Christian Bandré

There are infinitely many twin primes 30n+11 and 30n+13, 30n+17 and

We proved that lim inf n→+∞ (pn+1pn) = 2 where pn is the nth prime number. We showed the conditions on which an integer 10X + 1, 10X + 3, 10X + 7 or 10X + 9 can be a prime number. We studied the conditions required to get some twin primes and proved the twin primes conjecture. First we showed that some sets of formulas are governing each of the eight sets of composite integers 30n+11, 30n+31, 30n+13, 30n+23, 30n+7, 30n+17, 30n+19 and 30n+29. Then we showed that there are infinitely many couple of integers 30n+11 and 30n+13, 30n+17 and 30n+19, 30n+29 and 30n+31 which are not generated by the formulas of the corresponding sets of composite integers respectively. As a side result, it will open a new era for the study of gaps between primes and leads to the proofs of many open problems linked to prime numbers.

Contents

1. Introduction 2. Notation 3. The composite numbers and prime numbers 10X+1 4. The composite numbers and prime numbers 10X+3 5. The twin primes 30n+11 and 30n+13 6. The composite numbers and prime numbers 10X+7 7. The composite numbers and prime numbers 10X+9 8. The twin primes 30n+17 and 30n+19 9. The twin primes 30n+29 and 30n+31 References

Introduction

The issue of distribution of primes and the twin primes conjecture is a puzzle for mathematicians since the time of Euclid of Alexandria [START_REF] Brent | Irregularities in the distribution of primes and twin primes[END_REF][START_REF] Huxley | The distribution of prime numbers[END_REF]. The sequence of prime number seems to be random. This messy look of the sequence of prime numbers requires an explanation. The twin primes conjecture is one of the oldest mathematics problems [START_REF] Pintz | Are there arbitrarily long arithmetic progressions in the sequence of twin primes?[END_REF]. It asserts that "there exist infinitely many primes p such that p+2 is a prime". Recently Yitang Zhang has solved the Bounded Gap Conjecture [START_REF] Zhang | Bounded gaps between primes[END_REF]. The aim of this work is to give a strong and elegant proof of the twin primes conjecture and the distribution of prime numbers. Our method consisted in discovering the formulas of the eight groups of composite numbers, unveiling the deterministic structure which organizes the distribution of prime numbers.

Theorem 1. lim inf n→+∞ (p n+1 -p n ) = 2 where p n is the nth prime number.

In the following sections we give the proof of the theorem above. First we showed that some set of formulas are governing each of the eight set of composite integers 30n+31, 30n+11, 30n+13, 30n+23, 30n+7, 30n+17, 30n+19, 30n+29. Then we showed that there are infinitely many integers which are not generated by the formulas of the sets of composite 30n+11 and 30n+13, 30n+17 and 30n+19, 30n+29 and 30n+31.

Notation

X, Y, n, p, q, x, y, i, j, k, a, b, c are all natural integers Proposition 1. X is an integer > 0. 10X + 1 can be a prime if only X ≡ 0 (mod 3) or X ≡ 1 (mod 3). 10X + 3 can be a prime if only X ≡ 1 (mod 3) or X ≡ 2 (mod 3). 10X + 7 can be a prime if only X ≡ 0 (mod 3) or X ≡ 1 (mod 3). 10X + 9 can be a prime if only X ≡ 1 (mod 3) or X ≡ 2 (mod 3). 10X + 1 and 10X + 3 can be twin primes if only X ≡ 1 (mod 3). 10X + 7 and 10X + 9 can be twin primes if only X ≡ 1 (mod 3). 10X + 9 and 10X + 11 can be twin primes if only X ≡ 2 (mod 3). Proof. The table 1 shows that if n ≥ 0 the twin primes can be only : 10(3n + 1) + 1 and 10(3n + 1) + 3 10(3n + 1) + 7 and 10(3n + 1) + 9 10(3n + 2) + 9 and 10(3n + 2) + 11.

The composite numbers and prime numbers 10X+1

Proposition 2. If X ≡ 0 (mod 3) then 10X + 1 = 30n + 1 is a prime number if only X is not a term of at least one of the following sequences (1) to (6) :

(1) (A 1 x,y ) = 3(30xy + x + y) with x > 0 and y > 0

(2) (B 1 x,y ) = 3(30xy + 11x + 11y + 4) (3) (C 1 x,y ) = 3(30xy + 7x + 13y + 3) (4) (D 1 x,y ) = 3(30xy + 17x + 23y + 13) (5) (E 1 x,y ) = 3(30xy + 19x + 19y + 12) (6) (F 1
x,y ) = 3(30xy + 29x + 29y + 28) The sequences (1) to (6) constitute the set C 30n+1 . The sequences (7) to (10) constitute the set C 30n+11 . If X = 3n + 1 then 10X + 1 = 30n + 11 is a prime number if only X is not a term of at least one of the following sequences (7) to (10):

(7) (U 1 x,y ) = 3(30xy + x + 11y) + 1 with y > 0 (8) (V 1 x,y ) = 3(30xy + 7x + 23y + 5) + 1 (9) (W 1
x,y ) = 3(30xy + 17x + 13y + 7) + 1 (10) (Z 1 x,y ) = 3(30xy + 19x + 29y + 18) + 1 Proof. Consider the integers 10X + 1, p, q, x and y. If 10X + 1 is not a prime number then 10X + 1 has at least two factors such that :

10X + 1 = (10p + 1)(10q + 1) with p >0 and q >0 or 10X + 1 = (10p + 3)(10q + 7)

or 10X + 1 = (10p + 9)(10q + 9)
.

It is easy to check that by setting p=3x or 3x+1 or 3x+2 and q=3y or 3y+1 or 3y+2 then we get the previous sequences.

