynamic assessment is required). Subsequent transfers between off-field environmental media are considered in the LCIA (where steady state is typically assumed based on continuous diffusive, advective, and degradation processes).

Author-produced version of the article published in International Journal of Life Cycle Assessment, 2015, N°20(6), p. 765-776

The original publication is available at http://link.springer.com Doi: 10.1007/s11367-015-0871-1

Figures

Figure 1 :

 1 Figure 1: Conceptual representation of emissions to various environmental media occurring after application of a pesticide to a crop on an agricultural field (based on Birkved and Hauschild (2006))

Life Cycle Impact Assessment (LCIA)

	Author-produced version of the article published in International Journal of Life Cycle Assessment, 2015, N°20(6), p. 765-776
	The original publication is available at http://link.springer.com
	Doi: 10.1007/s11367-015-0871-1
	employs a local fate model that
	estimates the amounts emitted (meaning here leaving the agricultural field) to air, surface water, and
	ground water through the soil, respectively, based on application methods, local meteorological
	conditions, crop types, and other influencing factors. This model considers the agricultural soil as part
	of the technosphere;
	4) The recent U.S. field crop LCI database "USDA LCA Digital Commons" does not consider any fate and
	transport losses and clearly reports release of pesticides to agricultural soil, and also to air when
	relevant according to the application method inventoried (Cooper et al. (2013);
	http://www.lcacommons.gov);
	Choosing among these available approaches will have an important influence on the results of the LCI as
	illustrated in Table 2 for a simplified example like the application of 2,4-D to corn.
	(table 2 here)
	2.2 All current LCIA characterisation models for toxicity, such as IMPACT 2002 (Pennington et al. 2005) -used
	in IMPACT 2002+ (Jolliet et al. 2003), USES-LCA (van Zelm et al. 2009) -applied in ReCiPe (Goedkoop et al.
	2012), and USEtox (Rosenbaum et al. 2008) -adopted by ILCD (EC-JRC 2011) and TRACI 2.0 (Bare 2011),
	consider the fate (transport, distribution, and degradation) of a pesticide, once emitted to the ecosphere (=
	natural environment), i.e. air, water, and soil outside the agricultural field. Nevertheless, both USEtox and

  Author-produced version of the article published in International Journal of Life Cycle Assessment, 2015, N°20(6), p. 765-776 The original publication is available at http://link.springer.com Doi: 10.1007/s11367-015-0871-1 to formulation additives and pesticide degradation products; d) potential double counting with land occupation (in some LCIA methods, characterisation factors for land occupation may already account for reduced biodiversity due to pesticides used); e) consideration of water quality in water footprinting (classically, for water pollution caused by pesticides only the fraction directly going to water is considered in water footprints, but if a pesticide is emitted to soil and air, a fraction of these emissions will also end up in water via e.g. deposition, runoff, or leaching. How should this be accounted for?); f) default values should be applied to generic conditions and the selected model should be flexible to adapt values representing local conditions. Teunis Dijkman (DTU) presented and compared three examples of current practice in LCI modelling (Ecoinvent, U.S. LCI, and PestLCI 2.0, see Table2), with a focus on the delineation between technosphere and ecosphere and transport processes considered in PestLCI 2.0. He concluded that a) different LCI approaches and system boundary choices lead to incomparable LCA studies where toxicity results can differ by orders of magnitude, depending on the emission model chosen; b) modelling fate processes in LCI does not lead to double counting of fate processes; c) clearly defining a technosphere-ecosphere boundary is essential.Peter Fantke (DTU) provided an overview of current LCIA modelling practice. Among other he pointed out a number of potentially relevant agricultural chemical emissions which are not yet covered by LCIA methods.

  Author-produced version of the article published in International Journal of Life Cycle Assessment, 2015, N°20(6), p. 765-776 The original publication is available at http://link.springer.com Doi: 10.1007/s11367-015-0871-1

  Author-produced version of the article published in International Journal of Life Cycle Assessment, 2015, N°20(6), p. 765-776 The original publication is available at http://link.springer.com Doi: 10.1007/s11367-015-0871-1

Table 2 :

 2 Comparing four life cycle emission inventory approaches: percentages emitted to environmental media per unit of 2,4-D applied to corn

