Environmental Engineering Reference
In-Depth Information
as process losses. Therefore, Г consists of a proportion γ
ij
, defined as the ratio of the
output to the input. The action of this matrix on
A
can eliminate input flow that will
not be directed to the output. In other words,
Ã
is calculated by Eq. (9.1), in which
⊗ is the Hadamard product and element
i
,
j
of
Ã
is γ
ij
φ
ij
a
ij
.
A
=Γ⊗ Φ⊗
(
A
)
(9.1)
Let us now consider the phosphorus contained in residues such as wastewater, live-
stock manure, and slag. The input table describes the phosphorus that is input into
each industrial sector. However, the phosphorus contained in fertilizers does not en-
tirely transfer to agricultural products but accumulates in the soil, water, and other
residues as well. For example, phosphorus is used in the production of pig iron,
which uses 131 × 10
3
kilotons (kt) of iron ore, 20 × 10
3
kt of limestone, and 36 × 10
3
of coke, accompanied by 78.6 kt-P, 2.5 kt-P, and 9.4 kt-P amounts of phosphorus,
respectively. However, the phosphorus used for steel products is one of the most im-
portant aversive substances, thus almost all the phosphorus ends up being removed
as steelmaking slag. In this case, the yield ratio of phosphorus in steel materials is
almost zero.
The next stage of the process is to divide
n
into three types of exclusive and non-
empty groups—Product (
P
), Resource (
R
), and Material (
M
)—and divide
Ã
into
nine sub-matrices, as shown in Eq. (9.2), where
Ã
PM
is
n
P
×
n
M
,
Ã
PR
is
n
P
×
n
R
, and
:
nnnn
++=
PMR
AAA
AA A A
AAA
PP
PM
PR
(9.2)
=
MP
MM
MR
RP
RM
RR
P, R,
and
M
meet the following conditions according to their processing levels:
iR
a. Resources are collected from the global environment, not produced.
,
A
=
0
i PMR
b. Materials are produced from resources.
,
,
iM
i PM
c. Products are produced from materials and products.
A
=
0
,
,
RP
A
=
0
Under condition (a), resources are not produced within this system. In other words,
this condition represents the lowest level of material processing. Under condition
(b), materials are produced only from resources with a low level of processing, and
not from the materials themselves. Owing to the equality of all levels of processing,
these materials are not introduced into other materials. This requirement is neces-
sary to avoid double counting. Under condition (c), a product is made from materi-
als with a low level of processing, but a product with a low level of processing is
introduced into a product with a high level of processing. Resources are not input
directly into a product.
The application of this condition to
Ã
gives the submatrix in Eq. (9.3):