Example : For 10X + 1 = (10p + 1)(10q + 1) with p = 3x + 1 and q = 3y then 10X + 1 = (30x + 11)(30y + 1) = 10(90xy + 3x + 33y + 1) + 1 or also X = 90xy + 3x + 33y + 1 = 3(30xy + x + 11y) + 1 p > 0 and q > 0 means that y > 0 For 10X + 1 = (10p + 3)(10q + 7) with p = 3x + 1 and q = 3y + 1 then 10X + 1 = (30x + 13) × (30y + 17) = 900xy + 510x + 390y + 221 = 10(90xy + 51x + 39y + 22) + 1 and X = 90xy + 51x + 39y + 22 = 3(30xy + 17x + 13y + 7) + 1 For 10X + 1 = (10p + 3)(10q + 7) with p = 3x + 2 and q = 3y then X = 90xy + 21x + 69y + 16 = 3(30xy + 7x + 23y + 5) + 1 For 10X + 1 = (10p + 9)(10q + 9) with p = 3x + 1 and q = 3y + 2 then 10X + 1 = (30x + 19)(30y + 29) = 900xy + 870x + 570y + 551 = 10(90xy + 87x + 57y + 55) + 1 and X = 90xy + 87x + 57y + 55 = 3(30xy + 29x + 19y + 18) + 1 It follows that if X = 3n + 1 is a term of at least one of the sequences (7) to (10) then 10X + 1 = 30n + 11 is a composite number. Thus, we conclude that 10X + 1 = 30n + 11 is a prime number if X is not a term of at least one of the sequences (7) to (10). QED 11, 41, 71, 101, 131 are primes because 1, 4,7, 10 and 13 are not some terms of at least one of the sequences (7) to (10) Similarly, if X = 3n is not a term of at least one of the sequences (1) to (6) then 30n+1 is prime.QED 31, 61, 151, 181, 211 are primes because 3, 6, 15,18 and 21 are not some terms of at least one of the sequences (1) to (6) 4. The composite numbers and prime numbers 10X+3 Proposition 3. If X = 3n + 1 then 10X+3=30n+13 is a prime number if only X is not a term of at least one of the following sequences (11) to (14):

(11) (U 3 x,y ) = 3(30xy + 13x + y) + 1 with x>0 (12) (V 3 x,y ) = 3(30xy + 23x + 11y + 8) + 1 (13) (W 3 x,y ) = 3(30xy + 19x + 7y + 4) + 1 (14) (Z 3 x,y ) = 3(30xy + 29x + 17y + 16) + 1
The sequences (11) to (14) constitute the set C 30n+13

If X = 3n + 2 then 10X+3=30n+23 is a prime number if only X is not a term of at least one of the following sequences (15) to (18):

(15) (A 3 x,y ) = 3(30xy + 13x + 11y + 3) + 2 (16) (B 3 x,y ) = 3(30xy + 23x + y) + 2 x>0 (17) (C 3 x,y ) = 3(30xy + 19x + 17y + 10) + 2 (18) (D 3
x,y ) = 3(30xy + 29x + 7y + 6) + 2 The sequences (15) to (18) constitute the set C 30n+23 Proof. Consider the integers 10X+3,p,q, x and y If 10X+3 is not a prime number then it has at least two factors such that :

10X + 3 = (10p + 1)(10q + 3) with p > 0 or 10X + 3 = (10p + 7)(10q + 9)
It is easy to check that by setting p=3x or 3x+1 or 3x+2 and q=3y or 3y+1 or 3y+2 and using the same method of transformations in 3 then we shall get the sequences (11) to ( 14) and ( 15) to (18) It follows that if X = 3n + 1 then 10X+3=30n+13 is a prime number if only X is not a term of at least one of the sequences (11) to (14) QED. 13, 43, 73, 103, 163 are primes because 1, 4, 7, 10 and 16 are not some terms of at least one of the sequences (11) to (14) If X = 3n + 2 then 10X+3=30n+23 is a prime number if only X is not a term of at least one of the sequences (15) to (18)QED. 23, 53, 83, 113, 173 are primes because 2, 5, 8, 11 and 17 are not some terms of at least one of the sequences (15) to (18)

The twin primes 30n+11 and 30n+13

From (1), ( 2) and (3) it follows that 10X+1 and 10X+3 are twin primes if only X=3n+1 and is not a term of at least one of the sequences (7) to (14).

To prove that the twin primes 30n+11 and 30n+13 are infinite we must prove that the positive integers X=3n+1 which are not terms of at least one of the sequences (7) to (14)are infinite.

U n+1 = u n + 3a
The common difference of U n is 3a. Thus between U n and U n + 3a we have the terms U n + 3i of P n with i taking the values 1 to (a -1).

Thus if we have the set of numerical sequences U n ,U n + 3,..., U n + 3(a -1) we will get all the terms of P n = 3(n + b) + λ infinitely.

if we have the set of (a) sequences U n ,U n + 3,..., U n + 3(a -1) we will get all the terms of P n = 3(n + b) + λ infinitely. It follows that if we have a set of q numerical sequences where q < a we will not get all the terms of P n = 3n + b + λ between U n and U n+1 .

Given that the set of the sequences (7) to (14)does not satisfy the proved proposition 4 which is a condition both necessary and sufficient, it follows that we can find infinitely some terms of the sequence 3n + 1 that are not generated by the sequences (7) to (14). We conclude that the twin primes 30n+11 and 30n+13 are infinite. We also conclude that the number of twin primes p and p + 2 is infinite. example : 19 = 3 * 6 + 1 but 19 is not generated by at least one of the sequences (7) to (14). this is why 191 and 193 are twin primes. 64 = 3 * 21 + 1 but 64 is not generated by at least one of the the sequences (7) to ( 14). This is why 641 and 643 are twin primes. 67 = 90(0)(2) + 33(2) + 1 and 671 is not a prime number, this is why 671 and 673 are not twin primes 70 = 90(1)(0) + 57(1) + 21(0) + 13 so 703 is not a prime number,this is why 701 and 703 are not twin primes 6. The composite numbers and prime numbers 10X+7 .

It is easy to check that by setting p = 3x or p = 3x + 1 or p = 3x + 2 and q = 3y or q = 3y + 1 or q = 3y + 2 and using the same method of transformations in 3 then we shall get the sequences ( 19 x,y ) = 3(30xy + 7x + 7y + 1) + 1 (32) (Z 9

x,y ) = 3(30xy + 17x + 17y + 9) + 1 If X ≡ 2 (mod 3) then 10X+9=30n+29 is a prime number if only X is not a generated by at least one of the following formulas (37) to (40): The sequences (37) to (40) constitute the set C 30n+29

Proof. Consider the integers 10X + 9, p, q, xandy If 10X + 9 is not a prime number then it has at least two factors such that :

10X + 9 = (10p + 1)(10q + 9) with p > 0 or 10X + 9 = (10p + 3)(10q + 3) or 10X + 9 = (10p + 7)(10q + 7)
It is easy to check that by setting p = 3x or p = 3x + 1 or p = 3x + 2 and q = 3y or q = 3y + 1 or q = 3y + 2 and using the same method of transformations in 3 then we shall get the sequences (27) to (32) and (37) to (40):

19, 79, 109, 139, 199, 229 are primes because 1, 7, 10, 13, 19 and 22 are not some terms of at least one of the sequences (27) to (32) 29, 59, 89, 149, 179, 239 are primes because 2, 5, 8, 14, 17 and 23 are not some terms of at least one of the sequences (37) to (40)

The twin primes 30n+17 and 30n+19

From theorem (1), propositions (5) and (6) it follows that if X=3n+1 is not a generated by the set the set C 30n+17 C 30n+19 then 30n+17 and 30n+19 are twin primes.

