A borehole heat exchangers (BHEs) combined with pumping-injection well is established in areas where the groundwater is shallow and the seepage velocity is weak. The pumping and injection wells are set on both sides of the BHEs. According to the three-dimensional unsteady heat transfer model in aquifer, the convection-dispersion analytical solution of excess temperature is derived that considers groundwater forced seepage and thermal dispersion effects and axial effect of the BHEs. Then, the dimensional analysis method and similarity criteria we used to build a controllable forced seepage sandbox. The software FEFLOW 7.1 is adopted and the simulation results are validated by the theoretical analysis and the indoor experiment test. On this basis, the numerical simulation calculation is used to explore the influence of different pumping-injection flow volume on the Darcy flow velocity of the aquifer where the BHEs are located, the average heat transfer efficiency and the heat transfer rates with borehole depth. The results show that when the pumping flow volume increases from 200 m3∙d-1 to 1200 m3∙d-1, the Darcy velocity correspondingly increases to about 10 times. The average heat efficiency coefficient of the BHEs is increased by 11.5% in cooling stage, and by 7.5% in heating stage. When the pumping-injection flow volume is 400~600 m3∙d-1, the increment of heat transfer rates of the BHEs reaches 12.8~17.9 W∙m-1 and 3.6~4.2 W∙m-1 per unit of borehole depth during the cooling stage and heating stage respectively, and then decreases as the flow volume increases gradually.