Multi-objective optimization for free-phase LNAPL recovery using evolutionary computation algorithms

Figures & data

Fig. 2 Comparison between measured and calibrated hydraulic head values.

Fig. 1 Field site domain, flow boundary conditions and calibrated hydraulic head field.

Fig. 3 (a) Initial LNAPL distribution and location of extraction wells; (b) Final LNAPL thickness distribution after the PSO optimal pumping strategy has been implemented.

Table 1 Groundwater flow and LNAPL transport model parameters

Parameter	Value
Equivalent porosity	0.03
Hydrocarbon density	878.7 kg m^−1
Hydrocarbon viscosity	6.04 × 10^−4 Pa s
Number of pumping/resting periods	10
Brooks-Corey model
λ	2.4
Pd	2.9 cm
Sr	0.05

Table 2 Test for the selection of the optimal algorithm parameter values

	PSO
k	0.3	0.2	0.4	0.6
Objective value	−154.172	−150.503	−153.901	−152.175
φ1 = φ2	2.05	2.5	3	3.5
Objective value	−154.172	−144.504	−144.646	−143.359
	GA
Pc	0.8	0.6	0.7	0.9
Objective value	−142.872	−142.498	−141.838	−141.752
Pm	0.1	0.05	0.2	0.3
Objective value	−142.872	−142.103	−141.976	−141.513
	DE
Cr	0.8	0.6	0.7	0.9
Objective value	−152.796	−152.549	−152.114	−146.989
F	0.5	0.1	0.8	1.2
Objective value	−152.796	−146.783	−146.566	−143.626

Table 3 Optimization parameters

Parameter	Value
Population number	25
Maximum number of iterations	500
Pumping rate bounds: Q min, Q max	0 kg s^−1, 0.2 kg s^−1
Time period bounds	0.2–10 d
Cost coefficient: c 1	1 € m^−3
Weights: w 1, w 2	0.1–0.9

Table 4 Optimal pumping strategies for the GA, DE and PSO regarding pumping rates and pumping and resting times

Pumpingwell	Q (kg s^−1)			Time	t (d)
	GA	DE	PSO		GA	DE	PSO
P1	0.06	0.38	0.37	Pump1	5.63	3.71	1.34
P2	0.02	0.16	0.20	Rest1	9.72	6.02	4.38
P3	0.03	0.24	0.29	Pump2	0.61	1.32	0.20
P4	0.01	0.43	0.01	Rest2	9.95	9.80	5.98
P5	0.14	0.11	0.33	Pump3	0.79	0.12	0.25
P6	0.03	0.08	0.38	Rest3	9.78	4.38	2.86
P7	0.10	0.23	0.50	Pump4	1.91	0.10	0.20
P8	0.04	0.49	0.07	Rest4	9.19	8.75	10.00
P9	0.04	0.14	0.07	Pump5	0.57	0.11	1.27
P10	0.01	0.15	0.19	Rest5	9.88	9.20	8.11
M1	0.03	0.01	0.17	Pump6	0.64	0.66	3.24
M2	0.06	0.15	0.35	Rest6	9.89	6.74	5.29
M3	0.08	0.19	0.14	Pump7	0.09	0.53	0.90
M4	0.01	0.37	0.01	Rest7	9.66	8.59	7.37
M5	0.08	0.03	0.17	Pump8	0.90	1.72	0.25
M6	0.01	0.23	0.01	Rest8	8.51	9.07	7.88
M7	0.02	0.04	0.38	Pump9	0.67	0.41	0.20
M8	0.02	0.16	0.01	Rest9	8.68	3.68	9.96
M9	0.01	0.09	0.22	Pump10	1.32	0.33	0.20
M10	0.03	0.16	0.03	Rest10	2.64	3.71	1.34
	Objective function value
	−144.43	−181.55	−180.59	Total	101.3	78.95	71.22

Fig. 4 Convergence rate of GA, DE and PSO algorithms.

Fig. 5 Calculated Pareto points.