This Presentation is a brief of the Mass Balance Reconciliation Theory

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The Mass Balance Reconciliation Theory- in Brief

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In UAE. Any reproduction, usage or copy of the same shall be approved and permitted by the Owner.
Trust Technical ServicesTheory of Mass Balance Reconciliation
Single-component balance
• Examples: * mass balancing
*energy balancing
*utility NW
100
1
2
40 29
58
12
D 1 = -2 D 1 = + 1
balance difference D 2= - 2

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In UAE. Any reproduction, usage or copy of the same shall be approved and permitted by the Owner.
Trust Technical ServicesMaterial Balancing Theory
1
3 4
2
f (x , y , c) = 0
constant
F1-(F2+F3)=0
F3-F4=0
F3 is unmeasured
F4 is observable

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Trust Technical ServicesReconciliation Equations
xi
+ = xi + ei
Measured value is xi
Reconciled value is xi
+
e = measurement error
e is characterised by
standard deviation s

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measured
unmeasured
7
4
6
531
2
flows
1,2,3 measured redundant
4 measured non-redundant
7 unmeasured observable
5,6 unmeasured non-observable
Redundancy & Observability

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Trust Technical ServicesLeast Square Error Minimization
For redundant systems:
f (x+, y, c)  0
Solution: Xi=Reconciled value
X+= Measured
value
f (x, y, c) = 0
and
least sq error minimization formula
xi - reconciled values
min
2
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i i
i xx
s
s Standard deviation