El Bachir Ameur

Driss Sbibih

Member, IEEE Ahmad Almhdie

Member, IEEE Christophe Léger

New Spline Quasi-Interpolant for Fitting 3-D Data on the Sphere: Applications to Medical Imaging

Keywords: B-spline, medical data, quasi-interpolant, sphere-like surface reconstruction, uniform algebraic trigonometric B-splines (UAT B-splines)

In this paper, a new local spline quasi-interpolant is constructed for fitting 3-D data defined on the sphere-like surface . After mapping the surface onto a rectangular domain, we use the tensor product of cubic polynomial B-splines and 2 -periodic uniform algebraic trigonometric B-splines (UAT B-splines) of order four to introduce a new expression of the associated quasi-interpolant . The use of UAT B-splines is necessary to enforce some boundary conditions which are useful to ensure the 1 continuity of the associated surface. The new method is particularly well designed to render 3-D closed surfaces. It has been successfully applied to reconstruct human organs such as the lung and left ventricle of the heart.

I. INTRODUCTION

S PLINES have been widely used in medical imaging for surface reconstruction and visualization of human organs [1], [2]. Usually, medical representations are obtained from a few scattered noisy data [3]. However, physicians require realistic organ representations to refine their diagnoses. Depending on the availability or the nature of the original data, interpolated-based and/or smooth-based surface reconstruction methods are required. Various methods are developed in the literature for fitting 3-D data on the sphere-like surface, in particular see [4]- [11]. In this paper, we propose a new method for fitting 3-D data by using a spline quasi-interpolant. It is based on the tensor product method of polynomial B-splines and periodic uniform algebraic trigonometric B-splines (UAT B-splines) recently developed in [12]. This new method can be successfully applied to sphere-like surface of various organs (heart, lung, bladder, kidney, etc.).

II. PROBLEM STATEMENT

Let be a closed and bounded surface in which is topologically equivalent to a sphere, i.e., there exists a one to one mapping of onto the unit sphere. In many applications, one needs to construct a function , defined on , and which satisfies , where are given real numbers and are points on . The construction of is done so that its associated surface has at every point a tangent plane that varies continuously over the surface . Without loss of generality, we assume that is the unit sphere. Then it can be identified with the rectangular domain , where and , by the mapping such that , where , , and . The associated surface of the polar coordinates' representation of , defined on by , is identical to that of , i.e., . However, the smoothness properties of are not equivalent to those of its corresponding closed surface . According to [4],

is of class if it has at every point a tangent plane that varies continuously over the surface . More specifically, is of class if and satisfies the following boundary conditions: where and are constants. Now, if we set , then the problem of finding such that is of class and satisfies , , becomes equivalent to finding in that satisfies , where are the polar coordinates of , i.e.,

. Since the problem is now posed on a rectangular domain, it is natural to use tensor-products for the construction of an approximating function of the form (1) where (respectively, ) is a linearly independent set of functions on (respectively, on

). Various choices of and have been introduced in the literature (see [4] and [5]). The obvious one for both sets would be polynomial B-splines. However, since the trigonometric functions cosine and sine cannot be expressed in terms of polynomial splines, enforcing condition (C4) is impossible using this choice, especially for . Thus, condition (C4) can only be approximately satisfied. To overcome this problem, the authors in [6]- [8] have chosen the periodic trigonometric B-splines of order three for and the quadratic polynomial B-splines for . This work is generalized in [9] and [11] by using B-splines

I E E E P r o o f W e b V e

r s i o n

of high order, but in this case the trigonometric B-splines must be of odd order, in particular the cubic case cannot be used. Here, we use the cubic polynomial B-splines and -periodic UAT B-splines of order four to introduce a new expression of the associated quasi-interpolant . The use of UAT B-splines is necessary to enforce boundary conditions which are useful to ensure the continuity of the associated surface.

III. CUBIC POLYNOMIAL B-SPLINES For and given positive integers and , let with mesh length be a uniform partition of the interval defined by

The associated polynomial spline space of order is defined by where is a polynomial space of degree . The classical normalized B-splines of order satisfy and , for . They form a partition of unity, i.e., and the family forms a basis of . Here, we denote by the cubic B-splines on the interval endowed with the partition . We now give a local linear operator which maps a given function onto a cubic spline space and which has an optimal approximation order. This operator is the discrete cubic spline quasi-interpolant defined by (2) where the coefficients are defined as linear combinations of some values of on the set in order to have the exactness of the quasi-interpolant on , i.e., , for all . More specifically, these coefficients are defined as follows:

This quasi-interpolant has an order four approximation, i. . Similarly to those of the polynomial B-spline basis, the UAT B-spline basis has many optimal properties, such as the subdivision property, the variation diminishing property and the convexity preserving property.

In order to define the periodic UAT B-splines, we choose the additional knots such that The associated periodic UAT B-splines are hence defined by . ( 6) When , we denote by the periodic UAT B-splines of order four associated with the periodic knots . These B-splines are of class on the interval and their restrictions to are in the space . We can verify that

P r o o f W e b V e r s i o n

The algebraic trigonometric quasi-interpolant which maps a given function into is defined by (7) where is the linear functional defined by . In order to have the exactness of the quasi-interpolant on , i.e., , for all , the coefficients will satisfy the following equations:

If we choose , then the above linear system has the unique solution . By using the trigonometric Taylor's expansion of about the point , we have with and , and by using the usual Taylor's expansion of about the point , we have with and . Since and , we obtain . After computation, we obtain where . Consequently, we have: Lemma 4.1: The quasi-interpolant based on the UAT B-splines of order four has an order four approximation, i.e., .

V. QUASI-INTERPOLANT ON THE SPHERE In this section, we construct a local linear operator which maps a given function in the space into splines of the form (1) which also lie in . Using the linear functionals and described above, we define for (8) According to the preceding properties of and , the approximate function is of class on . On the other hand, the conditions (C1) -(C4) can be satisfied if the coefficients verify some additional conditions.

For these choices of and the approximating function in (1) can be written in the form (9) Using the fact that are -periodic, we easily verify that the function defined in (9) satisfies conditions (C1) and (C3). In order to satisfy the remainder conditions, some coefficients of are imposed as follows. Lemma 5.1: The function given in (9)

VI. NUMERICAL RESULTS AND APPLICATIONS

TO MEDICAL IMAGING The implementation of the proposed method can be summarized in four steps.

• The first step consists in transforming the cartesian coordinates of given 3-D scattered data to spherical coordinates.

• The second step includes the subdivision of the rectangular domain into subrectangles , and the application of the least-square method to the given scattered data in order to construct the initial matrix .

• The third step consists in constructing the matrix and consequently computing the associated spline quasi-interpolant of the form defined in (8).

• The last step reconstructs the associated approximating sphere-like surface , by retransforming the spherical coordinates of on to Cartesian coordinates.

To test the method, let be the function defined explicitly on the rectangular domain by , where with [5]. It is straightforward to verify that . Table I gives the maximum error and the time of execution corresponding to different values of and .

Two different sets of 3-D medical data have been used to evaluate the proposed method. The first experiment considers a set of 922 surface points of real data of the human left lung, provided from perfusion scintigraphy images [Fig. 1 detailed studies on the comparison of the new method with quasi-interpolant ones will be carried out in the future.

VII. CONCLUSION

The quasi-interpolation method proposed in this letter is based on the tensor product of cubic polynomial B-splines and periodic UAT B-splines of order four. In contrast to least-square methods, it has two major advantages. First, the local reconstruction of a disturbed subset of a given surface is possible without affecting the whole surface data set. Second, the reconstruction process is achieved without the need to solve a large linear system and is hence easy to compute. In addition, compared to previously developed spline quasi-interpolant methods, our proposed algorithm is based on a spline quasi-interpolant with an order four approximation, exact on , and the reconstructed closed surface is of class except on the two poles where it is of class . Promising results have been obtained using numerical and real medical data. The method is also suitable for other applications related to the problem of 3-D reconstruction. It will be evaluated shortly in aerial and satellite imaging domains.

APPENDIX PROOF OF THEOREM 5.1

In order to prove that lies in , it suffices to show that satisfies conditions (C1)-(C4). Indeed, from the fact that are -periodic, defined in (8) satisfies conditions (C1) and (C3). Now, let us show that satisfies conditions (C2) and (C4) which is equivalent to prove that the coefficients satisfy the conditions given in the lemmas 5.1 and 5.2 respectively. According to the definitions of the linear functionals and , we have . On the other hand, since , we have . Consequently, we obtain . In a similar way, we get . Thus, satisfies condition (C2). For the condition (C4), using the expressions of , and , we have Since , we have , and consequently we obtain By using the same technique, we obtain the result for the case . Finally, using the fact that the quasi-interpolants and have an order four approximation, we obtain .

I E E E P r o o f P r i n t V e r s i o n

I. INTRODUCTION

S PLINES have been widely used in medical imaging for surface reconstruction and visualization of human organs [1], [2]. Usually, medical representations are obtained from a few scattered noisy data [3]. However, physicians require realistic organ representations to refine their diagnoses. Depending on the availability or the nature of the original data, interpolated-based and/or smooth-based surface reconstruction methods are required. Various methods are developed in the literature for fitting 3-D data on the sphere-like surface, in particular see [4]- [11]. In this paper, we propose a new method for fitting 3-D data by using a spline quasi-interpolant. It is based on the tensor product method of polynomial B-splines and periodic uniform algebraic trigonometric B-splines (UAT B-splines) recently developed in [12]. This new method can be successfully applied to sphere-like surface of various organs (heart, lung, bladder, kidney, etc.).

