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The effects of CO2-water-rock interactions on the mechanical properties of shale are essential for estimating the possibility of sequestrating CO2 in shale reservoirs. In this study, uniaxial compressive strength (UCS) tests together with an acoustic emission (AE) system and SEM and EDS analysis were performed to investigate the mechanical properties and microstructural changes of black shales with different saturation times (10 days, 20 days and 30 days) in water dissoluted with gaseous/super-critical CO2. According to the experimental results, the values of UCS, Young’s modulus and brittleness index decrease gradually with increasing saturation time in water with gaseous/super-critical CO2. Compared to samples without saturation, 30-day saturation causes reductions of 56.43% in UCS and 54.21% in Young’s modulus for gaseous saturated samples, and 66.05% in UCS and 56.32% in Young’s modulus for super-critical saturated samples, respectively. The brittleness index also decreases drastically from 84.3% for samples without saturation to 50.9% for samples saturated in water with gaseous CO2, to 47.9% for samples saturated in water with super-critical carbon dioxide (SC-CO2). SC-CO2 causes a greater reduction of shale’s mechanical properties. The crack propagation results obtained from the AE system show that longer saturation time produces higher peak cumulative AE energy. SEM images show that many pores occur when shale samples are saturated in water with gaseous/super-critical CO2. The EDS results show that CO2-water-rock interactions increase the percentages of C and Fe and decrease the percentages of Al and K on the surface of saturated samples when compared to samples without saturation.

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In order to maintain a uniform distribution of pareto-front solutions, a modified NSGA-II algorithm coupled with a dynamic crowding distance (DCD) method is proposed for the multi-objective optimization of a mixed-flow pump impeller. With the pump meridional section fixed, ten variables along the shroud and hub are selected to control the blade load by using a three-dimensional inverse design method. Hydraulic efficiency, along with impeller head, is applied as an optimization objective; and a radial basis neural network (RBNN) is adopted to approximate the objective function with 82 training samples. Local sensitivity analysis shows that decision variables have different impacts on the optimization objectives. Instead of randomly selecting one solution to implement, a technique for ordering preferences by similarity to ideal solution (TOPSIS) is introduced to select the best compromise solution (BCS) from pareto-front sets. The proposed method is applied to optimize the baseline model, i.e. a mixed-flow waterjet pump whose specific speed is 508 min 1 m 3 s 1 m. The performance of the waterjet pump was experimentally tested. Compared with the baseline model, the optimized impeller has a better hydraulic efficiency of 92% as well as a higher impeller head at the design operation point. Furthermore, the off-design performance is improved with a wider highefficiency operation range. After optimization, velocity gradients on the suction surface are smoother and flow separations are eliminated at the blade inlet part. Thus, the authors believe the proposed method is helpful for optimizing the mixed-flow pumps.mixed-flow pump, waterjet pump, multi-objective optimization, numerical simulation, modified NSGA-II Citation: Huang R F, Luo X W, Ji B, et al. Multi-objective optimization of a mixed-flow pump impeller using modified NSGA-II algorithm.