Abstract
Therein used the well-known method of successive approximation of functions for solving the problem of transient deformation of an elastic medium under the influence of variable internal pressure in wells in paper. The desired function – the maximum tensile stresses – is represented as a product of power functions, each of which depends on only one parameter. The regularity of changes in the maximum tensile stresses and the main factors influencing this process, which is fully confirmed by the independent theory of dimensions, are established.
Highlights
The class of power functions [1] has become widespread for representing functional dependencies
As a function, which we are looking for, we take the value of the maximum tensile stresses in the first half-wave of its change, referred to the maximum amplitude of the internal pressure p0 before the relief
The time of pressure drop in the working agent is calculated in each case separately for a specific type of working agent and parameters of technological wells
Summary
The class of power functions [1] has become widespread for representing functional dependencies. The main advantages of such a presentation are the ability to assess the degree of influence of parameters on the function itself and determine the compliance of the physical content of the resulting dependencies with the properties of the original process function. For the case of plane deformation, the calculation of radial σr and tangential σθ stresses can be carried out using the formulas given in [4]. The main parameters influencing the process of transient deformation of an elastic medium include the inner radius of the well r0, the internal pressure p0 of the working agent, the elastic wave velocity in the massif υp, and the internal pressure in the working agent release time tc. All further calculations and transformations are reduced to the maximum value of tensile radial stresses in the first half-wave of stress variation at the site of inertial forces (Fig. 1) [5]
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