II. PROBLEM STATEMENT

Let be a closed and bounded surface in which is topologically equivalent to a sphere, i.e., there exists a one to one mapping of onto the unit sphere. In many applications, one needs to construct a function , defined on , and which satisfies , where are given real numbers and are points on . The construction of is done so that its associated surface has at every point a tangent plane that varies continuously over the surface . Without loss of generality, we assume that is the unit sphere. Then it can be identified with the rectangular domain , where and , by the mapping such that , where , , and . The associated surface of the polar coordinates' representation of , defined on by , is identical to that of , i.e., . However, the smoothness properties of are not equivalent to those of its corresponding closed surface . According to [4],

is of class if it has at every point a tangent plane that varies continuously over the surface . More specifically, is of class if and satisfies the following boundary conditions: where and are constants. Now, if we set , then the problem of finding such that is of class and satisfies , , becomes equivalent to finding in that satisfies , where are the polar coordinates of , i.e.,

. Since the problem is now posed on a rectangular domain, it is natural to use tensor-products for the construction of an approximating function of the form (1) where (respectively, ) is a linearly independent set of functions on (respectively, on

). Various choices of and have been introduced in the literature (see [4] and [5]). The obvious one for both sets would be polynomial B-splines. However, since the trigonometric functions cosine and sine cannot be expressed in terms of polynomial splines, enforcing condition (C4) is impossible using this choice, especially for . Thus, condition (C4) can only be approximately satisfied. To overcome this problem, the authors in [6]- [8] have chosen the periodic trigonometric B-splines of order three for and the quadratic polynomial B-splines for . This work is generalized in [9] and [11] of high order, but in this case the trigonometric B-splines must be of odd order, in particular the cubic case cannot be used.

Here, we use the cubic polynomial B-splines and -periodic UAT B-splines of order four to introduce a new expression of the associated quasi-interpolant . The use of UAT B-splines is necessary to enforce boundary conditions which are useful to ensure the continuity of the associated surface.

III. CUBIC POLYNOMIAL B-SPLINES For and given positive integers and , let with mesh length be a uniform partition of the interval defined by

The associated polynomial spline space of order is defined by where is a polynomial space of degree . The classical normalized B-splines of order satisfy and , for . They form a partition of unity, i.e., and the family forms a basis of . Here, we denote by the cubic B-splines on the interval endowed with the partition . We now give a local linear operator which maps a given function onto a cubic spline space and which has an optimal approximation order. This operator is the discrete cubic spline quasi-interpolant defined by (2) where the coefficients are defined as linear combinations of some values of on the set in order to have the exactness of the quasi-interpolant on , i.e., , for all . More specifically, these coefficients are defined as follows:

This quasi-interpolant has an order four approximation, i.e., IV. PERIODIC UNIFORM ALGEBRAIC TRIGONOMETRIC B-SPLINES Let and for a given positive integer and , let be a set of knots that subdivide the interval uniformly. In order to define a trigonometric B-spline basis of order , we add knots to the left of and to the right of namely and . Using the partition , we define the algebraic trigonometric spline space of order by where . A basis of a linear space is called a uniform algebraic trigonometric B-spline (UAT B-spline) basis of order if the basis functions are nonnegative, form a partition of unity and have a minimal support. To construct a UAT B-spline basis of , we first define a set of functions over . For , we put elsewhere

and for , we put

Some basic properties of the UAT B-spline basis of order are listed as follows: . Similarly to those of the polynomial B-spline basis, the UAT B-spline basis has many optimal properties, such as the subdivision property, the variation diminishing property and the convexity preserving property.

In order to define the periodic UAT B-splines, we choose the additional knots such that The associated periodic UAT B-splines are hence defined by . ( 6) When , we denote by the periodic UAT B-splines of order four associated with the periodic knots . These B-splines are of class on the interval and their restrictions to are in the space . We can verify that detailed studies on the comparison of the new method with quasi-interpolant ones will be carried out in the future.

I E E E P r o o f P r i n t V e r s i o n TABLE I (a) (b) (c)

VII. CONCLUSION

The quasi-interpolation method proposed in this letter is based on the tensor product of cubic polynomial B-splines and periodic UAT B-splines of order four. In contrast to least-square methods, it has two major advantages. First, the local reconstruction of a disturbed subset of a given surface is possible without affecting the whole surface data set. Second, the reconstruction process is achieved without the need to solve a large linear system and is hence easy to compute. In addition, compared to previously developed spline quasi-interpolant methods, our proposed algorithm is based on a spline quasi-interpolant with an order four approximation, exact on , and the reconstructed closed surface is of class except on the two poles where it is of class . Promising results have been obtained using numerical and real medical The is also suitable for other applications related to the problem of 3-D reconstruction. It will be evaluated shortly in aerial and satellite imaging domains. APPENDIX PROOF OF THEOREM 5.1

In order to prove that lies in , it suffices to show that satisfies conditions (C1)-(C4). Indeed, from the fact that are -periodic, defined in (8) satisfies conditions (C1) and (C3). Now, let us show that satisfies conditions (C2) and (C4) which is equivalent to prove that the coefficients satisfy the conditions given in the lemmas 5.1 and 5.2 respectively. According to the definitions of the linear functionals and , we have . On the other hand, since , we have . Consequently, we obtain . In a similar way, we get . Thus, satisfies condition (C2). For the condition (C4), using the expressions of , and , we have Since , we have , and consequently we obtain By using the same technique, we obtain the result for the case . Finally, using the fact that the quasi-interpolants and have an order four approximation, we obtain .

  Manuscript received July 14, 2006; revised September 19, 2006. The associate editor coordinating the review of this paper and approving it for publication was Dr. Xiang-Gen Xia.. E. B. Ameur is with the Faculté des Sciences et Techniques, Département d'Informatique, Université Moulay Ismail, 52000 Errachidia, Morocco (e-mail: ameurelbachir@yahoo.fr) D. Sbibih is with the Ecole Supérieure de Technologie, Laboratoire MATSI, Université Mohammed I, Oujda, Morocco (e-mail: sbibih@yahoo.fr) A. Almhdie is with the Laboratoire d'Electronique, Signaux, Images (LESI), Université d'Orléans, France. (e-mails: Ahmad.Almhdie@univ-orleans.fr) C. Léger is with the Laboratoire d'Electronique, Signaux, Images (LESI), Université d'Orléans, France. Tel: + 33 2 38 49 45 63, Fax: + 33 2 38 41 72 45. (e-mail: Christophe.Leger@univ-orleans.fr) A color version of Fig. 1 is available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/LSP.2006.888261

  e., IV. PERIODIC UNIFORM ALGEBRAIC TRIGONOMETRIC B-SPLINES Let and for a given positive integer and , let be a set of knots that subdivide the interval uniformly. In order to define a trigonometric B-spline basis of order , we add knots to the left of and to the right of namely and . Using the partition , we define the algebraic trigonometric spline space of order by where . A basis of a linear space is called a uniform algebraic trigonometric B-spline (UAT B-spline) basis of order if the basis functions are nonnegative, form a partition of unity and have a minimal support. To construct a UAT B-spline basis of , we first define a set of functions over . a partition of unity: ; • the family forms a basis of the spline space

Fig. 1 .

 1 Fig. 1. (a) 3-D given data of the lung (top) and the LV (bottom). (b) Surface meshes on the rectangle D. (c) Quasi-interpolant closed surfaces.

IEEE SIGNAL PROCESSING LETTERS 1 New

 1 Spline Quasi-Interpolant for Fitting 3-D Data on the Sphere: Applications to Medical Imaging El Bachir Ameur, Driss Sbibih, Ahmad Almhdie, Member, IEEE, and Christophe Léger, Member, IEEE Abstract-In this paper, a new local spline quasi-interpolant is constructed for fitting 3-D data defined on the sphere-like surface . After mapping the surface onto a rectangular domain, we use the tensor product of cubic polynomial B-splines and 2 -periodic uniform algebraic trigonometric B-splines (UAT B-splines) of order four to introduce a new expression of the associated quasi-interpolant . The use of UAT B-splines is necessary to enforce some boundary conditions which are useful to ensure the 1 continuity of the associated surface. The new method is particularly well designed to render 3-D closed surfaces. It has been successfully applied to reconstruct human organs such as the lung and left ventricle of the heart. Index Terms-B-spline, medical data, quasi-interpolant, sphere-like surface reconstruction, uniform algebraic trigonometric B-splines (UAT B-splines).

  Manuscript received July 14, 2006; revised September 19, 2006. The associate editor coordinating the review of this paper and approving it for publication was Dr. Xiang-Gen Xia.. E. B. Ameur is with the Faculté des Sciences et Techniques, Département d'Informatique, Université Moulay Ismail, 52000 Errachidia, Morocco (e-mail: ameurelbachir@yahoo.fr) D. Sbibih is with the Ecole Supérieure de Technologie, Laboratoire MATSI, Université Mohammed I, Oujda, Morocco (e-mail: sbibih@yahoo.fr) A. Almhdie is with the Laboratoire d'Electronique, Signaux, Images (LESI), Université d'Orléans, France. (e-mails: Ahmad.Almhdie@univ-orleans.fr) C. Léger is with the Laboratoire d'Electronique, Signaux, Images (LESI), Université d'Orléans, France. Tel: + 33 2 38 49 45 63, Fax: + 33 2 38 41 72 45. (e-mail: Christophe.Leger@univ-orleans.fr) A color version of Fig. 1 is available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/LSP.2006.888261

Fig. 1 .

 1 Fig. 1. (a) 3-D given data of the lung (top) and the LV (bottom). (b) Surface meshes on the rectangle D. (c) Quasi-interpolant closed surfaces.

The algebraic trigonometric quasi-interpolant which maps a given function into is defined by (7) where is the linear functional defined by . In order to have the exactness of the quasi-interpolant on , i.e., , for all , the coefficients will satisfy the following equations:

If we choose , then the above linear system has the unique solution . By using the trigonometric Taylor's expansion of about the point , we have with and , and by using the usual Taylor's expansion of about the point , we have with and . Since and , we obtain . After computation, we obtain where . Consequently, we have: Lemma 4.1: The quasi-interpolant based on the UAT B-splines of order four has an order four approximation, i.e., .

V. QUASI-INTERPOLANT ON THE SPHERE In this section, we construct a local linear operator which maps a given function in the space into splines of the form (1) which also lie in . Using the linear functionals and described above, we define for (8) According to the preceding properties of and , the approximate function is of class on . On the other hand, the conditions (C1) -(C4) can be satisfied if the coefficients verify some additional conditions.

For these choices of and the approximating function in (1) can be written in the form (9) Using the fact that are -periodic, we easily verify that the function defined in (9) satisfies conditions (C1) and (C3). In order to satisfy the remainder conditions, some coefficients of are imposed as follows. Lemma 5.1: The function given in (9)

VI. NUMERICAL RESULTS AND APPLICATIONS

TO MEDICAL IMAGING The implementation of the proposed method can be summarized in four steps.

• The first step consists in transforming the cartesian coordinates of given 3-D scattered data to spherical coordinates.