To prove that the twin primes 30n+17 and 30n+19 are infinite we must prove that the numbers X=3n+1 which are not a generated by at least one of the following formulas (23) to (32) are infinite.

It is easy to check that the set of sequences (23) to (32) cannot be converted to a set of sequences U n,i = 3(an + b + i) + λ with i taking the values 0 to (a -1), to get all the consecutive terms of the numerical sequence P n = 3(n + b) + λ infinitely.

Given that the set of formulas ( 23) to (32)does not satisfy the proved proposition 4 which is a condition both necessary and sufficient, it follows that we can find infinitely some terms of the sequence 3n + 1 that are not generated by the sequences (23) to (32).

It follows that the sequences (23) to (32) will never generates infinitely all the consecutive terms of the numerical sequence 3n + 1 after a given term 3b + 1. The number of natural integers X = 3n + 1 that are not generated by at least one of the formulas (23) to (32) is infinite. It follows that the number of twin primes 10X + 7 = 30n + 17 and 10X + 9 = 30n + 19 is infinite.

We conclude that the twin primes 30n + 17 and 30n + 19 are infinite. example : 1, 10, 13, 19, 22 are not generated by at least one of the sequences (23) to (32). This is why (17,19), (107,109), (137 139), (197,199), (227,229) are twin primes.

The twin primes 30n+29 and 30n+31

We set 10X + 9 = 30n + 29 and 10X + 11 = 30n + 31 with X = 3n + 2. We set Y = 3n + 3 then 10X + 11 = 10Y + 1 and Y -1 = X. If 10Y + 1 is not a prime number and Y ≡ 0 (mod 3)then Y is a term of at least one of the numerical sequences (1) to (6). By subtracting 1 to each of the numerical sequences (1) to (6) we get the following numerical sequences :

• 3(30xy + x + y -1) + 2, x > 0 and y > 0 • 3(30xy + 11x + 11y + 3) + 2 x,y ) = 3(30xy + 29x + 29y + 27) + 2 To prove that the twin primes 30n + 29 and 30n + 31 are infinite we must prove that the numbers X = 3n + 2 which are not generated by at least one of the formulas (37) to (46) are infinite.

Given that the set of formulas (37) to (46)does not satisfy the proved proposition 4 which is a condition both necessary and sufficient, it follows that we can find infinitely some terms of the sequence 3n + 2 that are not generated by the formulas (37) to (46). We conclude that the twin primes 30n + 29 and 30n + 31 are infinite. example : 14 = 3 * 4 + 2 but 14 is not generated by at least one of the formulas (37) to (46).This is why 149 and 151 are twin primes. 17 = 3 * 5 + 2 but 17 is not generated by at least one of the formulas (37) to (46).This is why 179 and 181 are twin primes. 23 = 3 * 7 + 2 but 23 is not generated by at least one of the formulas (37) to (46).This is why 239 and 241 are twin primes.

It follows that the set of numerical sequences (37) to (46) will not generates infinitely all the consecutive terms of the numerical sequence 3n + 2 after a given term 3b + 2. The number of natural integers X = 3n + 2 that are not some terms of at least one of the numerical sequences ((37) to (46) is infinite. It follows that the number of twin primes 10X + 9 = 30n + 29 and 10X + 9+ 2 = 30n + 31 is infinite. We conclude that the number of twin primes p and p + 2 are infinite.

(Received: (Revised:

Centre hospitalier MAX QUERRIEN, PAIMPOL, FRANCE E-mail : christian.bandre@ch-paimpol.fr

Proposition 4 .

 4 Consider the numerical sequence U n = 3(an + b) + λWe must have at least a set of (a ) numerical sequences U n,i = 3(an+b+i)+λ with i taking the values 0 to (a-1) to get all the consecutive terms of the numerical sequenceP n = 3(n + b) + λ inf initely .Example The 2 sequences 6n+1 and 6n+4 generates all the integers 3n+1 : 1, 4, 7 , 10 , 13,16,... The 3 sequences 9n+1, 9n+4 and 9n+7 generates all the integers 3n+1 : 1, 4, 7 , 10 , 13,16,... The 4 sequences 12n+1, 12n+4 and 12n+7, 12n+10 generates all the integers 3n+1 : 1, 4, 7 , 10 , 13,16,19,22... Proof. Consider the numerical sequence P n = 3(n + b) + λ It follows that P n+1 = P n + 3 and the common difference of P n is 3Consider the numerical sequence U n = 3(an+b)+λ It follows that

  x,y ) = 3(30xy + 29x + y) + 2 x>0 ) = 3(30xy + 7x + 17y + 3) + 2The sequences (27) to (32) constitute the set C 30n+19

Table 1 .

 1

		Values of 10X+1, 10X+3,10X+7, 10X+9 and 10X+11
	given X
	X	10X+1	10X+3	10X+7	10X+9	10X+11
	3n	30n+1	3(10n+1) 30n+7	3(10n+3) 30n+11
	3n+1 30n+11	30n+13	30n+17	30n+19	3(10n+7)
	3n+2 3(10n+7) 30n+23	3(10n+9) 30n+29	30n+31

  Proposition 5. If X ≡ 0 (mod 3) then 10X+7=30n+7 is a prime number if only X is not generated by at least one of the following formulas (19) to

