Two－Dimensional Model of Hydraulic Fracturing in Geosciences：Effects of Fluid Buoyancy

Ｔｗｏ－ＤｉｍｅｎｓｉｏｎａｌＭｏｄｅｌｏｆＨｙｄｒａｕｌｉｃＦｒａｃｔｕｒｉｎｇｉｎＧｅｏｓｃｉｅｎｃｅｓ：Ｅｆｆｅｃｔｓ　ｏｆ　Ｆｌｕｉｄ　ＢｕｏｙａｎｃｙＹｏｓｈｉｔｏＮａｋａｓｈｉｍａ；ＭｉｔｓｕｈｉｒｏＴｏｒｉｕｍｉ（ＧｅｏｌｏｇｉｃａｌＩ...

Two-Dimensional Model of Hydraulic Fracturing in Geosciences: Effects of Fluid Buoyancy

Hydraulic fracturing occurs in diverse fields of geosciences. We introduce effects of fluid buoyancy into the CGDD (Christianovich-Geertsma-DeKlerk-Daneshy) model of hydranlic fracturing. In the model, a two-dimensional one-sided crack in impermeable rock propagates from a horizontally lying wellbore or fluid reservoir at depth; the crack plane is inclined at a prescribed angle to the horizontal; incompressible and Newtonian fluid less dense than the surrounding rock is injected consecutively from the wellbore or fluid reservoir into the crack at a given injection rate. A solution of the crack propagation is obtained using lubrication theory for turbulent or laminar film flow and linear elastic fracture mechanics. The solution shows the importance of the buoyancy of the fluid in the crack as a driving force or a resisting force of the crack propagation. For example,when the water injection rate into a vertical fracture is 10-2 m2/s and the vertical length of the propagating fracture exceeds 100 m, the fluid buoyancy is important (1) as a driving force if the fracture is formed by the upward propagation of a vertical crack and (2) as a resisting force if it is formed by the downward propagation.