• The second step includes the subdivision of the rectangular domain into subrectangles , and the application of the least-square method to the given scattered data in order to construct the initial matrix .

• The third step consists in constructing the matrix and consequently computing the associated spline quasi-interpolant of the form defined in (8).

• The last step reconstructs the associated approximating sphere-like surface , by retransforming the spherical coordinates of on to Cartesian coordinates.

To test the method, let be the function defined explicitly on the rectangular domain by , where with [5]. It is straightforward to verify that . Table I gives the maximum error and the time of execution corresponding to different values of and .

Two different sets of 3-D medical data have been used to evaluate the proposed method. The first experiment considers a set of 922 surface points of real data of the human left lung, provided from perfusion scintigraphy images [Fig. 1


Bruno Gazengel

Jean Pierre Dalmont

Mechanical response characterization of saxophone reeds

Keywords: no. 43.75.Pq, 43.75.Zz, 43.20.Tb

The subjective quality of single cane reeds used for saxophone or clarinet may be very dierent from a reed to another although reeds present the same shape and the same strength. In this work, we propose an experimental system in order to try to classify reeds in dierent families which could represent the musician feeling. In the long term, this measuring would enable to enhance the quality of the reed classication during the manufacturing process. The aim of the measurement is to estimate the equivalent mechanical parameters of the reed. The reed is mounted on a tenor saxophone mouthpiece which cavity is excited with a loudspeaker is the frequency range 500 Hz -6 kHz. The acoustic pressure is measured in the mouthpiece and the reed displacement is measured using a optical sensor near the reed tip. The frequency Response Function is analyzed using a modal analysis technique (MDOF) and the equivalent reed parameters are estimated (mass, stiness and damping) for each mode. Dierent reeds chosen for their subjective dierences (rather dicult and dark, medium, rather easy and bright) are characterized with the measuring system and by measuring the mouth pressure and the spectral centroid of the acoustic pressure radiated at the saxophone horn. First results show that dierences between spectral centroid of the radiated pressure could be explained by dierences in the equivalent mass of the vibration mode estimated by means of the measuring system.

Introduction

The musical quality of woodwind instruments such as clarinet or saxophone depends strongly on the reed quality. Quality of single cane reed may vary from a reed to another. Using our own experience of musician, we consider that 30 % of reeds are good reeds in a box, whereas 40 % are mean quality reeds and 30 % are considered as bad.

Usually, the experimental characterization of mechanical properties is performed by measuring the mechanical stiness of the reed submitted to a static force at a particular location from the tip. This measurement enables to estimate the strength of the reed which is indicated for the clarinet or saxophone player. It appears that this method is necessary to sort out the reeds for dierent strength and to indicate the musician if the reed can be played with a particular mouthpiece. However this approach can (c) European Acoustics Association not explain the great dierences observed between reeds with the same strength and the same cut.

The characterization of physical properties of reeds has been studied using dierent approaches such as vizualisation of cane cells, mechanical measurement of vibration response or optical holography to identify the vibrational modes of the reed.

Kolezik [START_REF] Kolesik | Sedgley: Anatomical Characteristics Aecting the Musical Performance of Clarinet Reeds Made from Arundo donax L. (Gramineae)[END_REF] studies the anatomical characteristics of cane using confocal laser scanning microscopy.

Mukhopadhyay [START_REF] Mukhopadhyay | Saxophone reed inspection employing planar electromagnetic sensor[END_REF] proposes to characterize the quality of saxophone reeds using planar electromagnetic sensors. Obataya [START_REF] Obataya | Norimoto: Acoustic properties of a reed (Arundo donax L.) used for the vibrating plate of a clarinet[END_REF] studies the eect relative humidity on the dynamic Young's modulus of the reed using a free-free beam exural vibration method and by measuring small plates made with cane. Pinard et al. [START_REF] Pinard | Vachb: Musical quality assessment of clarinet reeds using optical holography[END_REF] observe the vibrational modes of 24 clarinet reeds in both dry and wet conditions using holographic interferometry. Picart [4] observes the modes of a clarinet reed using holography and measures the displacement of the reed tip during auto-oscillations created in an articial mouth. The aim of this work is try to explain why particular reeds produce dierent sounds (more or less bright) and dierent feeling for the player. On the one hand, vibroacoustical responses of reeds are measured using a experimental system which generates a sound inside a mouthpiece at low levels (compared to the the levels observed during the playing). The reed response is estimated by measuring the acoustic pressure inside the mouthpiece and the displacement of the reed tip. On the other hand, the pressure inside the mouth player and the acoustic pressure emitted at the saxophone horn are measured using the same reeds. For each reed and for dierent notes, the mean mouth pressure and the spectral centroid of the acoustic pressure are calculated.

The paper is organized as follow. First part presents the experimental system which enables to estimate the mechanical parameters of the reed. Second section presents the in vivo measurement system. Finally, the comparison between the two experiments are presented and the results are discussed in section 3.

Characterization of the reed mechanical response

The aim of this section is to present the experimental used for characterizing the vibroacoustical response of single cane reeds. Physical parameters describing the reed are also presented.

The experimental system is based on the system presented by Gazengel el al. [START_REF] Gazengel | Experimental investigation of the inuence of the mechanical characteristics of the lip on the vibrations of the single reed[END_REF]. The system is presented in gure 2. The reed is mounted on a tenor saxophone mouthpiece using a cap. The mouthpiece cavity is excited with a small loudspeaker. The acoustic pressure exciting the reed is measured using a electret microphone (Sennheiser KE4) at 5 mm from the tip of the mouthpiece. The reed displacement is measured using an optical sensor (Philtec RC 25) having a measuring area of about 1 x 4 mm. This sensor is mounted on a traverse system which enables to set precisely the distance between the reed and the sensor. As the optical sensor response is non linear, the distance between sensor and reed must be known and determines the functioning point. For all the experiments, the response of the reed is charactized by measuring the Frequency Response Function displacement over acoustic pressure at the middle of the reed (in the transverse direction) and at 2 mm from the tip.

This experimental system is very simple compared with other experiments using holography. It does not enable to perform easily a modal analysis of the reed as the system presented for example in [START_REF] Pinard | Vachb: Musical quality assessment of clarinet reeds using optical holography[END_REF]. If the physical parameters estimated from this measuring apparatus can explain (even partially) the reed quality, it could be used in the future for industrial applications.

The Frequency Response Function (FRF) is measured using a Stanford analyser SR875. An example of FRF obtained is shown in gure 3. This result shows that the rst exural mode is predominant. Other modes are torsion mode, second exural model and modes combining exion and torsion as shown in [START_REF] Pinard | Vachb: Musical quality assessment of clarinet reeds using optical holography[END_REF].

Characterization of saxophone reeds

In vivo measurements

In this section, we present the experimental system used for measuring the acoustic pressure at the saxophone horn and the pressure in the musician's mouth. The stationnary part of the signal is dened for E(t) ∈ [0.050.95]E max , where E max is the maximum energy obtained at the end of the note. The spectral centroid SC(n, r) is estimated for each reeed r and each note n by using 45 harmonics of the signal for each note using

SC(n, r) = 1 f 1 ∑ k=45 k=1 A k f k ∑ k=45 k=1 A k , ( 2
)
where f k is the frequency and A k is the amplitude of the spectral component k.

This enables to use the same number of harmonics for each note, the number of harmonics being limited by the maximum frequency (25 kHz). The mouth pressure is estimated as the mean pressure measured in the mouth during the stationnary part of the signal.

Results

Experimental conguration

The tests have been performed by a single tenor saxophone player using a Reference 54 Selmer saxophone and a Vandoren V16 T8 mouthpiece. 14 reeds have been tested. Three dierent trademark have been used with dierent strengths (Vandoren Jazz 3 and 3 1/2 , Vandoren Java 2 1/2 , Rico Royal 3 and 3 For each reed, the arppegio has been rst played ve times in order to estimate the average and the standard deviation of the spectral centroid and the mouth pressure. Once the musical phrase are recorded, the vibroacoutical response of each reed is measured ve times using the experimental system describedd in 2 and the equivalent parameters of the rst mode are estimated. where ASC(n) = 1

Discussion

Nr

∑ r=Nr r=1 SC(n, r) is the average spectral centroid for N r reeds , n is the note number, r the reed number and N r the number of reeds. The RSC is presented in gure 8 and shows that great dierences appear for dierent reeds whereas smaller dierences appear for dierent notes.

The relative mouth pressure is dened in the same manner RM P (n, r) = (M P (n, r)-AM P (n))/AM P (n),( 4)

where AM P (n) = 1 Nr ∑ r=Nr r=1 M P (n, r).
Finally, we calculate a single parameter depending only on the reed number. The Mean Relative Spectral Centroid (MRSC) is dened as

M RSC(r) = 1 N n r=Nn ∑ n=1 RSC(n, r), ( 5
)
where N n is the total number of notes. The Mean Relative Mouth Pressure (MRMP) is calculated using the same approach.

u = σ √ N n , ( 6
)
where σ is the standard deviation in the parameter estimation. Using these two indicators (MRSC and MRMP), the reeds can be sorted in a two dimensions plane as shown in gure 9.

In vitro measurements

The estimated values of the relative parameters (stiness, quality factor, mass) obtained by in vivo measurements are calculated by comparing the measured parameters to the mean value of these parameters.

The uncertainty in the parameters p is calculated as

u p = σ p √ N mes , ( 7
)
where σ p is the standard deviation in the estimated values of the parameter and N mes is the number of measurement (5 in our case). The error bar are shown on gure 10.

Figure 1 .

 1 Figure 1. View of the structure of the work.

Figure 2 .

 2 Figure 2. Principle of the measuring system used for the characterization of the reed vibroacoustic response.

Figure 3 .

 3 Figure 3. Frequency response Function of a reed. The displacement sensor is located at 2 mm from the tip and at the center of the reed.

  These two physical parameters enable to deduce the spectral centroid of the emitted sound and the mean pressure in the mouth for a particular note played by the musician.The mouth pressure is measured using a dierential pressure sensor Endevco 8507-C2 connected to a small tube introduced in the mouth of the player during the test. The acoustic pressure is measured using a microphone placed in front of the saxophone horn (gure 4). The signals are connected to an acquisition board National instruments BNC-2110 using a sampling frequency F s = 50 kHz. An example of measured signal is shown in gure 5.The estimation of the spectral centroid is performed as follow. The dierent notes are manually detected.