	(22) :
	(19)	(A 7 x,y ) = 3(30xy + 7x + y) with x > 0
	(20)	(B 7 x,y ) = 3(30xy + 17x + 11y + 6)
	(21)	(C 7 x,y ) = 3(30xy + 19x + 13y + 8)
	(22)	(D 7 x,y ) = 3(30xy + 29x + 23y + 22)
	If X ≡ 1 (mod 3) then 10X + 7 = 30n + 17is a prime number if only X
	is not generated by at least one of the following sequences (23) to (26):
	(23)	(U 7 x,y ) = 3(30xy + 7x + 11y + 2) + 1
	(24)	(V 7 x,y ) = 3(30xy + 17x + y) + 1, x > 0
	(25)	(W 7 x,y ) = 3(30xy + 19x + 23y + 14) + 1
	(26)	(Z 7 x,y ) = 3(30xy + 29x + 13y + 12) + 1
	The sequences (19) to (22) constitute the set C 30n+7
	The sequences (23) to (26) constitute the set C 30n+17
	Proof. Consider the integers 10X + 7, p, q, xandy
	If 10X + 7 is not a prime number then it has at least two factors such that
	:
		10X + 7 = (10p + 1)(10q + 7) with p > 0
	or
		10X + 7 = (10p + 3)(10q + 9)


Sara Bisone

Vincent Chatain
email: vincent.chatain@insa-lyon.fr

Denise Blanc

Mathieu Gautier

Rémy Bayard

Florence Sanchez

Rémy Gourdon

Geochemical characterization and modeling of arsenic behavior in a highly contaminated mining soil

Keywords:

The environmental assessment and management of historical mining sites contaminated with various inorganic species require a better knowledge of pollutant-bearing phases. Among elements present in mining soils, arsenic is a toxic metalloid with potential high content and high mobility capacity into the environment. The objective of this paper was to investigate the mobility and fractionation of arsenic (As) in a highly As contaminated soil (ca. 3 wt%). The soil was collected from an old gold mining site in France, where mining activities and smelting processes of gold ores took place. Single and sequential chemical extraction procedures were firstly 1 1,* 1 1 1 2 1 1 2 e.Proofing http://eproofing.springer.com/journals/printpage.php?token=-mclYg... 1 sur 23 04/01/2016 18:16

conducted. These leaching tests were used to assess the potential mobility of As depending on its fractionation in the contaminated soil, and also on the portion of As sorbed onto soil particles. Additionally numerical simulations were performed using the USGS software PHREEQC-3 in order to evaluate the role of adsorption on As mobilization. This multidisciplinary approach provided information on the nature of As fixation in this mining soil. Moreover the role of adsorption in the control of dissolved As was evidenced by geochemical modeling. Results showed that As appeared to be mainly (ca. 72 wt%) reversibly sorbed to iron (Fe) compounds in the soil, in particular Fe oxyhydroxides. Consequently a potential risk of As mobilization exists especially under acidic and/or reducing conditions, which frequently occurs in mining environments.

Introduction

Arsenic (As) is a toxic metalloid naturally present in the environment that comes from various sources such as volcanism and weathering of the bed rock. The As concentration in natural soils typically ranges from 0.1 to 50 mg•kg [START_REF] Baker | Chemical monitoring of soils for environmental quality and animal and human health[END_REF]. Anthropogenic activities also contribute to the geochemical cycling of As in a variety of ways [START_REF] Huang | Arsenic distribution in soils[END_REF][START_REF] Smedley | A review of the source, behavior and distribution of arsenic in natural waters[END_REF][START_REF] Tamaki | Environmental biochemistry of arsenic[END_REF]. Arsenic is used in agriculture as a component of pesticides, and in wood preservation and glassmaking. It is also dispersed into the environment through the burning of fossil fuels. Additionally, due to its geochemistry, As is used as an indicator element in geochemical prospecting for various types of mineral ores (gold, silver, copper, uranium, etc.) [START_REF] Boyle | The geochemistry of arsenic and its use as an indicator element in geochemical prospecting[END_REF][START_REF] Reith | Mobility and microbially mediated mobilization of gold and arsenic in soils from two gold mines in semi-arid and tropical Australia[END_REF].

during mining operations and minerals processing [START_REF] Azcue | Impact of abandoned mine tailings on the arsenic concentrations in Moira Lake, Ontario[END_REF][START_REF] Bodénan | Arsenic behaviour in gold-ore mill tailings, Massif Central, France: hydrogeochemical study and investigation of in situ redox signatures[END_REF][START_REF] Hudson-Edwards | 16 geochemistry of alluvium contaminated by metal mining in the Rio Tinto area, southwest Spain[END_REF][START_REF] Navarro | Abandoned mine sites as a source of contamination by heavy metals: a case study in a semi-arid zone[END_REF][START_REF] Savage | Arsenic speciation in pyrite and secondary weathering phases, Mother Lode gold district, Tuolumne County, California[END_REF]. Arsenic concentrations in tailings piles and tailingcontaminated soils can reach up to several thousand mg• kg [START_REF] Smedley | A review of the source, behavior and distribution of arsenic in natural waters[END_REF]. However, unlike organic contaminants, As in soils cannot be decomposed chemically or biologically.

It is commonly acknowledged that total As concentration in the soil is not a good indicator of potential mobility and leaching. Chemical interactions between soil and As are important to understand its fate in the environment and choose the suitable management strategy [START_REF] Bolan | Remediation of heavy metal(loid)s contaminated soils-To mobilize or to immobilize?[END_REF] ). These last years, part of the research concerned remediation [START_REF] Gonzalez-Fernandez | Distribution of metals in soils and plants around mineralized zones at Cartagena-La Unión mining district (SE, Spain)[END_REF][START_REF] Drouhot | Responses of wild small mammals to arsenic pollution at a partialy remediated mining site in Southern France[END_REF][START_REF] Jana | Analysis of arsenic and antimony distribution within plants growing at an old mine site in Ouche (Cantal, France) and identification of species suitable for site revegetation[END_REF][START_REF] Dzombak | The behavior of arsenic and antimony at Pezinok mining site, southwestern part of the Slovak Republic[END_REF]. In this context, the better understanding of the fractionation and the potential of mobilization of arsenic is required and helpful to improve the efficiency of these technics.

