Open AccessEstablishment and Solution of Mathematical Model for Unconventional Cracks in Multi-stage Fracturing of Horizontal Wells
Author(s) -
Zhanjun Chen,
Xuefen Liu,
Feng Cao
Publication year - 2019
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1325/1/012138
Subject(s) - superposition principle , discretization , geology , mechanics , hydraulic fracturing , fracture (geology) , inversion (geology) , mathematical model , geotechnical engineering , mathematics , mathematical analysis , physics , paleontology , structural basin , statistics
Cracks tend to be asymmetrical during complex fracture processes. In this paper, the mathematical model of well test interpretation of vertical cracks under finite diversion conditions is established by the basic theory of point source function. The interpretation model of multi-stage fracturing unconventional fracture horizontal well test well is obtained by using the principle of pressure drop superposition. The semi-analytical solution of the model is obtained by integral transformation. By numerically discretizing the cracks, combined with the semi-analytical solution and the Duhamei principle, according to the Stehfest numerical inversion method, the bottom hole pressure and pressure derivative curves of the multi-stage fracturing unconventional crack horizontal wells are drawn.