Figure 4 .

 4 Figure 4. View of the in vivo measuring system.

Figure 5 .

 5 Figure 5. Example of signal measured when the musician is playing. (top) Mouth pressure. (bottom) Acoustic pressure at the saxophone horn output.

4. 2 . 1 .

 21 In vivo measurements The estimated values of the spectral centroid (SC) and mouth pressure (MP) obtained in the in vivo conguration are presented in gure 6 and 7. Both parameters show a signicative dependance on the played note. SC values are symetric around the highest note (high C), whereas MP is asymetric, showing greater values at the beginning of the phrase corresponding the notes of the low register of the saxophone (low C).

Figure 6 .

 6 Figure 6. View of the estimated spectral centroid as a function of the note number.

Figure 7 .

 7 Figure 7. View of the estimated mouth pressure as a function of the note number.

Figure 8 .

 8 Figure 8. View of the RSC as a function the reed index for dierent notes.

Figure 9 .

 9 Figure 9. View of the values of RMSC and RMMP for the 14 reeds.

Figure 10 .

 10 Figure 10. View of the values of stiness and quality factor for the 14 reeds.

Figure 11 .

 11 Figure 11. View of the values of equivalent mass of rst vibration mode and spectral centroid for the 14 reeds.

  this paper, we have studied the quality of 14 tenor saxophone cane reeds using experimental approaches leading to objective indicators. On the one hand, the reed is characterized in vitro. The vibroacoustical response of the reeds are characterized using a specic bench which enables to measure the displacement of the reed at a point and the acoustic pressure generated in the mouthpiece with a loudspeaker. The stiness and quality factor of the rst vibration mode have been deduced from this measurements. On the other hand, the acoustic pressure at the saxophone horn and the mouth pressure are measured in vivo. Specic indicators are proposed in order to take account the relation between the spectral centroid, the mouth pressure and the played note. Comparisons between results obtained in vitro and in vivo show that the spectral centroid seems to be related to the equivalent mass of rst vibration mode of the reed. Future work will consider the effect of high acoustic levels and of the lip on the reed mechanical behaviour to try to explain the dierences observed during the playing.

Acknowledgement

We want to thanks Emmanuel Brasseur for his help in this project.


Jun Wei Lim
email: jwlim3@e.ntu.edu.sg

Anaerobic Co-digestion of Brown Water and Food Waste for Energy Recovery

Keywords: Anaerobic digestion, food waste, brown water, biogas, co-digestion

The anaerobic digestion of brown water (BW), food waste (FW) and their mixture (MW) in batch digesters was evaluated under mesophilic conditions. BW collected from separating toilets and FW are high strength organic substrates that can be treated in a decentralized reactor via anaerobic digestion. The bio-methane potential of these substrates at different feed/inoculum ratios (F/Is) was studied using 100-mL serum bottles and biogas and methane production, pH and VS reductions were measured periodically to determine the extent of substrate degradation. The feasibility of co-digestion was also investigated to determine if further improvement of biogas yield could be achieved. Preliminary results suggested that BWs and FWs are potential substrates for biogas production. Brown water appeared to be the most biodegradable substrate in this study and its biogas yield was inhibited by the addition of food waste.

INTRODUCTION

Anaerobic digestion (AD) has been widely applied in the treatment of organic wastewaters due to its high degree of waste stabilization and methane generation. Methane is a potentially valuable by-product that can be used as a fuel in producing heat and electricity, and the significance of this advantage is increasingly being emphasized in our energy conscious society. Having a fuel value of approximately 5,850 kg-cal/m 3 , biogas has been widely used in heating digesters and gas engines (Wang et al., 2007). The anaerobic digestion of food waste and animal manure (El-Mashad and Zhang, 2010;Neves et al., 2008;Ahn et al., 2010) has been extensively studied on while that on human faeces is not as common and extensive. Human faeces collected from toilet systems are known as brown water (without urine) and black water (mixed with urine), and their COD concentrations are dependent on the toilet flushing system. The concentration of black water collected from vacuum toilets ranged between 8.7 -12.3 gCOD/L (Wendland et al., 2007;Marthe S. de Graaff et al., 2010), while that of brown water was around 38.8 gCOD/L (Elmitwalli et al., 2006). Wastewaters in Singapore are currently being transported long distances to centralized plants for treatment, which consumes too much unnecessary energy and water. An alternative approach would be to treat concentrated wastewaters in a decentralised plant. Source-separated domestic wastewaters tend to be more concentrated and this would improve the potential of energy recovery via anaerobic digestion. There have been some research activities on the AD of black water in rural areas and findings indicated the feasibility of treating human waste in decentralised sanitation systems (Wendland et al., 2007;Kujawa-Roeleveld et al., 2005;Zeeman et al., 2008). However, such research in the urban context has been scarce. With increasing population and concerns over water and fuel shortage, an onsite decentralised and anaerobic treatment of domestic wastewaters in urban cities might provide the sustainable solution. This paper aims to discuss the feasibility of anaerobic co-digestion of high strength domestic wastewaters -namely brown water and kitchen food waste in urban decentralised units for energy recovery. This paper will describe the anaerobic digestion batch study of brown water and food waste alone, and then the co-digestion of the mixture of these two wastes.

MATERIAL & METHODS

Collection and preparation of inoculum and substrates

Sludge collected from an anaerobic digester at the Ulu Pandan Water Reclamation Plant (designed for domestic wastewater treatment) was used as inoculum in this study. As shown in Table 1, the total solids (TS) and volatile solids (VS) concentrations of sludge were 17.83 ± 0.04 g/kg and 12.52 ± 0.05 g/kg, respectively. Freshly collected sludge was stored at 35°C for one week to remove any remaining biodegradable fraction before using it as inoculum for the batch test. Two different types of organic waste -brown water and food waste were used as substrates in this study. Brown water (fecal waste without urine) mixed with 2 L of flush water was collected from a urine separation toilet located near the university's laboratory and then stored in a refrigerator at 4°C. Food waste used in this study was collected from the university's campus canteen, where the majority of the waste came from Chinese, Indian, Indonesian and Malay food stalls. After removing bones and non-food materials, the food waste was blended into slurry form with an average size of 2.0 mm using a kitchen blender. The blended food waste was then mixed well, and stored in a refrigerator at 4°C. As shown in Table 1, the TS and VS concentrations of brown water were 4.44 ± 0.06 g/kg and 3.77 ± 0.08 g/kg, respectively, and those for food waste were 295.16 ± 1.50 g/kg and 283.45 ± 1.53 g/kg, respectively. All these substrates were stored in a refrigerator at 4°C after collection and used within 7 days.

Experimental design and set-up

The batch digestion tests were carried out using 100mL reactors (with 70mL working volume) at mesophilic temperature (35°C) for a period of 21 and 30 days. In each reactor, 14mL of inoculum (20% v/v) was added to 56mL of substrate diluted with tap water to achieve the desired VS load. The head space of all the reactors was purged with nitrogen gas for thirty seconds to create anaerobic conditions before the reactors were tightly closed with rubber septa and screw caps. Three blank reactors that contained only inoculum and tap water were also set up to monitor the biogas produced from the inoculum for the correction of biogas produced from the substrates under study. A total of ten reactors were set up for each condition and the contents were analysed periodically for pH, VS reductions and VFA by sacrificing two reactors each time. To ensure even mixing between substrate and inoculum, the reactors were placed on a shaker with speed 120 rpm throughout the study period. Four different conditions as shown in Table 2, (VS loading from 0.3g VS/L to 2.5g VS/L) were carried out for the batch study of brown water and food waste. For the co-digestion experiment, four different conditions were designed, with brown water and food waste mixed in different proportions. Mixtures A, B and C had VS loading of 1g VS/L while mixture D had VS loading of 2g VS/L. The brown water to food waste ratio for mixtures A, B, C and D were 1:1, 3:7, 7:3 and 1:1 respectively.

Analytical methods

TS, VS, total chemical oxygen demand (TCOD) and soluble chemical oxygen demand (SCOD) were measured in the well-mixed samples in triplicates by standard methods (APHA, 1998). The pH value was measured using a pH meter (CORNING 145,England). The organic carbon and nitrogen content of substrates and sludge was determined using a Total Organic Carbon/ Nitrogen Analyzer multi N/C 2100/ 2100s (Analytikjena). Samples were oven dried at 105°C for 2 hours before the addition of concentrated HCl to remove the inorganics. Approximately 20mg of the sample was analyzed and each sample was tested in triplicates. The determination of VFA was carried out using gas chromatography and the samples were filtered through Whatman 0.2µm nitrocellulose membrane filters. Biogas production was monitored daily using a syringe, while the biogas composition (methane and carbon dioxide contents) was analyzed by gas chromatography (GC) (HP5890A, HACH, Avondale, PA, USA) which was equipped with a thermal conductivity detector (TCD). Helium was used as carrier gas at a flow rate of 40 mL min -1 . The measurements were done at least once a week for each reactor. Biogas samples injected into the GC were extracted from the reactors head space after releasing the gas, using a 100-µL gas tight syringe (Fisher Scientific, Pittsburgh, PA, USA).

Data processing

Since the biogas production rates and methane content of the substrates vary considerably over the digestion period, the weighted average methane content (WA) and standard deviation (STDV) over the digestion period was calculated using the method as described by (El-Mashad and Zhang, 2010) as follows:

WA (%) = STDV =
where: DBP i = biogas production on day i, MP i = methane content on day i, n = number of observations.

RESULTS AND DISCUSSION

Anaerobic digestion of brown water

A summary of the weighted average methane content, biogas and methane yields and VS reduction of brown water at different F/I after 21 and 30 days of digestion are shown in Table 2. The average biogas yields and rates during the 30-day anaerobic digestion of brown water are also shown in Figs. 1a and1b. As shown in Fig. 1a, BW3 with F/I of 0.40 produced the highest biogas yield, as compared to brown water with other F/Is. The biogas yield after 30 days was calculated to be 762, 736, 916, and 754 L/kg VS added and approximately 88%, 93%, 96%, and 98% of the final biogas yield for BW1, BW2, BW3 and BW4 respectively, could be obtained after 21 days of digestion. With weighted average methane contents of 70%, 73%, 73% and 78%, the average methane yield after 30 days of digestion was 537, 535, 672 and 587 L/kg VS added and 88%, 92%, 96% and 98% of the final methane yield for BW1, BW2, BW3 and BW4 respectively, could be obtained after 21 days of digestion. Although BW4 had the highest methane content at 78% (Table 2), the methane yield of BW3 was still higher than the others.