Although a wide variety of leaching tests are available in the literature to determine the potential mobility of pollutants [START_REF] Kosson | An integrated framework for evaluating leaching in waste management and utilization of secondary materials[END_REF][START_REF] Van Der Sloot | Harmonization of leaching/extraction tests[END_REF] ), very few have been designed to provide information on the nature of their fixation processes in studied matrices. On the other hand, hydrous ferric oxides (HFO) are known to be important in the retention of inorganic arsenic in soil. The interaction between HFO and ions can be described by surface complexation model (SCM) [START_REF] Dzombak | The behavior of arsenic and antimony at Pezinok mining site, southwestern part of the Slovak Republic[END_REF]. This approach has been successfully used to study As adsorption/desorption onto HFO in sediments, soils and groundwater [START_REF] Biswas | Role of competing ions in the mobilization of arsenic in groundwater of Bengal Basin: Insight from surface complexation modeling[END_REF][START_REF] Bowell | Sorption of arsenic by iron oxides and oxyhydroxides in soils[END_REF][START_REF] Jiang | Adsorption of arsenate on soils. Part 2: modeling the relationship between adsorption capacity and soil physiochemical properties using 16 Chinese soils[END_REF][START_REF] Lumsdon | Use of solid phase characterisation and chemical modelling for assessing the behaviour of arsenic in contaminated soils[END_REF]. Used concurrently with geochemical characterization, the modeling has proved to be useful to describe As behavior [START_REF] Carrillo-Chávez | Geochemistry and mineralogy of mine-waste material from a "skarn-type" deposit in central Mexico: modeling geochemical controls of metals in the surface environment[END_REF][START_REF] Brgm | Stabilization/solidification of arsenic in cemented paste backfill: geochemical modeling as a mineralogical characterization tool[END_REF][START_REF] Sracek | Behavior of arsenic and geochemical modeling of arsenic enrichment in aqueous environments[END_REF].

In this context, an approach was developed based on the use of leaching tests (single and sequential chemical extraction procedures) in conjunction with a mineralogical study and a geochemical modeling. Indeed, knowledge of the pollutants operational fractionation in the studied matrix is required to better understand mechanisms regulating the leaching behavior of inorganic contaminants of interest.

The work reported in this article focused on the determination of the nature of As distribution and association to the soil constituents, and the impact of these characteristics on the leaching behavior observed. The scientific objective was to better understand the mechanisms regulating the leaching behavior in order to better assess and model the potential mobilization of As under the effect of environmental conditions. A further objective was to validate the experimental methodology developed for that purpose.

The correlation between mineralogy, leachability and modeling of As was examined in a contaminated soil collected from a French gold mining site. Mineralogical analyses were carried out following leaching tests to characterize the studied matrix. The numerical simulation of batch leaching experiments was performed using PHREEQC (version 3) [START_REF] Parkhurst | Study of mineralogy and leaching behavior of stabilized/solidified sludge using differential acid neutralization analysis: Part II: use of numerical simulation as an aid tool for cementitious hydrates identification[END_REF].

Our research was developed in order to better understand the distribution of As in a representative sample by combining (i) experimental data obtained from single and sequential chemical extraction procedures (leaching tests), (ii) mineralogical characteristics determined with various analytical tools and (iii) geochemical modeling. This multidisciplinary approach tends to improve geochemical assemblage definition and As comportment.

Materials and methods

Sampling and preparation of the soil

An As-contaminated soil collected from a gold mining site in France, where mining activities and smelting processes of gold ores took place until 2004, was used for the study [START_REF] Chatain | Characterization of arsenic and other inorganic constituents potential mobilization from soils collected from a gold mining site[END_REF]. It was already known to present high concentrations of As [START_REF] Bayard | Mobilisation of arsenic from a mining soil in batch slurry experiments under bio-oxidative conditions[END_REF].

From the soil top surface (sampling depth: 5-35 cm), four representative soil samples, of about 50 kg were collected from the site. Prior to characterizations and liquid-solid partitioning experiments, the soil samples were air-dried at room temperature (20 ± 3 °C) for 1 day, sieved through a stainless steel 2 mm mesh sieve to remove coarse debris and gravel, homogenized, and finally stored at 4 °C in the dark (Chatain et al. 2005a ).

Chemical and mineralogical characterization

The natural pH of the soil was measured in a 10:1 mixture of soil to deionized water after a contact period of 48 h (SR003.1 protocol, [START_REF] Kosson | An integrated framework for evaluating leaching in waste management and utilization of secondary materials[END_REF] using a WTW combined glass electrode. The redox potential (ORP) was measured in the same soil slurry using a Radiometer analytical platinumkalomel electrode (Pt-Ag/AgCl, +197 mV vs. NHE).

After mineralization by acid digestion [START_REF] Afnor | behavior of S (Fig. 3 a) and Fe (Fig. 3 b) was well correlated to experimental data whether adsorption was used or not. For As[END_REF], total soil concentration of trace elements and major constituents was determined by Inductively Coupled Plasma Optical Emission Spectrometry (ICP-OES, Jobin-Yvon Ultima 2 ).

X-ray diffraction

Three replicates of the soil fraction <2 mm were ground to a fine powder (<50 µm) and studied with a SIEMENS D500 X-ray diffractometer (XRD) equipped with a copper anticathode. The samples were scanned on a reflection angle (2θ) from 3° to 70° at a scan rate of 0.02° 2θ/s. Results were processed using the DIFFRAC EVA© software (BRUKER AXS ) and the ICDD database (International Centre for Diffraction Data).

Scanning electron microscopy equipped for energy dispersive spectroscopy

Mineralogical investigation was also performed on two replicates of the same fraction (<2 mm) by scanning electron microscope (SEM, JEOL 840A LGS) coupled with an X-ray energy dispersive spectrometer (EDS). Samples were prepared by pasting the soil particles on an adhesive tape placed on a stub (sample holder of the SEM). Sample coating with a conductive material was not required. The backscattered electron (BSE) mode was used with a voltage of 20 kV.

Leaching tests

A sequential chemical extraction specifically adapted by [START_REF] Matera | A methodological approach for the identification of arsenic bearing phases in polluted soils[END_REF] to study As-bearing phases on amorphous and crystal iron was chosen. The seven following arsenic fractions were extracted: (F1) soluble in MgCl

® ® Plus ® ® ® 2 -1 3 -1 3 2 -1 3 4 2 2 4 2 -1 2 2 4 -1 4 2 2 4 2 -1 2 2 4 -1 6 8 6 -1 3 2 2 3 4 -1 3
Single extraction techniques were also performed to verify that As adsorption on Fe oxyhydroxides was the major process of As trapping in the soil [START_REF] Clozel | Physical, chemical, and biological treatability of contaminated soils[END_REF]. These extractions were carried out in triplicate using 1 mol• L sodium hydroxide (NaOH) solution, and 0.1 mol• L dipotassium hydrogen orthophosphate (K HPO ) solution. A liquid/solid (L/S) ratio of 10 mL• g and a contact time of 48 h were used.

