Method of real-time prognosis of flooding phenomenon in packed column
A method of real-time prognosis of a flooding phenomenon in a packed column includes steps as follows. An online data collection step is conducted, wherein a plurality of values of a pressure drop are collected from the packed column under operation. A detrending step is conducted to obtain a plurality of values of a detrended pressure drop. A fitting step is conducted, wherein the values of the detrended pressure drop are fitted with an EGARCH(p, q) model to obtain a value of at least one of model coefficients. A repeat step is conducted to obtain another value of the at least one of model coefficients. A statistical step is conducted, wherein a value of the monitoring statistic is calculated. A control step is conducted, wherein the value of the monitoring statistic is compared to a control limit.
1. A method of real-time prognosis of a flooding phenomenon in a packed column, comprising:
conducting an online data collection step, wherein a plurality of values of a pressure drop are collected from the packed column under operation;
conducting a detrending step, wherein a trend of the values of the pressure drop is removed to obtain a plurality of values of a detrended pressure drop;
conducting a fitting step, wherein the values of the detrended pressure drop are fitted with an exponential generalized autoregressive conditional heteroskedasticity model with orders of p and q (EGARCH(p, q) model) to obtain a value of at least one of model coefficients;
conducting a repeat step, wherein another value of the at least one of model coefficients is obtained;
conducting a statistical step, wherein a value of the monitoring statistic is calculated based on the values of the at least one of model coefficients;
conducting a control step, wherein the value of the monitoring statistic is compared to a control limit, and an alarm is triggered when the value of the monitoring statistic is greater than the control limit; and
conducting an adjustment step after the alarm is triggered, wherein an operational condition of the packed column is adjusted to make the value of the monitoring statistic less than the control limit.
2. The method of real-time prognosis of the flooding phenomenon in the packed column of claim 1 , wherein the EGARCH(p, q) model is represented by Formula (1):
ln
(
σ
t
2
)
=
α
0
+
∑
i
=
1
p
β
i
log
σ
t
-
i
2
+
∑
j
=
1
q
α
j
[
ɛ
t
-
j
σ
j
-
E
{
ɛ
t
-
j
σ
t
-
j
}
]
+
∑
j
=
1
q
ξ
j
(
ɛ
t
-
j
σ
t
-
j
)
;
(
1
)
wherein t is a time point, σ i 2 is a conditional variance of pressure drop at the time point of t, α 0 , β i , α j and ξ j are the model coefficients, ε i-j is a residual, i is an integer from 1 to p, and j is an integer from 1 to q.
3. The method of real-time prognosis of the flooding phenomenon in the packed column of claim 1 , further comprising repeating the repeat step before conducting the statistical step.
4. The method of real-time prognosis of the flooding phenomenon in the packed column of claim 1 , wherein the p and the q of the EGARCH(p, q) model are determined based on an Akaike information criterion (AIC) or a Bayesian information criterion (BIC).
5. The method of real-time prognosis of the flooding phenomenon in the packed column of claim 1 , wherein the p equals to 1, and the q equals to 1.
6. The method of real-time prognosis of the flooding phenomenon in the packed column of claim 1 , wherein the online data collection step is implemented by measuring and delivering the values of the pressure drop to a computer via a sensing and transmitting element installed in the packed column, and the values of the pressure drop are recorded by the computer.
7. The method of real-time prognosis of the flooding phenomenon in the packed column of claim 6 , wherein the packed column further comprises a blower and a liquid pump, and the blower change a gas flow rate and/or the liquid pump changes a liquid flow rate according to an instruction of the computer.
8. The method of real-time prognosis of the flooding phenomenon in the packed column of claim 1 , wherein the trend of the values of the pressure drop is a linear trend, and the linear trend is obtained by fitting the values of the pressure drop with a least square method.
9. The method of real-time prognosis of the flooding phenomenon in the packed column of claim 1 , wherein the value of the monitoring statistic and the control limit are obtained by a nonparametric statistical process control (SPC) method.
10. The method of real-time prognosis of the flooding phenomenon in the packed column of claim 9 , wherein the nonparametric SPC method is a nonparametric SPC method using Mann-Whitney test.
11. The method of real-time prognosis of the flooding phenomenon in the packed column of claim 1 , wherein, in the control step, the value of the monitoring statistic and the control limit are plotted in a control chart.
12. A method of real-time prognosis of a flooding phenomenon in a packed column, comprising:
conducting an online data collection step, wherein a plurality of values of a pressure drop are collected from the packed column under operation;
conducting a detrending step, wherein a trend of the values of the pressure drop is removed to obtain a plurality of values of a detrended pressure drop;
conducting a fitting step, wherein the values of the detrended pressure drop are fitted with an exponential generalized autoregressive conditional heteroscedasticity model with orders of p and q (EGARCH(p, q) model, to obtain a value of at least one of model coefficients;
conducting a control step, wherein the value of at least one of model coefficients is compared to a control limit, and an alarm is triggered when the value of at least one of model coefficients is greater than the control limit; and
conducting an adjustment step after the alarm is triggered, wherein an operational condition of the packed column is adjusted to make the value of at least one of model coefficients less than the control limit.
13. The method of real-time prognosis of the flooding phenomenon in the packed column of claim 12 , wherein the EGARCH(p, q) model is represented by Formula (1):
ln
(
σ
t
2
)
=
α
0
+
∑
i
=
1
p
β
i
log
σ
t
-
i
2
+
∑
j
=
1
q
α
j
[
ɛ
t
-
j
σ
j
-
E
{
ɛ
t
-
j
σ
t
-
j
}
]
+
∑
j
=
1
q
ξ
j
(
ɛ
t
-
j
σ
t
-
j
)
;
(
1
)
wherein t is a time point, σ i 2 is a conditional variance of pressure drop at the time point of t, α 0 , β i , α j and ξ j are the model coefficients, ε i-j is a residual, i is an integer from 1 to p, and j is an integer from 1 to q.
14. The method of real-time prognosis of the flooding phenomenon in the packed column of claim 12 , wherein the p and the q of the EGARCH(p, q) model are determined based on an AIC or a BIC.
15. The method of real-time prognosis of the flooding phenomenon in the packed column of claim 12 , wherein the p equals to 1, and the q equals to 1.
16. The method of real-time prognosis of the flooding phenomenon in the packed column of claim 12 , wherein the trend of the values of the pressure drop is a linear trend, and the linear trend is obtained by fitting the values of the pressure drop with a least square method.
17. The method of real-time prognosis of the flooding phenomenon in the packed column of claim 12 , wherein the value of at least one of model coefficients and the control limit are obtained by a nonparametric SPC method.
18. The method of real-time prognosis of the flooding phenomenon in the packed column of claim 17 , wherein the nonparametric SPC method is a nonparametric SPC method using kernel density estimation.
19. The method of real-time prognosis of the flooding phenomenon in the packed column of claim 12 , wherein, in the control step, the value of at least one of model coefficients and the control limit are plotted in a control chart.