Throughout the 30 days of anaerobic digestion, the pH value of reactor content was determined periodically, as shown in Fig. 2a. The pH of brown water at all F/Is showed a similar trend. After 6 days of digestion, the pH value of BW1, BW2, BW3 and BW4 dropped from 7.21, 7.06, 6.94 and 6.76 to 6.51, 6.56, 6.48 and 6.29 respectively. After that, the pH recovered slightly and was raised to the range of 6.53 to 6.63 for all four sets after 12 days of digestion. The pH remained constant for the next 7 days but increased further to 6.78, 6.83, 6.77 and 6.95 respectively after 23 days of digestion. The final pH measured after 30 days of digestion dropped slightly to 6.69, 6.67, 6.67 and 6.86 respectively.

The average VS reductions after 30 days of digestion were calculated to be 49%, 55%, 55% and 60% and after 21 days of digestion, approximately 96%, 96%, 95% and 90% of the final VS reductions for BW1, BW2, BW3 and BW4, respectively could be obtained.

Anaerobic digestion of food waste

Exactly the same conditions were designed for the anaerobic digestion of food waste. A summary of the weighted average methane content, biogas and methane yields and VS reduction of food waste at different F/Is after 21 and 30 days of digestion are shown in Table 2. The average biogas yields and rates during the 30-day anaerobic digestion of food waste are also shown in Figs. 1c and1d. The biogas yield after 30 days was calculated to be 343, 343, 425 and 303 L/kg VS added and approximately 92%, 97%, 99% and 81% of the final biogas yield for FW1, FW2, FW3 and FW4 respectively could be obtained after 21 days of digestion. With weighted average methane contents of 73%, 67%, 68% and 56%, the average methane yield after 30 days of digestion was 250, 229, 288 and 173 L/kg VS added and approximately 92%, 97%, 99% and 78% of the final methane yield for FW1, FW2, FW3 and FW4 respectively could be obtained after 21 days of digestion. Similar to brown water, food waste with F/I of 0.40 produced the highest biogas and methane yield. As compared to brown water with F/I of 0.40, the biogas and methane yield for food waste with F/I of 0.40 was 54% and 57% lesser respectively, suggesting that brown water is a more biodegradable substrate as compared to food waste. As shown in Table 2, biogas yield increased with increasing F/I in the range of 0.12 to 0.40 due to the greater availability of substrate. When F/I was raised to 1.0, biogas yield decreased, indicating the possibility of substrate overloading, resulting in some inhibition of methanogenic bacteria due to VFA accumulation.

The initial pH value of food waste with different F/Is ranged from 6.82 to 7.09. Other than food waste with F/I of 1.0 (FW4), the pH of FW1, FW2 and FW3 remained relatively constant at around 6.81, 6.60 and 6.47 respectively from day 2 until the end of the study. The pH of FW4 dropped sharply from 6.82 to 5.52 after 2 days and dropped further to 5.34 after 6 days of digestion. The measured pH on day 12 increased to 5.75 and it continued to increase until the end of the digestion period to 6.43. The significantly lower biogas and methane yield of FW4 (Fig. 1c and Table 2) could be accounted for by the large drop in pH, causing the inhibition of methanogenic bacteria. In comparison with brown water, the pH values of food waste mixtures did not recover as much after 21 days of digestion.

The average VS reductions after 30 days of digestion were calculated to be 45%, 29%, 60% and 43%, and after 21 days of digestion, approximately 97%, 95%, 99% and 95% of the final VS reductions for FW1, FW2, FW3 and FW4 respectively could be obtained. For food waste at all F/Is, the VS reduction percentages and biogas yields followed the same trend.

In general, the weighted average methane content, biogas yield and VS reductions of food waste mixtures were lower than that of brown water (Table 2). As majority of the food waste collected came from Chinese, Indonesian, Indian and Malay food stalls, the food waste contained large amounts of gravy, fats and salts. Hence, these complicated food components could have brought about some inhibitory effects on the methanogens (Cho et al., 1995), leading to lower biogas and methane yield as compared to brown water with similar F/I. Long chain fatty acids that are present in food with high fat content and in food preservatives have inhibitory effects on methanogenic bacteria. Further studies on the effect of the complicated composition of food waste on biogas yield and process stability are required.

In comparison with the batch anaerobic digestion of food waste under mesophilic conditions reported by other authors, the biogas yield in this study appeared to be much lower. El-Mashad et al. reported an average biogas yield of 657 L/kg VS added from a 2gVS/L food waste with F/I of 0.19 (El-Mashad and Zhang, 2010). In this study, FW2 with a similar F/I of 0.20, produced only 343 L of biogas/kg VS added . Even at a much higher loading (F/I of 3.1), (Liu et al., 2009) reported an average biogas yield of 430 L/kg VS added from a 12.5gVS/L food waste mixture.

Anaerobic co-digestion of brown water and food waste

Since approximately 90% of the VS reductions, biogas and methane yields could be obtained after 21 days of digestion, as seen from the results of brown water and food waste (Table 2), the digestion period for the mixture of brown water and food waste was reduced to 21 days. The anaerobic digestion of mixed waste (F/I of 0.40) with three mixing ratios based on VS was carried out to study the effect of brown water and food waste mixing ratio on the biogas and methane yield. The anaerobic digestion of MW4, which had the same mixing ratio as MW1 but two times its VS concentration, was carried out to study if biogas and methane yield will improve when VS loading increased to more than 1gVS/L (the organic loading for MW1, MW2 and MW3).

A summary of the weighted average methane content, biogas and methane yields and VS reduction of mixed waste at different mixing ratios after 21 days of digestion are shown in Table 2. The average biogas yields and rates during the 21 days of digestion are shown in Fig. 1e and 1f. After 21 days of digestion, the biogas yield was calculated to be 287, 301, 301 and 417 L/kg VS added for MW1, MW2, MW3 and MW4 respectively. With an average methane content of 74%, 71%, 72% and 68%, the methane yield was calculated to be 212, 217, 220 and 287 L/kg VS added respectively. As shown in Fig. 1e, the biogas yield of MW1, MW2 and MW3 showed no significant difference, indicating that the mixing ratio of brown water and food waste did not affect the biogas yield. On the other hand, increasing the F/I from 0.40 to 0.80 improved the biogas yield by approximately 70%, as shown by MW4 in Fig. 1e. This is in contrast to the results obtained from brown water or food waste alone whereby the biogas yield started to drop when F/I was increased beyond 0.40.

The addition of food waste did not improve the biogas yield of brown water. Instead, the biogas yield was affected negatively when food waste was introduced to the anaerobic digestion of brown water. Comparing FW2 with MW1, MW2 and MW3, where all had the same amount of food waste added (0.5gVS/L), showed that their biogas yield after 21 days of digestion were similar at 333, 287, 301 and 301 L/kg VS added respectively.

The pH values of the brown water and food waste mixtures were in the range of 6.91 to 7.08 before the start of digestion and dropped to the range of 6.33 to 6.41 after 21 days of digestion (Fig. 2c).

In general, there were no lag phase and biogas production started after the first day of digestion for all substrates and conditions studied (Fig. 1b,1d,1f). Multiple peaks in biogas production rates were observed throughout the 30-day digestion period.

CONCLUSIONS

The biogas and methane yields of brown water, food waste and their mixture at different F/Is using an anaerobic batch digester at 35 ± 2°C were determined in this study. The batch digestion tests for brown water and food waste were performed for 30 days to achieve complete digestion. Since about 90% of the final biogas yield and VS reductions from brown water and food waste could be obtained after 21 days of digestion, the digestion period of the subsequent study on the mixture of brown water and food waste was reduced to 21 days. At a F/I of 0.40, the biogas yields obtained for brown water, food waste and their mixtures were 876, 421 and approximately 300 L/kgVS added respectively after 21 days of digestion. As brown water produced the highest biogas yield, highest methane content in the biogas produced, and highest average VS reduction (Table 2), it appeared to be more biodegradable than food waste. The biogas yield of brown water was also inhibited by the addition of food waste, as shown by the biogas yields produced by mixtures of brown water and food waste (Fig 1e). The feasibility study of co-digesting brown water and food waste revealed that their biogas yields were lower than that obtained from brown water or food waste alone (with the same F/I), which could be due to some inhibition effects brought about by food waste. As it would be both economically and environmentally advantageous for such a co-digestion process to take place in decentralised anaerobic digesters, further studies should be carried out to investigate the effect of intermediates such as volatile fatty acids on biogas yield and digestion performance. • Zeeman, G., Kujawa, K., de Mes, T., Hernandez, L., de Graaff, M., Abu-Ghunmi, L., Mels, A., Meulman, B., Temmink, H., Buisman, C., van Lier, J., Lettinga, G., 2008. Anaerobic treatment as a core technology for energy, nutrients and water recovery from source-separated domestic waste(water). Water Sci Technol 57, 1207-1212.

Figs

  Figs. 1a-f: (a) and (b) biogas yield and rate of brown water, (c) and (d) biogas yield and rate of food waste, (e) and (f) biogas yield and rate of mixtures of brown water and food waste.

