Innovations in Supercritical Fluids - American Chemical Society

Chapter 25

Release Mechanisms of Extractable Compounds from Plant Matrices During Supercritical Fluid Extraction Downloaded by UNIV OF CALIFORNIA SAN DIEGO on November 16, 2015 | http://pubs.acs.org Publication Date: May 5, 1995 | doi: 10.1021/bk-1995-0608.ch025

Mathematical Modeling Ö. Hortaçsu, Ο. (Navaro) Aeskinazi, and U. Akman Department of Chemical Engineering, Bogaziçi University, 80815 Bebeck, Istanbul, Turkey Two mathematical models: Cellular Permeable-Tube Arrays (CPTA) model and Serially-Interconnected Perfectly-Mixed Tanks (SI-PMTs) model were proposed in an attempt to explain the release mechanisms of extractable compoundsfromplant matrices during supercritical fluid extraction. Models enable phenomenological description of probable three-phase mass transfer taking place within plant cells. A complex chromatographic-type release is envisioned for the supercritical-fluid extraction of materials from plant matrices. A parametric sensitivity analysis is conducted on the SI-PMTs model. Extraction of various natural compoundsfromplants is still an important and growing research area within the field of supercritical-fluid (SF) technology. Presently, in addition to the growing number of experimental studies both in extraction-process development and in physical-property determination areas, some mathematical modeling work on the extraction phenomena is appearing in the related literature (7,2). The mathematical models suggested for the purpose of defining the extraction phenomena from plant materials seem to consider the plant matrices as catalyst-like porous structures in/on which the extractable components are present. However, the mechanisms of transport even in the most complicated porous solid structures are quite simple when compared with the phenomena in the cellular plant structures. Thus, a more realistic modeling of the plant matrices would be beneficial for a better understanding of the extraction mechanismsfromplant materials. In contrast to a porous catalyst particle, the internal structure of which cannot be clearly defined, plant materials have structures which have definite characteristics depending upon the functions of the various parts of the plants. These structures in a simplified manner may be modeled as comprising of a cellular portion, an intercellular space, and a pore-like tubular section between the membranes of the adjacent cells (3). Living plant cells, which are surrounded by membranes, contain other functional parts such as the nucleus, cytoplasm, vacuoles, etc. It is now well known that the 0097-6156/95/0608-0364$12.00/0 © 1995 A m e r i c a n Chemical Society

In Innovations in Supercritical Fluids; Hutchenson, K., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1995.

Downloaded by UNIV OF CALIFORNIA SAN DIEGO on November 16, 2015 | http://pubs.acs.org Publication Date: May 5, 1995 | doi: 10.1021/bk-1995-0608.ch025

25.

HORTACSU ET AL.

Extractable Compounds from Plant365 Matrices

vacuoles play an important role in the plant cells and they are instrumental in storing the waste and toxic products as well as the useful materials such as oils, proteins, flavanoids, alkaloids and pigments, etc., which are mainly produced in the cytoplasm of the cell (4). In case of plants available for extraction however, the plant body is made up mostly of dead mature cells which are at least partially dehydrated. In these structures, it is expected that most of the materials aimed for recovery via supercritical-fluid extraction (SFE) are stored in the vacuoles which are bounded by the vacuolar membrane, which in turn is bounded by the cell membrane. In such cells, a reasonable assumption would be that the vacuolar volume and the cell volume are quite close quantities. In living cells, the interrelationships between a cell (with its vacuole, membranes, etc.) and its contents are very complicated. The different mobilities of dissolved substances in the cells remind us of a chromatogram, in which compounds are separated from one another by their solubility in a solvent and by the tenacity with which they adhere to another material such a filter paper or a column packing (3). Thus, a chromatographic-type behavior may be expected during the release of componentsfromthe cell during SFE. The objective of this paper is to suggest the preliminary fundamentals of structured plant materials and the role of such structures during extractions using a solvent like supercritical carbon dioxide ( S C - C O 2 ) . Noting the above simple, but important, facts about the plant structures, we feel that the mathematical models suggested to explain the extraction phenomena from such matrices should contain elements which represent the facts as closely as possible. For this purpose, we have proposed two main types of models for SFE of materials from plant matrices constituting of mature dead cells. Thefirstmodel is a Cellular Permeable-Tube Arrays (CPTA) model comprising of cells made up of tubes with permeable walls, which have boundaries to pore-like intercellular pathways and the latter is a SeriallyInterconnected Perfectly-Mixed Tanks (SI-PMTs) model. Model equations are developed which enable the phenomenological description of probable three-phase mass-transfer taking place within the plant cells. A sensitivity analysis is conducted on the SI-PMTs model and the importance of each parameter in the model is investigated. The CPTA model is given as the basis of our ultimate aim. Mathematical Modeling Basic Assumptions. Plant materials most often used for extracting various substances via SFs could be classified into the following main groups: leafy materials, plant bulk, flowers, and seeds or fruits. It is well documented in literature that gaseous, liquid, and crystalline substances may be present in the plant cells and that these substances are quite mobile in the living plant structure (4). For example, gases may move at velocities near 50 m/hr in living plants, the plant materials in the solution form are quite mobile in the cytoplasm and diffusion of liquids and gases are possible through the cell membranes (3). As already noted in almost all cases, when the plant material is ready for extraction, the cells it contains are dead, and in many or most instances, the plant material is at least partially dry. Besides, mostly in the seed-type plant materials a large percentage (up to 80% by weight) of the cell material may be composed of various