Batch leaching experiments were conducted following the SR002.1 protocol [START_REF] Kosson | An integrated framework for evaluating leaching in waste management and utilization of secondary materials[END_REF]. Under ambient conditions, 10 g of soil sample and 100 ml of prepared solutions were mixed for 48 h (L/S ratio of 10 mL/g of dried soil). HCl and NaOH solutions of varying concentrations were used as leachants in order to obtain a range of pH varying from 1 to 13.

Leachate analyses

All leachates were filtered through 0.45 µm pore size acetate-cellulose Whatman membranes. They were subsequently analyzed for concentrations of the constituents of interest using ICP-OES. Sulfates and chlorides were analyzed using IC (ion chromatography, Dionex DX320 HPIC ). Total organic carbon (TOC) in solution was measured using a TOC analyzer (Total Organic Carbon analyzer, Shimadzu TOC-5000A ).

Geochemical modeling

The PHREEQC program is based on the calculation of equilibrium between aqueous solutions and minerals, gases, solid solutions, exchangers, and sorption surfaces. As suggested by Peyronnard et al. ( 2009), a simplified mineral assemblage was defined on the basis of the mineralogical study (XRD and SEM analysis) and chemical characterization. The acid attack was simulated on the assemblage by adding nitric acid or sodium hydroxide. Finally, quantification of minerals was optimized by comparing simulated curves to experimental data in a reiterated process.

Simulation was performed on a 1 L volume of liquid, which means that the solid assemblage should represent 100 g of soil to comply with the L/S ratio of the leaching experiment. During simulation, the equilibrium between liquid and solid was reached and no gases were considered.

The geochemical model was developed to evaluate the role of adsorption in As solubilization. The assemblage which best fit buffer capacity and solution concentration was used to compare two models: with and without considering

-1 -1 2 4 -1 ® ® ® e.
Proofing http://eproofing.springer.com/journals/printpage.php?token=-mclYg... adsorption. The adsorption phenomena is modelled with a surface complexation model: the DDL (diffuse-double layer) [START_REF] Dzombak | The behavior of arsenic and antimony at Pezinok mining site, southwestern part of the Slovak Republic[END_REF], already incorporated in PHREEQC, was used. From the mineralogical analysis data, it was assumed that the dominant adsorption/desorption phase was hydrous-ferric oxide (HFO). In the DDL, the major surface complexes for As(III) and As(V) are ≡FeH AsO and ≡FeHAsO , respectively. With the decrease in pH the formation of ≡FeHAsO is favored, whereas at higher pH ≡FeH AsO is prevalent.

The Lawrence Livermore National Library (llnl) thermodynamic database supplied with PHREEQC was used for solubility products and dissolution reactions of mineral phases. Surface complexation constants from [START_REF] Dzombak | The behavior of arsenic and antimony at Pezinok mining site, southwestern part of the Slovak Republic[END_REF] are already implemented in the llnl database for reactions between ferrihydrite and major cations (Ca, S, Ba, Cd, Zn, Cu, Pb, Mg, Mn, Fe) and anions. The database was modified by adding surface complexation constants for arsenate and arsenite on HFO from the minteq.v4 database. Fe(OH) (am) phase [START_REF] Hummel | Nagra/PSI chemical thermodynamic data base 01/01[END_REF], reactions involving H AsO and their corresponding equilibrium constants were included as well. Table 1 reports the surface complexation constants for sorption of As on HFO.

Results and discussion

Chemical characterization

The major physicochemical characteristics and the elemental total concentrations as determined by acidic digestion of the studied soil are summarized in Table 2 . The soil was mainly characterized by a water content of 10, 3 wt% of As, 9 wt% of Fe and 1.9 wt% of total organic carbon. Its natural pH and ORP measured after 48 h of contact with deionized water at a L/S ratio of 10 mL/g, were 6.5 and +400 mV vs. NHE, respectively. Moreover, a very low soluble (0.016 wt%) fraction of As was obtained from the single extraction procedure using deionized water as the extractant.

Mineralogical characterization

This characterization was achieved by using scanning electron microscopy coupled with an EDS analyzer and XRD analysis. Results from the XRD analysis (Table 3 ) indicated that the soil was mainly composed of quartz, gypsum, feldspars, micas (as muscovite), calcite, and dolomite. XRD analyses indicated the presence of traces of hematite, jarosite and scorodite, which are the common pyrite weathering products with which As can be typically bound [START_REF] Clozel | Physical, chemical, and biological treatability of contaminated soils[END_REF]. The absence of residual mixed sulfide phases in the soil could be due to the weathering and oxidation of pyritic minerals during the post-mining period.

Microscopy analyses performed using the BSE images by SEM coupled with EDS microanalysis can be used to complement the XRD analysis. The major minerals identified were quartz, gypsum, and particles containing Fe and As, with a composition in accordance with XRD results. A close similarity between the arsenic and iron cartography was observed in SEM results (Fig. 1 ).

Fig. 1

SEM-EDX mapping of the 0.2-2 mm fraction of the soil (12X)

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Leaching behavior

The results of sequential extractions are summarized in Fig. 2 . The largest portion of As (about 66 wt%) was extracted as fraction F3-Fe(a) (bound to amorphous Fe oxides). Globally the first six fractions represented about 73 wt% of the total As and only 27 wt% was in the residual fraction, and then strongly bound to the soil matrix. A very low fraction of As and Fe (i.e., <1 wt%) was extracted as exchangeable and bound-to-carbonates fractions. These results confirmed that As was mainly bound on soil amorphous oxyhydroxide particles, as previously shown by the results from XRD and SEM.

Fig. 2

Sequential chemical extractions performed on the <2 mm fraction of the soil (conc. in wt%)

The results obtained from single extractions, using 1 mol• L NaOH solution, and 0.1 mol• L K HPO solution, are summarized in Table 4 . They are compared with those acquired during single extraction using deionized water (natural). Concerning NaOH extraction, about 74 wt% of the total As was extracted within these extreme conditions of pH (ca. 14). A mechanism of As desorption from the Fe oxyhydroxide surface by competition with OH ions might explain the abrupt increase in As extractability [START_REF] Carbonell-Barrachina | The influence of redox chemistry and pH on chemically active forms of arsenic in sewage sludgeamended soil[END_REF][START_REF] Yang | Adsorption, sequestration, and bioaccessibility of As (V) in soils[END_REF]. Fe solubility remained very low (ca. 0.2 wt% of the total Fe content). Fe solubility might have been controlled by Fe oxyhydroxide precipitates.