TABLE 1 : Characterization of substrates Parameter Units Brown Water Food Waste Sludge

 1

	TS	g/kg, wet basis	4.44 ± 0.06	295.16 ± 1.50	17.83 ± 0.04
	VS	g/kg, wet basis	3.77 ± 0.08	283.45 ± 1.53	12.52 ± 0.05
	pH		6.70	4.40	6.90
	COD-total	g/L	8.16 ± 0.56	394.10 ± 13.80	14.71 ± 0.07
	TOC	g/kg	471.40 ± 10.58	323.92 ± 16.59	377.75 ± 13.51
	TN	g/kg	9.75 ± 0.35	1.12 ± 0.18	7.64 ± 0.71

TABLE 2 : Results of batch anaerobic digestion of brown water, food waste and their mixture

 2

	Initial VS Loading	F/I	CH 4 content	Biogas yield	CH 4 yield	VS reduction
				(%)	(L/kg VS added ) (L/kg VS added )	(%)
				21	30	21	30	21	30	21	30
				days	days	days	days	days	days	days	days
	Brown water (BW)
	BW1 -0.3gVS/L		0.12	69.91 70.38	672	762	470	537	47.27 49.10
	BW2 -0.5gVS/L		0.20	72.60 72.66	681	736	494	535	52.97 55.32
	BW3 -1.0gVS/L		0.40	73.36 73.35	876	916	642	672	52.62 55.35
	BW4 -2.5gVS/L		1.0	77.95 77.82	738	754	575	587	53.30 59.53
	Food waste (FW)
	FW1 -0.3gVS/L		0.12	72.77 72.85	316	343	230	250	44.16 45.44
	FW2 -0.5gVS/L		0.20	66.58 66.74	333	343	221	229	27.60 28.91
	FW3 -1.0gVS/L		0.40	67.74 67.77	421	425	286	288	59.17 59.72
	FW4 -2.5gVS/L		1.0	54.78 57.30	246	303	135	173	41.32 43.33
	Mixture	BW:FW
	MW1 -1.0gVS/L	1:1	0.40	74.08 *n.d.	287	*n.d.	212	*n.d. 16.94 *n.d.
	MW2 -1.0gVS/L	3:7	0.40	71.16 *n.d.	301	*n.d.	217	*n.d. 26.85 *n.d.
	MW3 -1.0gVS/L	7:3	0.40	72.45 *n.d.	301	*n.d.	220	*n.d. 28.35 *n.d.
	MW4 -2.0gVS/L	1:1	0.80	68.24 *n.d.	417	*n.d.	287	*n.d. 33.47 *n.d.
	*n.d. = not determined

  REFERENCES• APHA, 1998. Standard methods for the examination of water and wastewater American Public Health Association. Washington DC, USA. • Ahn, H.K., Smith, M.C., Kondrad, S.L., White, J.W., 2010. Evaluation of biogas production potential by dry anaerobic digestion of switchgrass--animal manure mixtures. Appl Biochem Biotechnol 160, 965-975. • Cho, J., Park, S., Chang, H., 1995. Biochemical methane potential and solid state anaerobic digestion of Korean food wastes. Bioresour Technol 52, 245-253. • El-Mashad, H.M., Zhang, R., 2010. Biogas production from co-digestion of dairy manure and food waste. Bioresour Technol 101, 4021-4028. • Elmitwalli, T.A., van Leeuwen, M., Kujawa-Roeleveld, K., Sanders, W., Zeeman, G., 2006. Anaerobic biodegradability and digestion in accumulation systems for concentrated black water and kitchen organic-wastes. Water Sci Technol 53, 167-175. • Kujawa-Roeleveld, K., Fernandes, T., Wiryawan, Y., Tawfik, A., Visser, M., Zeeman, G., 2005. Performance of UASB septic tank for treatment of concentrated black water within DESAR concept. Water Science and Technology 52, 307-313. • L. K. Wang, N. K. Shammas, Y. Hung, 2007. Biosolids Treatment Processes, in: Wang, L.K. (Ed.), Biosolids treatment processes. Humana Pr Inc, , pp. 820. • Liu, G., Zhang, R., El-Mashad, H.M., Dong, R., 2009. Effect of feed to inoculum ratios on biogas yields of food and green wastes. Bioresour Technol 100, 5103-5108. • Marthe S. de Graaff, Temmink, H., Zeeman, G., Buisman, C.J.N., 2010. Anaerobic Treatment of Concentrated Black Water in a UASB Reactor at a Short HRT. Water 2, 101-119. • Neves, L., Gonçalo, E., Oliveira, R., Alves, M.M., 2008. Influence of composition on the biomethanation potential of restaurant waste at mesophilic temperatures. Waste Manag 28, 965-972. • Wendland, C., Deegener, S., Behrendt, J., Toshev, P., Otterpohl, R., 2007. Anaerobic digestion of blackwater from vacuum toilets and kitchen refuse in a continuous stirred tank reactor (CSTR). Water Sci Technol 55, 187-194.

11thWWW YES, Arcueil, France, 6 -10 June 2011 LIM, J.W.

14-WWW-YES-2011-Lim-Paper-2011_04_05.doc


Seyed Mohammad Hosseini +

Abdul Hamidi
email: cehamidi@eng.usm.my

Aziz

Syafalni
email: cesyafalni@eng.usm.my

Meisam Valizadeh Kiamahalleh

Keywords: Rice straw, thermochemical pretreatment, Response Surface Method, water resource, pollution

A municipal solid waste produced in urban and rural communities is a serious pollution source of water resource in developing country. One of the main problem in treatment of organic solid waste is its non-readily biodegradability due to the complexity of organic material especially hemicellolluse. This study reports Sodium Hydroxide (NaOH) thermochemical pretreatment of rice straw as a indicators of cellulosic compound to enhance its biodegradability. Laboratory-scale experiments were carried out in completely mixed reactors, 500 ml capacity. In order to optimization of hydrolysis of rice straw, Response Surface Method (RSM) based on three factors and one response design was performed to optimize experimental conditions. The effects of reaction parameters including sodium hydroxide concentration (0-30 g/l), reaction time (10-180 min) and temperature (30-200 o C) were evaluated. The optimum conditions resulted by RSM were: NaOH concentration 29.9 g/l, reaction time 133.1 min. and temperature 157.6 o C. The actual experimental soluble chemical oxygen demand (SCOD) of rice straw soluble was 41200 mg/l under optimum condition, which compared well to the maximum predicted value of 41211 mg/l.

Optimization of NaOH thermo-chemical pretreatment for enhancing solubilisation of rice straw by Response Surface Methodology

INTRODUCTION

Large amount of solid waste is produced each year in the world. Agricultural, municipal and industrial activities are three main generation sources of the solid waste. Lack of planning in this section can be caused pollution in water, soil and air resources . Organic fraction of municipal solid wastes (OFMSW) is composed of two main parts: readily and non-readily biodegradable. The part of non-readily biodegradable is formed a high content of lignocellulosics fiber (5-25% of the total waste mass) . Unlike readily bio degradable such as starch and sucrose that can be easily bio degradation into the monosaccharide, for the utilization of lignocellulosic materials in a bioconversion process, pretreatment is necessary . Therefore, the first step is integrated of chemical and physical treatment systems for dissolving hemicellulose and improving of accessibility of the cellulose for hydrolytic enzymes (Godliving, 2009). Alkaline thermochemical pretreatment process is a well know method that can be used to dissolving complex substrates before biological treatment. Compared with acid or oxidative reagents, alkali treatment appears to be the most effective method in breaking the ester bonds between lignin, Design of experiment (DOE) is a structured, organized method that is used to determine the relationship between the different factors (X i ) affecting a process and the output of the process (Y). DOE uses the smallest possible number of experimental runs to discover and find the optimum settings for the process . DOE provides a cost-effective means for solving problems and developing new processes. The simplest, but most powerful, DOE tool is two-level factorial design, where each input variable is varied at high (+) and low (-) levels and the output observed for resultant changes. Statistics can then help to determine which inputs have the greatest effect on outputs . Response surface methodology (RSM) has been widely used in the empirical study of the relationship between one or more measured responses such as yield , on one hand, and a number of input variables such as time, temperature, pressure, and concentration on the other hand . RSM is a collection of mathematical and statistical techniques that are useful for the modelling and analysis of problems in which a response of interest is influenced by several variables and the response surface can be explored to determine important characteristics such as optimum operating conditions. In the present study, response surface methodology (RSM) was also employed to identify the optimum conditions for enhancing of rice straw dissolving by analyzing the relationships among a number of parameters that affect the overall process. Here we report on the chemical property of rice straw and the optimization of NaOH thermochemical pretreatment process parameters for maximum soluble chemical oxygen demand (SCOD) production. Maximum SCOD production means ability to produce maximum methane gas in anaerobic process or minimum residual of un-compostable materials in compost process. Another word, results of this study could enhance the biogas production or composting process from organic fraction of solid waste.

METHOD

Collection of sample

Around 10 kg of rice straw was collected from a local farm of Sungai Dua in Pulau Penang, Malaysia. Firstly, rice straw was cut to nominally 5-10cm length, washed thoroughly with tap water and then air-dried. It was then grinded to 2-3mm size and used for further treatment. Grinding of rice straw reduces the technical digestion time by 23-59% and increase methane production by 5-25% .

Analytical procedures

The selected physicochemical properties of the raw composting materials were measured prior to starting the thermochemical process experiment. The water-soluble extract was prepared by the following procedure: 5g of sample were first mixed with 100ml of deionised water, then shaken for 2h, and leave for 30 min. The supernatant was then filtered through a filter paper (Whatman No. 1) . SCOD and TKN (total Kjeldahl nitrogen) were measured by dichromate digestion and Kjeldahl method, respectively (Paola Castaldi, 2008). SCOD of samples were determined by Chemical Oxygen Demand (COD) reactor-Hach, and DR2800 Spectrophotometer. pH values were measured by using a pH digital meter (EUTECH, pH 510)), and an EC meter (VSI, Model 30M, 100FT, USA) in aqueous extract (weight : volume = 1:10). Moisture content of raw materials was determined by drying the samples at 105 o C for 24h. Ash was determined in a muffle furnace at 550 o C for 24h, and the organic matter (OM) was calculated as the difference between ash and dry weight as a percentage . A typical hydrolysis mixture consisted of 5g of rice straw and 20ml of sodium hydroxide. The mixture was heated at 30-200 o C on the magnetic stirrer hotplate.

Response surface methodology

The experimental design for the selected process variables was carried out using Central Composite Design (CCD). In order to obtain the required data, the suitable range of values of each of the three variables was identified as shown in Table 1. For three variables (n=3) and five levels (low (-) and high (+)), the total number of experiments were 20 determined by the expression 2 n (2 3 =8 factorial points), 2n (2×3=6 axial points), 6 (centre points, six replications) as given in Table 2. Specific capacitance (SCOD) was selected as the response for the combination of the independent variables. Experimental runs were randomized to minimize the effects of unexpected variability in the observed responses.

Statistical analysis

A quadratic polynomial equation was developed to predict the response as a function of independent variables and their interactions. In general, the response for the quadratic polynomials is described in Eq. ( 1).

)

1 ( 2 0 ∑∑ ∑ ∑ + + + = j ij ij i ii i i x x x x Y β β β β
Here, Y is the response (SCOD value), is the intercept coefficient, is the linear terms, is the squared terms and is the interaction terms, and and are the uncoded independent variables. The model evaluated the effect of each independent variable to a response. The fit quality of the models was judged from their correlation of determination ( 2R ) (Ahmadi et al., 2005;Jo et al., 2008).