366

INNOVATIONS IN SUPERCRITICAL FLUIDS

oils, proteins and sometimes alkaloids, whereas flavonoids and coloring materials may be the desired extractable materials in some of the leafy and flowery materials (5). For a first approximation, we will concern ourselves with oil-rich seed-type materials, which may still have some water (about 5-10%) in their cellular structure, and cells are taken as the smallest possible plant portion of independent entity. The extractable materials from the tubes may be picked up by SF via extraction (or dense-gas stripping)fromthe free liquid in the cells and/or via desorption from the cell walls. It will also be assumed that all of the extractable materials in the plant matrices are in the cells and not in the intercellular regions. It also seems to be very reasonable to presume that the extractable solutes in the plant matrices may exist both in an extractable liquid state and in an adsorbed state on the cell walls. Afinalpoint to note is that the models suggested below are for a single-solute system. Extension of these models to mixtures, some or all of which may be SF- extractable solutes is possible via proper thermodynamic modeling and will be dealt with in the future. Cellular Permeable-Tube Arrays Model. The physical picture for the Cellular Permeable-Tube Arrays (CPTA) model, an idealized version of natural occurrences in plant structures, is depicted in Figure 1. Figure la shows a single cellular tube with a permeable membrane. Figure lb depicts how the CPTA model may be used for a plant section which may be made up of tube arrays of differing geometry in the axial direction, each array having tubes of different lengths. Finally, in Figure le, a vertical cross-section of a cylindrical plant element representing the cellular and intercellular regions is shown. When Figures la, lb and lc are compared with actual plant structures, it is evident that some degree of idealization of the structure has been made for the purpose of simpler mathematical formulation. At this point, it should be adequate to say that the actual plant structures may be determined under proper microscopic investigation, and the idealized structures may be assumed on this basis. The shape of the extracted body should also be defined for the purpose of proper mathematical formulation. Here, only as an example, a cylindrical-shaped plant structure is considered. As it is depicted in Figure lb, plant material may initially be thought to be constituted of series of cylindrical sections of different lengths, each having a somewhat different internal structure. In this geometry each tube may be taken to represent a set of horizontally-connected plant cells, and the shaded spaces between the tubes could be taken as the intercellular regions as in plants. In plant structures made up of mature dead cells which have at least partially lost their water, it is reasonable to assume that the cell membranes and the intercellular spaces are present at minimum volumes, thus taking up only a very small portion of the total structure. All the extractable materials are assumed to be in the cellular tubes in the form of free liquid in the cell and as adsorbed on the cell walls. In the permeable membrane (wall region), it is assumed that diffusion of the extracted solute and the solvent may simultaneously occur with the adsorption and/or desorption of the solute(s) on the membrane matrix. The intercellular spaces themselves have an axial solvent flow and they also receive fluxfromthe neighboring cellular tubes. The physical picture of the CPTA model as depicted in Figure 1, may be considered to have two distinct regions: the tubes making up the tubular array and the


HORTACSU ET AL.

25.

