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232 3. Heterogeneous Processes and Reactor Analysis

generally defined as mass divided by vWhile mass is an easily measurable quan- olume.
olume. So, tity, it is not the case for v referring to a porous particle, which is its v olume and
how can it be estimated? What should be done with the pores of the particles? Depending
ied, on the how this volume is specif there are various types of density .
Definitions

A porous particle contains many interior voids known as open or closed pores. A pore is char-
acterized as open when it is connected to the exterior surface of the particle, whereas a pore
is closed (or blind) when it is inaccessible from the surface. So, a fluid flowing around a par-
There are several densities used in the lit- ticle can “see” an open pore, b ut not a closed one.
erature and therefore one has to know which density is being referred to (Table 3.15). True
density may be defined as the mass of a powder or particle divided by its volume excluding
all pores and voids. True density is also referred to as absolute density or crystalline density
in the case of pure compounds. However, this density is very difficult to be determined and
can be calculated only through X-ray or neutron dif fraction analysis of single-crystal sam-
ples. Particle density is defined as the mass of a particle divided by its hydrodynamic v ol-
ume. The hydrodynamic volume includes the volume of all the open and closed pores.
Practically, the hydrodynamic volume is identified with the volume included by the outer
surface of the particle. The particle density is also called “apparent” or “en density v elope” .
The term “skeletal density” is also used. The sk eletal density of a porous particle is higher
than the particle one, since it is the mass of the particle divided by the volume of solid mate-
rial making up the particle. In this volume, the closed pores volume is included . The interre-
lationship between these two types of density is as follows (ASTM, 1994; BSI, 1991):

p (3.556)
s
1 p

b (3.557)
p
1
where:
p the internal particle porosity
the bed density
b
the bed porosity
the particle density .
p
,
Bulk density, or packing density includes all pores and voids (interparticle spaces) in its
calculation. This value depends on the form of the particle (powder, tablets, or e xtrudates)
and the packing procedure. It is extensively used in reactor designing since this value con-
nects the solid volume with that of the reactor .
When a porous particle is immersed in a fluid, it has an ef fecti v ferent from e density dif
e density” the skeletal and particle density. This density is termed “wet” or “ef (Perry v fecti
and Green, 1999).

(1 ( ) (3.558)
)
h p f s p s p s f p f p