Analysis of variance

Analysis of variance (ANOVA) was applied to estimate the effects of main variables and their potential interaction on the SCOD value. The ANOVA table can also be used to test for the statistical significance of the ratio of mean square due to regression and mean square due to residual error. Fisher F-test was used to check for the adequacy of the model, while p-value and Student's test were used to check for the significance of the equation parameters for a response. Three-dimensional response surfaces and contour plots were used for facilitating a straightforward examination of the influence of experimental variables on the responses . The analysis of the experimental design and calculation of the predicted data were carried out using Design Expert Software (version 6.0.6, Stat ease Inc., Minneapolis, USA) to estimate the response of the independent variables.

RESULTS AND DISCUSSION

Physicochemical property of rice straw

Physicochemical parameters were selected based on effective parameter on methane production process and composting process. The results obtained from analyzing the physical and chemical properties of the rice straw are shown in Table 3. Based on these results rice straw residues are brimful in organic matter (OM) content (88.4%) and total carbon (51.272%), have low total nitrogen (0.645%) and high Carbon/Nitrogen (C/N) ratio (79.49). This property is suitable as a carbon source in biogas production or composting process. The results of other studies, (Iranzo, et al., 2004), are slightly different because the climate and soil characteristics of rice filed in Malaysia are different from them solubility of carbon material in water is determined by SCOD. SCOD of rice straw, was determined after 4hr, 6hr, 16hr and 24hr stirring and the obtained results are shown in table 4.

Pretest of thermochemical hydrolysis of rice straw by NaOH

In order to compare the solution rate of rice straw organic matter in water with NaOH, 10 runs of COD test were done. The results from Figure 1 shows SCOD extracted at 2hr by alkaline thermochemical(5g/l), equalled to 15240mg/l, while for water was 1889 mg/l which is 8 times lower in the same condition. It indicated that the alkaline pretreatment has a large effect on solubility of carbon compounds of rice straw in water for utilization. Also, the alkaline pretreatment makes it more accessible for enzymes and bacteria in bio gas production or composting processes . In the study carried out by Penaud, et al (1999), max. SCOD, 63% was obtained at 5g NaOH/l. Heating enhanced the COD solubility to 85% at the higher concentration of sodium hydroxide (26.1g/l) when heated to 140°C for 30 min compared to that of 53.2% which was obtained by Penaud and co-workers at ambient temperature . The result of investigation from anaerobic digestion with waste activated sludge (WAS) by several of pretreatment indicated that when NaOH at 0 to 21g/l was added the SCOD increased from 17.6% to 86.5%

Model fitting and statistical analysis

The results obtained from the experiments conducted are summarized in The response functions are representing Y as the response for SCOD value, A as the coded value of variable temperature, B as the coded value of stirring time and C as the coded value of alkaline concentration. The closer the value of R 2 to unity, the better the empirical models fits the experimental data. On the other hand, the smaller the value of R 2 , the lesser will be the relevance of the dependent variables in the model has in explaining the behavior of variations . Parity plot between the observed data versus predicted data using Eq. ( 2) for the SCOD value and the responses are graphically shown in Figure 2. As can be seen, the predicted values match the observed values reasonably well within the ranges of experimental conditions, with a R 2 value of 0.945. This result suggests the applicability and reliability of the equation in representing the reaction over a range of experimental conditions with sufficient degree of accuracy. Thus, it can be used to simulate the cellulose solublization reaction. Statistical analysis obtained from the analysis of variance (ANOVA) for the response surface 2FI model is shown in Table 5. The value of "PNF" for the models is less than 0.05 to indicate that it is significant and desirable as it indicates that the terms in the model that have a significant effect on the response. The value of P<0.0001 indicates that there is only a 0.01% chance that a "model F-value" this large could occur due to noise in the experiment. Generally P-values lower than 0.01 indicates that the model is considered to be statistically significant at the 99% confidence level . Values greater than 0.1000 indicate the model terms are not significant. Therefore, A, B, C, AB, AC and BC are significant model terms to affect the SCOD value. The "Lack of Fit Fvalue" of 429.82 implies the Lack of Fit is not significant relative to the pure error. Therefore, there is a 19.09% chance that a "Lack of Fit F-value" this large could occur due to noise. Insignificant lack of fit is good as the primary objective was the model should fit the experimental data.

Effect of process conditions

Influence of individual effect

Most of results of studies indicated that pre-treatment can be implemented at low temperatures but with a relatively long time and high concentration of the alkaline . In this study the SCOD evaluated in vary temperature of 30-200 o C. SCOD value was enhanced by increasing of temperature as shown in Figure 3. The result indicated max. SCOD is obtained in around 157.5 o C. Increasing of temperature has inverse effect on production of SCOD. The increase of the SCOD was noticed by increasing the stirring time (Figure 4). Volume of thermochemical reactors is depended to stirring time. So, the selected stirring time should be based on desire rate of SCOD and economic limitation. In a study that was performed in detention time 2.5 to 6.5hr, the solubility of solid waste increased 8.5 to 12.5% . In some study experiments were performed in a fixed temperature and the influence of temperature on solubility have not been evaluated (Suna, et al. 2000;Zhang & Cai, 2008). As shows in Figure 5, the minimum SCOD is obtained at around 7.5-10 g/l. the SCOD is increased as the concentration of sodium hydroxide solution increased from 15 to 30 g/l.

Increasing of SCOD indicates that alkali pretreatment increases the rice straw solubility and its property is improved for bio gas generation process and composting process (Lo´pez Torres & Ma. del C. Espinosa, 2008 ;Fernandes, et al. 2009). Figure 7 shows the effect of the concentration of NaOH and temperature on SCOD produced. From the plot in Figure 7, at higher NaOH concentration, the increase in temperature of reaction until 157.5 o C associates a increasing in solubility of rice straw. For example, at high NaOH concentration of 30 g/l, the SCOD increased from 14547.98 to 41663.52 mg/l when the temperature was increased from 30 to 157.5 o C. From another perspective, by fixing the stirring time, the SCOD also varies with NaOH concentration in two distinct ways, depending upon the extreme of operating conditions employed. Minimum SCOD is obtained in concentration of NaOH of 7.5 g/l with fixed stirring time at 155.7 min. Therefore, it is evident that in order to obtain optimum SCOD by fixing the stirring time, it is indispensable to analyze the relationships of factors A and C. This is because of the indefinite trend observed in investigating such variation in this study as observed in Figure 7.

Figure 8 shows the interaction between the concentration of NaOH and stirring time and their effects on the SCOD produced. Figure 8 indicates the 3D surface plot and the contour plot. In Figure 8, it is evident that the trend observed is the similar to those in Figures 6 and7. This is signifies that the variation of SCOD is highly indefinite and relies solely on the operating conditions such as stirring time and NaOH concentration. By analyzing the Figure, it can be easily seen that at high NaOH concentration at fixed temperature 166.5 o C, the SCOD rises proportionally with stirring time. For example, at 30 g/l of NaOH, when the sample was subject to an alkaline thermochemical process stirring time increment of 180 min from 10 min., it consequently led to a proportional increase of SCOD to 41611.81 mg/l by approximately 17939.83 mg/l.

Besides that, by analyzing the table 2 in another perspective, the increase of the SCOD from 3837.5 mg/l to 41200 mg/L was obtained when NaOH concentration was increased from 0 g/l to 30 g/l, more than 90% decrease. In the condition temperature and stirring time were 200 o C and 180 min. Hence, it has been elucidated that SCOD is influenced indefinitely by the concentrations of NaOH and stirring time, as well as the temperature of reactor.

PROCESS OPTIMIZATION

In the alkaline hydrolysis of rice straw process, its yield can be increased by manipulating the parameters such as the concentrations of alkaline, temperature and detention time. Nevertheless, optimization the response is difficult as the variation of each parameter with hydrolysis of rice straw is highly indefinite as discussed in the previous section. Therefore, in order to optimize the response, the function of desirability was applied using Design Expert software version 6.0.6. In this study, numerical optimization was chosen. Numerical optimization presents a comprehensive and up-to-date description of the most effective methods in continuous optimization. It responds to the growing interest of optimization in engineering, science, and business by focusing on the methods that are best suited to practical problems . To do so, the upper and lower limit of each variable (NaOH concentration, temperature and stirring time) and its response as predicted by the model were provided based on the contour and surface plot obtained previously. The ultimate goal of this optimization was to obtain the maximum response that simultaneously satisfies all the variables properties. Table 6 below shows constraints of each variable and the desired response. Table 7 exhibits the 6 possible solutions which fulfilled all specified conditions. All solution gave desirability value of 1 representing the ideal solution. Therefore, the optimum conditions in any of the given solutions can be chosen for further validation. In this study, solution number 1 (157.6 o C, 133.1 min and 29.9 g/l NaOH) was selected due to its highest prediction of response (41211 mg/l).

For validation purpose, comparisons were made between the predicted optimum condition and its subsequent response with the results obtained from experimental work. As observed the maximum SCOD production predicted for solution 1 was 41211 mg/l (157.6 o C, 133.1 min and 29.9 g/l NaOH). The maximum value of same response obtained from run 20 of experimental work with almost similar condition was 41200 mg/l (200 o C, 180 min and 30 g/l NaOH). The percentage difference between both experimental and predicted values was 0.00027%. The low percentage proved that the model was significant in predicting the response. SCOD extracted in optimum condition of this study is more than other study. For example The optimal solubilization condition for OFMSW was 2.3 g Ca (OH)2/L) and 6.0 h . Under these conditions, dissolving reached levels up to 11.5%. Moreover, in optimal concentration, SCOD decreased from 19,359 to 14,664 mg/L, a finding that also supports the above results . Another study that develops an alkali pretreatment process prior to anaerobic digestion of pulp and paper sludge to enhanced the methane productivity. Maximum SCOD , 83% was achieved in 8 g NaOH/100 g TS sludge

CONCLUSION

A well dissolving of cellulosic compounds in rice straw is achieved by alkaline thermochemical hydrolysis. Alkaline thermochemical hydrolysis process leads to the increasing of transformation of non-solution complex cellulosic compounds to soluble simple compounds. The mathematical model developed could predict the SCOD yield at any point in the experimental domain as well as the determination of the optimal solubilization conditions with sufficient degree of accuracy.

