A coupled factorial-analysis-based interval programming approach and its application to air quality management

Figures & data

Table 1. Technical data

Technical Data	Period 1	Period 2	Period 3
SO2-generation rates, Sik (tonne/day)
Power plant	[141.5, 151.5]	[164.5, 174.5]	[199.0, 209.0]
Petroleum refinery	[38.0, 48.0]	[40.3, 50.3]	[42.6, 52.6]
Steel mill	[7.9, 8.5]	[8.2, 8.8]	[8.5, 9.1]
SO2-emission standards, eik (tonne/day)
Power plant	[39.2, 44.2]	[37.7, 42.7]	[36.2, 41.2]
Petroleum refinery	[8.0, 8.6]	[7.5, 8.1]	[7.1, 7.6]
Steel mill	[2.2, 2.5]	[1.7, 2.0]	[1.2, 1.5]
SO2-loading capacities, apk (μg/m^3)
Agricultural zone	[27.2, 31.2]	[25.9, 29.9]	[23.8, 27.8]
Residential zone	[55.0, 65.0]	[46.0, 56.0]	[37.0, 47.0]

Table 2. SO₂-emission control techniques installed by different sources

Source	Control Technique
Power plant	OPA, AA, LWS, SC
Petroleum refinery	OPA, AA, SC
Steel mill	OPA, AA, SC
Notes: OPA = oxidation packed absorption; AA = alkali absorption; LWS = limestone wet scrubbing; SC = spray chamber.

Table 3. SO₂-treatment efficiencies and operating costs of different pollution control techniques

Technique	Efficiency (%)	Period	Operating Cost ($/tonne)
OPA	[78, 88]	k = 1	[40.0, 54.0]
		k = 2	[48.0, 60.0]
		k = 3	[54.2, 70.2]
AA	[89, 99]	k = 1	[60.0, 70.0]
		k = 2	[66.5, 76.5]
		k = 3	[73.6, 83.6]
LWS	[67, 77]	k = 1	[27.0, 37.0]
		k = 2	[31.8, 41.8]
		k = 3	[37.3, 47.3]
SC	[84, 94]	k = 1	[50.0, 60.0]
		k = 2	[58.3, 68.3]
		k = 3	[67.7, 77.7]

Figure 1. The study system.

Table 4. Effective stack heights of different sources

Source	Effective Stack Height (m)
Power plant	282
Petroleum refinery	140
Steel mill	130

Table 5. Solutions obtained from the CFA-IP model

Source i	Period k	Control Measure j	Treated SO2 Amounts (tonne/day)
Power plant	1	OPA	0
		AA	0
		LWS	88.00
		SC	[53.50, 63.50]
	2	OPA	0
		AA	0
		LWS	57.53
		SC	[106.97, 116.97]
	3	OPA	0
		AA	[138.95, 148.95]
		LWS	60.05
		SC	0
Petroleum refinery	1	OPA	5.33
		AA	0
		LWS	0
		SC	[32.67, 42.67]
	2	OPA	0
		AA	[0.96, 10.96]
		LWS	0
		SC	39.34
	3	OPA	11.95
		AA	[30.65, 40.65]
		LWS	0
		SC	0
Steel mill	1	OPA	[7.90, 8.50]
		AA	0
		LWS	0
		SC	0
	2	OPA	4.87
		AA	0
		LWS	0
		SC	[3.33, 3.93]
	3	OPA	1.81
		AA	[6.69, 7.29]
		LWS	0
		SC	0
Total operating cost ($10^6) [62.10, 82.34]

Figure 2. SO₂-abatement schemes for (a) power plant, (b) petroleum refinery, and (c) steel mill.

Table 6. Effects of significant factors and their interactions for lower and upper bounds of system cost

	Lower-Bound Solution			Upper-Bound Solution
Factor	Standardized Effects	Sum of Squares	% Contribution	Standardized Effects	Sum of Squares	% Contribution
A: Power plant ESp1	−0.37	8.97	0.21	−0.42	11.17	0.22
B: Power plant ESp2	−0.56	20.25	0.48	−0.85	45.96	0.92
C: Power plant ESp3	−1.31	110.05	2.63	−1.41	126.81	2.55
K: OPA efficiency	−3.25	677.98	16.19	−2.69	464.11	9.33
L: AA efficiency	−1.55	154.18	3.68	−1.34	114.59	2.30
M: SC efficiency	−1.35	117.16	2.80	−1.62	168.10	3.38
N: LWS efficiency	−6.09	2375.25	56.71	−7.42	3527.18	70.94
AN	0.37	8.97	0.21	0.42	11.17	0.22
BN	0.31	6.34	0.15	—	—	—
CN	−0.37	8.75	0.21	−0.34	7.21	0.15
KL	1.39	123.61	2.95	1.09	76.05	1.53
KM	1.40	125.09	2.99	1.49	141.86	2.85
KN	1.49	142.79	3.41	0.84	45.42	0.91
LM	1.38	121.89	2.91	1.22	95.24	1.92
MN	0.45	13.00	0.31	0.40	10.16	0.20
Notes: ESp1, ESp2, and ESp3 are the abbreviations for emission standards during periods 1, 2, and 3, respectively.

Figure 3. Pareto charts of effects for (a) lower-bound system cost and (b) upper-bound system cost.

Figure 4. Contributions of factor interactions to lower and upper bounds of system cost.

Figure 5. Interaction plot for power plant ESp2 and LWS efficiency.