This paper throws light upon the process of the rate of injection Q, the pressure gradient vertical fracture formation during the hydraulic＿ and the fracture width is: rupture of a reservoir by a non-penetrating axf) liquid. Formulae are deduced for determining the change of pressure in time at the drilling hole bottom with a constant injection rate of the The distribution of pressure along the fracrupture liquid, and the change in the length, ture depends on the form of the fracture, which thickness and configuration of the fracture. is also unknown. Let us assume that Ap Fractures are formed in the plane, perpen- = = p - p, is the difference between the liquid dicular to that of the formation - "vertical pressure in the fracture and in the bed. At the cracks", - in case of hydraulic rupture of the beginning of the fracture Ap = Apw at the formation by highly viscous, hard penetrating drilling hole wall; Ap decreases along the fraco r non-penetrating liquid. Let us consider tho ture. Ap = 0 at point 2'0. A part of the simplest case of the formation mechanism of fracture between the point positioned at such a symmetrical fracture in the homogeneous 2'0 and the fracture's end is filled with the reservoir reservoir, providing that there was an initial liquid. There is no liquid pressure on the wall fracture at the drilling hole face. here.
It is assumed that the bed is subjected to a Let us assume that the fracture form at the confining compression caused by the rock preso < <5' 1 part is determined by the following sure. The compressing tensions resulting from equation: the rock pressure, are equal to 5, = - qoD in infinity, where q,> 0. Let us assume that the PI case plotted on Fig. 1 is taking place in all horizontal sections of the bed at a given mo- where 260 is the maximum width of the fracture ment. The length of the fracture at this mo- at the drilling hole wall. Suppose - 2) = s and ment is 2, while that of the fracture's part filled 1 with the viscous liquid is equal to 2'0. It should A is a dimensionless parameter. be taken into account that the viscous liquid does not cover the whole length of the fracture, [31 and the mechanism of the reservoir rupture is to a certain extent analogous to that of the Then, integrating Eq. [i], we obtain: wedge. The rate of the liquid injection into one of the fractures is Q, the reservoir thick- 5 ness h, and the liquid viscosity,. 26 is the width of the fracture. The resulting relation between - (*) Academy of Sciences, Moscova, TJSSR. 580 PROCEEDINGS FOURTH WORLD PETROLEIJM CONGRESS-SECTION II /T .O .P. as Ap = 0 at the fracture point with the ab- Now let usIsolvelanother, still more simplified problem. As the diameter of the hole is scissa 5 0 TO = - then 1 rather small, if compared to the leng