These results suggest that most of the As present in the soil is sorbed onto Fe oxyhydroxides, which is consistent with the mineralogical analysis and

-1 -1 2 4 -1 -3 -4 -1 -1 -1 2 4 -3 - e.
Proofing http://eproofing.springer.com/journals/printpage.php?token=-mclYg... sequential extraction. The remaining fraction (ca. 26 % of the total As content) can be considered to represent the part co-precipitated with Fe and/or bound to resistant compounds (i.e., silicates or sulfides).

The results of As extraction from the contaminated soil by K HPO solution are also shown in Table 4 . The addition of this solution was found to have no significant effect on pH and ORP conditions and Fe release, compared to those obtained with deionized water (natural conditions). However, a drastic increase in As solubilization (as much as 400-fold at a pH value about 7), and in phosphate adsorption onto Fe oxyhydroxides (ca. 76 %) was evidenced. These results are consistent with studies performed by [START_REF] Afnor | Extraction of arsenic in a synthetic arsenic-contaminated soil using phosphate[END_REF] and [START_REF] Clozel | Physical, chemical, and biological treatability of contaminated soils[END_REF], confirming that As is for the most part reversibly sorbed onto Fe oxyhydroxides.

Contaminant mobility as a function of pH and geochemical modeling

Batch leaching tests showed a low solubility of As between pH 3 and 7.5. Mobility increased with acid and alkaline conditions with a maximum for pH below 1.

All minerals observed in the XRD analysis (Table 3 ) were included in the model. The presence of amorphous hydroxide was evidenced by previous studies [START_REF] Bayard | Mobilisation of arsenic from a mining soil in batch slurry experiments under bio-oxidative conditions[END_REF][START_REF] Chatain | Arsenic behavior in mining soil[END_REF]Chatain et al. , 2005b ; ;[START_REF] Clozel | Physical, chemical, and biological treatability of contaminated soils[END_REF] and confirmed by the sequential extraction presented in section " Leaching behavior ". It was therefore introduced in the assemblage as amorphous Fe(OH) . Arsenic was introduced as arsenopyrite (present in the original minerals) and scorodite, a secondary mineral which currently occurs in waste rocks rich in arsenopyrite and/or arsenian pyrite as a weathering product [START_REF] Nordstrom | Solubility and stability of scorodite, FeAsO •2H O: discussion[END_REF][START_REF] Paktunc | Solubility of nanocrystalline scorodite and amorphous ferric arsenate: implications for stabilization of arsenic in mine wastes[END_REF]. Lastly, the model was set so that hematite and iron(III) hydroxide could dissolve but not precipitate. Since the time contact of the experiment was relatively short (48 h), the equilibrium condition of PHREEQC calculations would overestimate the precipitation of these phases. For the same reason, the assemblage does not represent the entire soil mineralogy but the reactive fraction, bringing the total mass of the mineral assemblage to 41.2/100 g. Table 5 presents reactions, equilibrium constants and initial mass of minerals used to represent the leaching behavior of the soil. As recommended by [START_REF] Dzombak | The behavior of arsenic and antimony at Pezinok mining site, southwestern part of the Slovak Republic[END_REF] a specific surface area of 600 m • g was defined, while surface density was adjusted to match batch experiments. A density of 0.09 sites•mol was chosen for strong sites and 0.5 sites•mol for the weak sites. In this respect, [START_REF] Sracek | Behavior of arsenic and geochemical modeling of arsenic enrichment in aqueous environments[END_REF] pointed out that in many cases, the quantity of Fe(III) oxides and hydroxides indicated by mineralogical methods poorly matches modeled data and the amount of adsorbent has to be adjusted accordingly.

The best fitting assemblage was used to evaluate the role of adsorption in As release. In Fig. 3 , S, Fe and As experimental solubility (Exp.) as a function of pH was compared with their solubility estimated by two models: without (Model 1) and with (Model 2) adsorption. In PHREEQC modeling, scorodite was the only phase containing As that could possibly precipitate at low pH. As stated by [START_REF] Paktunc | Solubility of nanocrystalline scorodite and amorphous ferric arsenate: implications for stabilization of arsenic in mine wastes[END_REF], scorodite has its lowest solubility around pH 3. In contrast, for pH less than 2 and greater than 6, its solubility is quite high. It is reported in the literature that As may precipitate as secondary sulfides (orpiment, arsenic trisulfite or pyrite) in a reduced environment that causes the reduction of SO [START_REF] Sracek | Behavior of arsenic and geochemical modeling of arsenic enrichment in aqueous environments[END_REF] ). Given the oxidant conditions of the leaching test in the present study, SO reduction and consequently secondary sulfide precipitation can be excluded. In the experimental data, As concentration in solution decreased until pH 6. Since scorodite precipitation alone cannot explain As behavior for pH higher than three, adsorption was taken into account. In fact, the model with adsorption (Model 2) was better correlated with As behavior, especially at neutral (6-7) and alkaline pH. For pH lower than 3, modeling suggests that amorphous iron(III) hydroxide (Fe(OH) (am)) may be completely dissolved and that scorodite precipitation would remain the governing process.

In conclusion, modeling confirmed that As release is mainly controlled by adsorption on ferric hydroxide. High concentrations of As were attributed to the dissolution of iron oxyhydroxides, causing the release of arsenic initially associated with this phase. In the absence of SCM, As concentration in solution at neutral pH would be three orders of magnitude higher. Modeling also revealed the contribution of scorodite to explain As behavior at low pH (<3).

Conclusions and perspectives

An As-contaminated soil collected from a gold mining site in France has been studied. In order to better understand the parameters controlling the potential release of As from contaminated soils into surface or ground-waters, an experimental methodology was developed that combined the use of leaching tests (single and sequential chemical extraction procedures) in conjunction with a mineralogical study. This experimental procedure was applied to contaminated soil samples collected from a gold mining site.

The results obtained indicated first that although As concentration in the considered soil was quite high, the release of As into deionized water was very limited in leaching tests. This was attributed primarily to the low solubility and the stability of the solid-bearing phases of As in the soil under slightly acidic natural conditions.