367

Extractable CompoundsfromPlant Matrices

intertubular (intercellular) regions. In the tubular array, each tube may be considered independently and the model equations given below are valid for each tube individually. This concept actually brings theflexibilityto the model that all tubes in the array do not have to have the same characteristics, however, the assumption of geometrically identical tubes will bring important simplicities to the formulation and to the solution of the model. A tube of length L j is considered to have a homogenous inner region of radius Rj, which is surrounded by a permeable wall of thickness (R - Rj), as indicated in Figure 1 as w. In the tubes two phases exist: namely the stationary liquid content of the cellular region which originally contains almost all the extractable solute species except for the already adsorbed on the cell walls, and the SF solvent phase which flows in the tubes picking up the solute speciesfromthis major source, as indicated in Figure 1 as L and G, respectively. Thus, the material balance equations have to be written for each phase. For the solvent-phase region (0 < r < Rj), the concentration profile of a solute component C ( t , z , r ) , is governed by the following PDE and the initial and boundary conditions:


0

T

G

T

T

J_jLi

dCcVl , OGLaGL(Co(CL)-CG) ^ CG(0,z ,r ) = C°(z ,r ) = C° =0, C (t,0,r ) = C (t,z ,r )-^^ K

r

DGz

UG

+DGr

"âT- "^T" âz7

T

T

T

T

G

T

p

z =o T

dC (t,L ,r ) _ dC (t,z ,0) Sz^ ' οϊγ G

T

T

G

c (* * * \-c ί* * τι \ C (t,z ,Ki)-L (t,z ,Ki)

T

G

T

w

(2)

T

It is assumed that the possible mass-transfer of the solute species to the other parts of the plant matrix originates from the stationary liquid contents of the tubular cells. For the stationary liquid-phase region (0 < r < Rj), the concentration profile of a solute component C (t,z ,r ), is governed by the following PDE and the initial and boundary conditions: T

L

ac _

^c

L

T

T

Γι d ( ac V

L

L

KoGL GL ( C G ( C L ) - C G ) a

(3)

6L

C (0 z ,r ) = q ( z r ) = q , L

)

T

T

T )

T

^(^»Γ,0)

=

3C (^ ,R )

()>

L

r

i

=

0 >

-D^^Mi^Lpfc^CLO.O.rr^-CpCt.Zp.rp)], (4) D z L

aCL(

T

^ '

rT)

=K p[c;{C (t,LT,rr)}-C (t,z ,r )] L

L

p

p

p


p

p

368

INNOVATIONS I N SUPERCRITICAL FLUIDS

Now we look at the permeable tube-wall region. All solute brought into this region is picked up by the solvent flowing within the inner region of the tube. As the solvent diffuses through the permeable tube-wall, either solute is adsorbed on the wall surfaces or is desorbed from the wall surfaces depending upon the level of saturation of the solvent phase. Therefore, in the tube wall region (Rjrr) = Qw w

T

()

T

The driving force ( q ^ - q ) will become positive for adsorption and negative for desorption. The second group of equations, as noted earlier, deal with the intertubular region which is the hatched region in Figure lc. In this region initially no extractable solute is assumed to be present, and the solvent is assumed to be in bulk flow. However, as the extraction proceeds, solute is carried into this region from the permeable walls of the adjoining tubes. In real plant structures, some portion of this intertubular region is bounded by the cylindrical tubes forming closed triangularshaped regions (as shown in Figure lc by the small hatched regions surrounded by three tubes of triangular layout). However, difficulties associated with mathematical modeling of the boundary conditions between cylindrical tubes and triangular-shaped intertubular duct, forces one to treat all the hatched regions in Figure lc as homogenous (i.e., tube-pitch is somewhat greater than 2RQ). Therefore, here, the intertubular region will be considered as a cylindrical annular region with radius equal to the approximate radius of the bundle of tubes ( R ) . Also, it will be envisioned that the plant pellets or the pellet-like plant cuts with radii R and length L contains randomly-distributed cellular tubes (that may have different lengths L and radii R ) w

P

P

p

T


Q

25. HORTACSU ET AL.

Extractable CompoundsfromPlant Matrices 369

as shown in Figure lb. From this point of view, the concentration profile of a solute component C ( t , z , r ) within a pellet-shaped intertubular region (0Dwr axial and radial dispersion coefficients in the permeable wall region inletflowrateoffreshsolvent to n cell (n) mass-transfer coefficient for sorption in the wall-region A W mass-transfer coefficient for hquid/mtertubular-region mass transfer L P K mass-transfer coefficient for tube-to-pellet region mass transfer overall gas/liquid mass-transfer coefficient OGL solid/gas mass-transfer coefficient Ho U


Λ

G

Λ

L

A

F

K

K

P T

K

solid/liquid mass-transfer coefficient pellet-like intertubular region length tube length outletflowratefromη cell

LP

M

Λ

( n )

Λ

Innovations in Supercritical Fluids - American Chemical Society

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