Field application shows that asphaltene precipitation will occur in heavy oil reservoirs during the CO2 huff–puff process in horizontal wells, leading to blockage, which will greatly reduce the effect of subsequent huff and puff cycles. Based on the huff and puff test of composite long core with both horizontal and vertical placement, the development effect of horizontal well is compared with that of vertical well, and the IOR mechanism is revealed. Then, based on the CO2 huff and puff experiment of long core under different pressure conditions, the IOR and carbon storage potential were determined, and the maximum number of effective huff–puff cycles were determined too. The distribution and difference of inorganic matter and organic matter precipitation under different pressure conditions were compared. The study shows that CO2 huff–puff can increase the recovery factor of a heavy oil reservoir by 17.70% and the primary carbon storage efficiency by 18.20%. The recovery factor of an individual cycle decreased significantly when the cycle number grows, and the economical number was 2 cycles. The precipitation of organic matter caused by low pressure huff and huff mainly occurs in the near well position. The higher the pressure is, the farther the plugging part will be from the producing well, and the maximum proportion of permeability reduction ratio is 8.68%. The inorganic precipitation mainly occurs in the middle-end part of the reservoir, and the influence of pressure can be ignored, and the maximum permeability reduction ratio is 4.56%.