Alexander M. Linkov

Analytical solution of hydraulic fracture problem for a non-Newtonian fluid

The paper presents the analytical solution to a hydraulic fracture driven by a non-Newtonian fluid and propagating under plane strain conditions in cross sections parallel to the fracture front. Conclusions are drawn on the influence of fluid properties on the fracture propagation.

Complex variables BIE and BEM for a plane doubly periodic system of flaws

Abstract New complex variable, singular and hypersingular, boundary integral equations (CV‐BIE) are derived for doubly periodic plane elasticity problems. They refer to systems of blocks (grains), inclusions, holes and cracks. Their forms, convenient when adjusting conventional programs for non‐periodic systems to periodic problems, are suggested. Simple formulae are presented to calculate effective compliances in complex variables. Numerical implementation of the derived complex variable hypersingular (CVH) BIE in the mentioned forms is carried out by appropriately adjusting a program of CVH‐BEM, previously developed for non‐periodic problems. It is used to check accuracy and to obtain new results for doubly periodic systems of cracks. Stress intensity factors (SIFs) and effective compliances are calculated for straight cracks in square and triangular lattices to compare them with published results. They show agreement within the accuracy reached by other authors. New data on SIFs and effective complianc...

Modeling of fluid flow, stress state and seismicity induced in rock by an instant pressure drop in a hydrofracture

The paper presents a methodology and results of simulations of fluid flow, stress state, and seismicity induced in rock by instant pressure drop in a hydrofracture.

Numerical Modeling of Rock Deformation under Compression

A procedure is proposed and substantiated for automatic tracing the trajectories of the normal tension cracks for a quantitative investigation of their growth and rock deformation under compression. For isolated cracks, the error of hypotheses simplifying models of the processes in question is estimated. For doubly periodic systems of cracks, the features of crack growth and their role in changing the effective properties of medium are considered.

Comparative study of rheological properties of suspensions by computer simulation of Poiseuille and Couette flows

The article presents results of numerical experiments performed to evaluate the effective rheological properties of a mixture of a fluid with solid particles. The numerical simulation of the Couette and Poiseuille flows shows that in the both cases, the effective viscosity and non-Newtonian properties of the suspension coincide to the accuracy of standard deviation. The authors define the area of applicability of Newtonian fluid model to modeling fluid and proppant mix and determine conditions for plugs at high concentrations of proppant.

Comparative Study of Stresses Near Crack Tip for Layered and Homogeneous Models of Composite

Layered composite, bonded with two half planes, one of which contains a crack, is compared with homogeneous anisotropic media, bonded similar half planes. This problem is analyzed for the case of antiplane strain. Stress singularities are investigated, and numerical results are presented and compared for these models. Conclusions drawn concern thresholds within which the model of homogeneous media can serve to simulate a layered composite.

On Amplification of Seismic Waves near Disturbances

The theory describing amplification of failure near disturbances is generalized on homogeneous waves incident on the contact losing the strength. Viscous deformations on the contact are taken into consideration. The equations describing reflected and refracted waves of amplification are derived. The general conditions are given for arising amplification. Parameters controlling the process are estimated for particular cases.

On solving continuum-mechanics problems by fast multipole methods

It is shown analytically and numerically that the kernel-independent fast multipole method provides the accuracy and computational complexity of the analytical method if circular (spherical in 3D) equivalent surfaces are used.

Numerical solution of plane hydrofracture problem in modified formulation under arbitrary initial conditions

The solution to a hydraulic fracture problem for the model of Khristianovich–Geertsma–de Klerk is obtained on the basis of the modified formulation of the problem, which, in contrast with the conventional approach, employs the particle velocity rather than the flux. This served to complement the system of ordinary differential equations, resulting after spatial discretization, with the speed equation. The complete system is solved by the Runge–Kutta method for arbitrary initial conditions. The decaying influence of the initial conditions on key characteristics of a fracture (opening and length) at the end of a treatment, is established and numerically analyzed.

Modified Formulation, ε-Regularization and the Efficient Solution of Hydraulic Fracture Problems

Analytical models and numerical simulation are important means to increase understanding and to enhance efficiency of hydraulic fracturing. The reasons for developing and using them are clearly explained, for instance, by Mack and Warpinski [1]. Thus, there is no need to dwell on them. Rather we focus on improving analytical and numeric methods used to the date. Our objective is to suggest new approaches for developing accurate, robust and stable simulators on the basis of recent analytical and computational findings [2-6].