					USDA LCA
	Approach Ecoinvent	U.S. LCI	PestLCI 2.0	Digital
					Commons
	Emission medium	%	%	%	%
	Soil	100	-	-	100
	Air	-	96	0.61	-
	Surface water	-	4	0.02	-
	Ground water	-	-	0.62	-
	Degradation, crop uptake, etc.	-	-	98.7	-

Table 3 :

 3 Recommendations for the definition of an interface between LCI and LCIA for agricultural pesticide emissionsAuthor-produced version of the article published in International Journal of Life Cycle Assessment, 2015, N°20(6), p. 765-776 The original publication is available at http://link.springer.com Doi: 10.1007/s11367-015-0871-1

	Topic	Recommendation	Reasoning
	Boundary between	No fixed definition of the	Potential impacts may occur both on and
	technosphere/ecosphere	boundary or allocation of the	off the agricultural field. The consideration
	and allocation of the	agricultural field to either	of the agricultural field as part of
	agricultural field to	technosphere or ecosphere is	technosphere or ecosphere therefore
	either technosphere or	defined. Instead, we recommend	depends on the goal and scope of a LCA
	ecosphere	a number of emission flows, both	study and should not be fixed, but defined
		on and off the field, that need to	in each study correspondingly. Instead, the
		be quantified in the LCI in order to	definition of emission flows to be
		characterise specific impacts,	quantified in the LCI (with specific impact
		which may take place on or off the	pathways in mind) allows for LCIA
		field. Then the choice of	developers to provide CFs for specific
		characterisation factor defines	impact pathways, which may represent
		which impacts are characterised.	impacts on or off the field. This defines a
		Furthermore, the consideration of	clear interface between LCI and LCIA
		the agricultural field as part of	rather than fixing which impacts can be
		technosphere or ecosphere	considered in an LCA.
		should be clearly defined in the
		goal and scope of a study.
	Buffer zones	Buffer zones should be considered	Buffer zones are a measure to limit off-
		as part of the crop production	field emissions, but affect yield. Therefore
		system and the change in yield	the presence of buffer zones is an
		per ha and the emission fractions	important factor affecting potential
		to environmental media via initial	impacts that needs to be accounted for,
		distribution to off-field	especially when considering different
		soil/surface water accounted for	agricultural practice (e.g. intensive vs.
		accordingly.	extensive).
	Spatial dimensions of	Spatial dimensions are dynamic	For both the spatial and temporal
	the agricultural field	and may depend on various	dimensions, the essential requirement is
		factors, such as crop and pesticide	compatibility between LCI and LCIA
		type and its use, the goal and	modelling, which requires the definition of

Our interpretation of this phrase is that it refers to the spatial variability of a number of (partially) correlated factors including local environmental conditions, crops produced, and agricultural management practices applied.Author-produced version of the article published in International Journal of Life Cycle Assessment,

2015, N°20(6), p. 765-776 The original publication is available at http://link.springer.com Doi: 10.1007/s11367-015-0871-1

Acknowledgements

The authors are grateful for the financial support provided by Syngenta and the TOX-TRAIN project (EU Grant Agreement no. 285286), which was used for the organisation of the workshop and the open-access publication of this manuscript.

-Care should be taken to avoid potential double counting between terrestrial ecotoxicity on agricultural soil and land use impacts on biodiversity due to agricultural soil use. Therefore, the characterisation models for these impact categories need to be harmonised (i.e. a decision is required on how and in which impact category these are modelled) when developing impact assessment methods for these impact categories;

• Further observation raised during the meeting:

-Ecotoxicological impacts linked to background concentrations from earlier applications (e.g. with persistent substances) after crop harvest as function of crop rotation practice need to be accounted for; -For direct impact on the on-field soil, only the additional impact on ecosystem due to the PPP application (above the already considered effect of agricultural land use) should be considered when we are comparing different scenarios.

Next steps and future work discussed and identified during the workshop focused on the operationalisation of the recommendations in order to integrate them into LCA practice. Identified actions were:

• Establishment of recommended default emission fractions to environmental media via initial distribution including the definition of the underlying temporal dimension of the dynamic LCI modelling. The results should be integrated into LCI databases. This is the goal of a follow-up workshop on 10 th May 2014 in Basel;

• Organisation of interaction with LCI database developers in order to help implement the recommendations;

• Interaction among LCIA developers to extend current methods with new elements/processes mentioned in the recommendations, including targeted technical workshops on "how to" model specific processes;

• Launching of a similar initiative to establish consensus about fertilizer emissions and impact assessment.