The high accuracy of the model indicates that a two factors interaction (2FI) model could be used to optimize the SCOD value. The effect of alkaline and the thermochemical hydrolysis conditions to achieve an optimal response with 41211 mg/l of SCOD value were found to be 157.6 o C for the reaction temperature, 133.1 min for the stirring time and 29.9 g/l for the NaOH concentration. The interactions between reaction temperature, stirring time and NaOH concentration had been accurately demonstrated and elucidated. These results proved that alkaline thermochemical pretreatment was highly potential for increasing the SCOD value of rice straw and the use of RSM based on CCD was practical for the simultaneous study of effects by process variables on the SCOD value and the possible interaction between them. Also from the results, a process for the production of biogas or compost from organic solid waste shall have two main stages. The two-stage design must involve alkaline pretreatment, followed by anaerobic digestion or composting process unit. In this situation the rejected and risk of water and soil resource waste will be decreased to minimum.

BIBLIOGRAPHY

• Abdelhamid, M.T., Horiuchi, T., Oba, S., 2004. Composting of rice straw with oilseed rape cake and poultry manure and its effects on faba bean (Vicia faba L.) growth and soil properties.

Bioresource Technology, 93, 183-189. • Ahmadi, M., Vahabzadeh, F., Bonakdarpour, B., Mofarrah, E., Mehranian, M., 2005. Application of the central composite design and response surface methodology to the advanced treatment of olive oil processing wastewater using Fenton's peroxidation. Journal of Hazardous Materials,123,[187][188][189][190][191][192][193][194][195] • Anderson, M.J., Kraber, S.L., 1999. Eight keys to successful DOE Quality Digest Magazine, http://www.qualitydigest.com/july99/html/doe.html.

• Cao, W., Zhang, C., Hong, P., Ji, H., 2008. Response surface methodology for autolysis parameters optimization of shrimp head and amino acids released during autolysis. Food Chemistry, 109, 176-183.

• Chow, W.S., Yap, Y.P., 2008. Optimization of process variables on flexural properties of epoxy/organo-montmorillonite nanocomposite by response surface methodology. Express Polymer Letters, 2, 2-11. • Corral, M.C., Samani, Z., Hanson, A., Smith, G., Funk, P., Yu, H., Longworth, J., 2008. Anaerobic digestion of municipal solid waste and agricultural waste and the effect of co-digestion with dairy cow manure. Bioresource Technology, 8288-8293.

• Delgenés, J.P., Penaud, V., Moletta, R. • Jo, M.S., Rene, E.R., Kim, S.H., Park, H.S., 2008. An analysis of synergistic and antagonistic behavior during BTEX removal in batch system using response surface methodology. Journal of Hazardous Materials, 152, 1276Materials, 152, -1284. .

Figure 1 :Figure 2 :

 12 Figure 1: Variation of SCOD of alkaline thermochemical Hydrolysis as function of stirring time (NaOH, 5 g/l, t: 140 o C)

Figure 3 :

 3 Figure 3: Influence of temperature and stirring time on SCOD

Figure 4 :

 4 Figure 4: Influence of stirring time on SCOD.

Figure 5 :

 5 Figure 5: Influence of alkaline concentration on SCOD.

Figure 6 :

 6 Figure 6: Influence of temperature and stirring time on SCOD.

Figure 7 :

 7 Figure 7: Influence of NaOH concentration and stirring time on SCOD.

Figure 8 :

 8 Figure 8: Influence of stirring time and NaOH concentration on SCOD.

  , 2002. Biomethanization of the Organic Fraction of Municipal Solid Wastes. IWA Publishing. • Gaspar, M., Kalman, G., Reczey, K., 2007. Corn fibre as a raw material for hemicellulose and ethanol production. Process Biochem., 42, 1135-1139. • Godliving, M.Y.S., 2009. Review of Recent advances in pretreatment of lignocellulosic wastes and production of value added products. African Journal of Biotechnology, 1398-1415. • Goyal, S., Dhull, S.K., Kapoor, K.K., 2005. Chemical and biological changes during composting of different organic wastes and assessment of compost maturity. Bioresource Technology, 1584-1591. • Heerah, A.S., Mudhoo, A., Mohee, R., Sharma, S.K., 2008. STEAM PRE-TREATMENT OF LIGNOCELLULOSIC WASTES FOR BIOMETHANOGENESIS. Rasayan J. Chem, 503-514.

Table 1 . Independent variables and their levels used for the Central Composite Design

 1

	Coded levels of variables

Table 1 . Complete experimental conditions tested and corresponding observed and predicted values of SCOD value

 1

	Run order	Type		Factors			SCOD value (Response)
			A	B	C	Observed	Predicted
	1	Fact	30.0	10.0	0.0	1654
	2	Fact	200.0	10.0	0.0	2167
	3	Fact	30.0	180.0	0.0	2542
	4	Fact	200.0	180.0	0.0	3838
	5	Fact	115.0	95.0	7.5	9233
	6	Fact	115.0	52.5	15.0	7567
	7	Fact	72.5	95.0	15.0	4617
	8	Fact	115.0	95.0	15.0	7333
	9	Axial	115.0	95.0	15.0	7300
	10	Axial	115.0	95.0	15.0	6983
	11	Axial	115.0	95.0	15.0	6967
	12	Axial	115.0	95.0	15.0	7433
	13	Axial	115.0	95.0	15.0	7183
	14	Axial	157.5	95.0	15.0	7917
	15	Centre	115.0	137.5	15.0	7717
	16	Centre	115.0	95.0	22.5	19750
	17	Centre	30.0	10.0	30.0	3300
	18	Centre	200.0	10.0	30.0	15517
	19	Centre	30.0	180.0	30.0	8250
	20	Centre	200.0	180.0	30.0	41200

Table 3 . Selected physiochemical properties of rice straw

 3

	NO	Parameters	Rice Straw
	1	Organic Matter (%)	88.4
	2	Total Carbon (% dw)	51.272
	3	Total Nitrogen (% dw)	0.645
	4	Carbon/Nitrogen	79.49
	5	PH	7.15
	6	Electrical Conductivity (µSm-1)	2381
	7	Moisture Content (%)	9.76

*All analysis was reported on a dry weight (dw) basisTC= OM(%)×0.58

Table 4 -SCOD of Water soluble of rice straw sample as function of time

 4

	sampling no.	Duration of Stirring (hr)	SCOD of Sample (mg/lit.)
	1	2	1889
	2	4	2580
	3	6	3150
	4	16	4185
	5	24	4220

  table 2. The SCOD value ranged from 1654.17to 41200 mg/l depending on the experimental conditions. Further analysis on the results showed that they developed highest order polynomials equation (in coded units) that could relate SCOD value to the parameters studied. The two factors interaction (2FI) model is given in Eq. (2).

	Y= 8217.91 + 5720.59 A + 3913.72 B + 7450.00 C -12246.72 A 2 -6746.72 B 2 + 20653.26 C 2 + 2689.58 AB + 5419.79 AC + 3509.38 BC	(2)

Table 5 . ANOVA analysis for the quadratic model

 5

	Source	Sum of Squares	Degree of freedom	Mean Square	F Value	Prob > F
			(DF)
	Model	2.782E+008	9	1.513E+008	19.09	< 0.0001	significant
	A	1.302E+008	1	2.782E+008	35.11	0.0001
	B	4.718E+008	1	1.302E+008	16.43	0.0023
	C	2.799E+007	1	4.718E+008	59.55	< 0.0001
	A2	8.495E+006	1	2.799E+007	3.53	0.0896
	B2	7.961E+007	1	8.495E+006	1.07	0.3248
	C2	5.787E+007	1	7.961E+007	10.05	0.0100
	AB	2.350E+008	1	5.787E+007	7.30	0.0222
	AC	9.853E+007	1	2.350E+008	29.66	0.0003
	BC	2.782E+008	1	9.853E+007	12.44	0.0055
	Residual	7.922E+007	1	7.922E+006
	Lack of Fit	7.904E+007	10	1.581E+007	429.82	< 0.0001	No significant
	Pure Error	1.839E+005	5	36777.29
	Cor Total	1.441E+009	5	R-Squared	0.9450
	Std. Dev.	2814.65	19	Adj. R-Squared	0.8955
	Mean	8923.33		Pred. R-Squared	-0.6740
	Critical Value	31.54		Adeq. Precision	19.568
	(C.V)
	PRESS	2.412E+009		R-Squared	0.9450

Table 6 . Constraints of each variable for the numerical optimization of the SCOD

 6

	Type of variable	Goal	Lower Limit	Upper Limit
	NaOH Concentration, g/l	is in range	0	30
	Process temperature, °C	is in range	30	200
	Stirring time, min	is in range	10	180
	Specific capacitance	maximize	1654.17	41200

Table 7 . Optimum conditions for maximum SCOD production

 7

	No.	Temperature , oC	Time, min	NaOH, g/l	SCOD, mg/l	Desirability
	1	157.6	133.1	29.9	41211	1.000
	2	142.9	145.7	30.0	41204	1.000
	3	166.6	164.2	30.0	41387	1.000
	4	163.4	136.1	30.0	41422	1.000
	5	173.8	142.8	30.0	41243	1.000
	6	122.8	115.8	30.0	38712	0.937
	7	116.4	97.8	0.0	21430	0.500
	8	116.8	98.6	0.0	21429	0.500
	9	122.8	108.9	0.0	21273	0.496

11thWWW YES, Arcueil, France, 6 -10 June 2011

• KIM, J., PARK, C., KIM, T.-H., LEE, M., KIM, S., KIM, S.E.-W., LEE, J., 2003. Effects of Various Pretreatments for Enhanced Anaerobic Digestion with Waste Activated Sludge. JOURNAL OF BIOSCIENCE AND BIOENGINEERING, 95, 271-275. • Kumar, R.N., Kong, W.C., Abubakar, A., 1999. UV radiation curing of surface coatings based on ENR-cycloaliphatic diepoxide-glycidyl methacrylate system by cationic photoinitiatorsoptimization of process variables through response surface methodology. Journal of Coatings Technology, 71, 79-88. • Lo´pez Torres, M., Ma. del C. Espinosa, L.n., 2008 , 99, 1320-1328. 15-WWW-YES-2011-Hosseini-Paper-2011-07-11.doc