Abstract: After the hydraulic fracturing work ends and the pumping stops, the cracks fractured will show a tendency to close. Though fracturing sands try to stand in its way, there still exist closing and pressing to a certain degree. Thus the effect of hydraulic fracturing is not so optimistic as was calculated in the past. So, this paper tries to inquire into the problem that cracks are pressed and closed after the fracturing work ends and the puming stops. In light of the analysis of the sand deposit state in the fractured cracks, the pressing and closing of fractured cracks will be divided into two developing courses in which fracturing fluid continues to lose and sand heap is pressed. Therefore, a mathematical model is established for the problem that cracks are pressed and closed after the fracturing work ends and the pumping is stopped.

Key words: Hydraulic fracturing, Closed fracture, Rock stress, Compaction, Mathe-matical model