The multidisciplinary approach (leaching and mineralogy) developed in this work provided information on the nature of As fixation processes that may control As reactivity in the subsurface environment. It was observed that most of the As (72 %) appeared to be reversibly sorbed onto Fe phases in the soil particles, in particular Fe oxyhydroxides. These results indicated a potential risk of As mobilization over the long term under specific leaching conditions (i.e., pH or ORP gradient, chelation effect, etc.) which frequently occur in mining environments. Indeed, many factors can significantly affect the geochemical status of contaminated soils such as climate, fluctuating groundwater levels, periodic inundation, activity of microorganisms, vegetation, or deterioration of the physical properties of the substrate.

The role of adsorption in the control of dissolved As was supported by geochemical modeling. The retention of As at neutral pH seems to be governed by HFO adsorption, indicating that Fe oxyhydroxides dissolution is responsible for As release.

  (1 mol•L ) at pH 7; (F2) bound to carbonates (CH COONa (1 mol•L )/CH COOH pure at pH 5); (F3-Mn) bound to Mn-oxides (NH OH•HCl (0.04 mol• L ) in CH COOH 25 % at pH 2) (F3-Fe(a)) bound to amorphous Fe oxides ((NH ) C O •H O (0.2 mol• L )/H C O (0.2 mol•L ) at pH 2); (F3-Fe(c)) bound to crystalline Fe oxides ((NH ) C O • H O (0.2 mol•L )/H C O (0.2 mol• L )/C H O (0.1 mol•L ) at pH 2); (F4) bound to organic matter and sulfides (HNO and H O 30 % at pH 2; and CH COONH (3.2 mol• L ) in HNO 20 %)); (F5) residual fraction (obtained by difference after total digestion).

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Fig. 3 S

 3 Fig. 3 S (a), Fe (a) and As (a) solubility as a function of pH (L/S ratio, 10 mL•g ). Experimental (Exp.) and modeled data: without surface complexation (Model 1) and with surface complexation (Model 2)

Fig. 4

 4 Fig. 4 Saturation indices of arsenopyritescorodite (a) and scoroditearsenopyrite (b) as a function of pH (L/S ratio, 10 mL•g ) calculated for model with surface complexation (Model 2)

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Table 1

 1 Adsorption reactions and equilibrium constant of surface complexation of As with HFO

	5.41

≡FeOH + H AsO ↔ ≡FeH AsO + H O 8.67 ≡FeOH + H AsO ↔ ≡FeHAsO -+ H O + H 2.99 ≡FeOH + H AsO ↔ ≡FeOHAsO + 3H -10.15 ≡FeOH + H AsO ↔ ≡FeH AsO + H O

Table 2

 2 Physicochemical characteristics (L/S ratio: 10 mL•g ; contact time: 48 h) and concentration of trace elements as determined by acid digestion of the studied soil

	Water content (wt%)

Table 3

 3 Mineral

	Quartz	++++

composition by XRD analysis (relative abundance: ++++ very abundant; +++ abundant; ++ present; + traces)

Table 4

 4 Results

	Deionized water	1.60 × 10	1.0 × 10	6.5	+400
	1 mol• L NaOH solution	73.51	1.7 × 10	13.8 +60
	0.1 mol• L K HPO solution	4.89	3.40 × 10	7.5	+430

from single extractions (LS ratio: 10 mL•g ; contact time: 48 h)

Table 5

 5 Reactions, equilibrium constant and initial mass of assemblage minerals /eproofing.springer.com/journals/printpage.php?token=-mclYg...

	Quartz Kaolinite K-Feldspar Muscovite Chamosite-7A Clinochlore-7A Cronstedtite-7A Ripidolite-14A Gypsum Jarosite Calcite Dolomite Tenorite Hematite Fe(OH) (amorphous) Pyrite Chalcopyrite Except for Fe(OH) (am) (Hummel et al. 2002 ), all log Ksp values come from the SiO = SiO -3.9993 12.0168 Al Si O (OH) + 6 H = 2 Al + 2 SiO + 5 H O 6.8101 0.2582 KAlSi O + 4 H = +Al + K + 2 H O + 3 SiO -0.2753 4.1745 KAl Si O (OH) + 10 H = K + 3 Al + 3 SiO + 6 H O 13.5858 0.0398 Fe Al SiO (OH) + 10 H = SiO + 2 Al + 2 Fe + 7 H O 32.8416 0.0342 Mg Al Si O (OH) + 16 H = 2 Al + 3 SiO + 5 Mg + 12 H O 70.6124 0.2779 Fe Fe SiO (OH) + 10 H = SiO + 2 Fe + 2 Fe + 7 H O 16.2603 0.0400 Mg Fe Al Si O (OH) + 16 H = 2 Al + 2 Fe + 3 Mg + 3 SiO + 12 H O 60.9638 0.0619 CaSO • 2H O = Ca + SO + 2 H O -4.4823 10.3320 KFe (SO ) (OH) + 6 H = K + 2 SO + 3 Fe + 6 H O -9.3706 0.0501 CaCO + H = Ca + HCO 1.8487 1.0009 CaMg(CO ) +2 H = Ca + Mg + 2 HCO 2.5135 0.9220 CuO + 2 H = Cu + H O 7.6560 0.0716 Fe O + 6 H = 2 Fe + 3 H O 0.1086 3.1940 Fe(OH) + 3 H = Fe + 3 H O 5.0000 6.4128 FeS + H O = +0.25 H + 0.25 SO + Fe + 1.75 HS -24.6534 0.0120 CuFeS + 2 H = Cu + Fe + 2 HS -32.5638 0.0220 Lawrence Livermore National Laboratory (llnl) database supplied with PhreeqC 2 2 2 2 5 4 + 3+ 2 2 3 8 + 3+ + 2 2 3 3 10 2 + + 3+ 2 2 2 2 5 4 + 2 3+ 2+ 2 5 2 3 10 8 + 3+ 2 2+ 2 2 2 5 4 + 2 2+ 3+ 2 3 2 2 3 10 8 + 3+ 2+ 2+ 2 2 4 2 2+ 4 2-2 3 4 2 6 + + 4 2-3+ 2 3 + 2+ 3 -3 2 + 2+ 2+ 3 -+ 2+ 2 2 3 + 3+ 2 3 3 + 3+ 2 2 2 + 4 2-2+ -2 + 2+ 2+ -3 ® e.Proofing http:/13 sur 23 04/01/2016 18:16

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Acknowledgments

The authors are grateful to the Région Rhône-Alpes and the Association RE.CO.R.D. (Waste Research Cooperative Network, France) for financial support.