Singular Integral Equations. By N.I. Muskhelishvili. Translated fromthe 2nd Russian edition by J.R.M. Radok. Pp. 447. F1. 28.50. 1953. (Noordhoff, Groningen)

Publisher Summary
This chapter focuses on fundamentals of poroelasticity. The presence of a freely moving fluid in a porous rock modifies its mechanical response. Two mechanisms play a key role in the interaction between the interstitial fluid and the porous rock: (i) an increase of pore pressure induces a dilation of the rock; and (ii) compression of the rock causes a rise of pore pressure, if the fluid is prevented from escaping the pore network. These coupled mechanisms bestow an apparent time-dependent character to the mechanical properties of the rock. If excess pore pressure, induced by compression of the rock, is allowed to dissipate through diffusive fluid mass transport, further deformation of the rock progressively takes place. The rock is more compliant under drained conditions than undrained ones. The chapter discusses the formulation and analysis of coupled deformation–diffusion processes, within the framework of the Biot theory of poroelasticity. The Biot model of a fluid-filled porous material is constructed on the conceptual model of a coherent solid skeleton and a freely moving pore fluid.

Fundamentals of Poroelasticity

A system for remotely monitoring an individual. The system includes a server system for generating a script program from a set of queries. The script program is executable by a remote apparatus that displays information and/or a set of queries to the individual through a user interface. Responses to the queries that are entered through the user interface together with individual identification information are sent from the remote apparatus to the server system across a communication network. The server system also includes an automated answering service for providing a series of questions from a stored set of questions for an individual at the remote apparatus to respond to, storing responses to each provided question in the series of questions and providing a service based on the individual's response to the questions.

Networked system for interactive communication and remote monitoring of individuals

A system and method is described that enables a health care provider to monitor and manage a health condition of a patient. The system includes a health care provider apparatus operated by a health care provider and a remotely programmable patient apparatus that is operated by a patient. The health care provider develops a script program using the health care provider apparatus and then sends the script program to a remotely programmable patient apparatus through a communication network such as the World Wide Web. The script program is a computer-executable patient protocol that provides information to the patient about the patient's health condition and that interactively monitors the patient health condition by asking the patient questions and by receiving answers to those questions. The answers to these health related questions are then forwarded as patient data from the remotely programmable patient apparatus to the health care provider apparatus through the communication network. The patient data may also include information supplied by a physiological monitoring device such as a blood glucose monitor that is connected to the remotely programmable patient apparatus. When the patient data arrives at the health care provider apparatus, the patient data is processed for further management of the patient's health condition by the health care provider, such as forwarding another script program to the remotely programmable patient apparatus.

Remote health monitoring and maintenance system

article i nfo We describe a novel cubic Hermite collocation scheme for the solution of the coupled integro-partial differential equations governing the propagation of a hydraulic fracture in a state of plane strain. Special blended cubic Hermite-power-law basis functions, with arbitrary index 0b αb1, are developed to treat the singular behavior of the solution that typically occurs at the tips of a hydraulic fracture. The implementation of blended infinite elements to model semi-infinite crack problems is also described. Explicit formulae for the integrated kernels associated with the cubic Hermite and blended basis functions are provided. The cubic Hermite collocation algorithm is used to solve a number of different test problems with two distinct propagation regimes and the results are shown to converge to published similarity and asymptotic solutions. The convergence rate of the cubic Hermite scheme is determined by the order of accuracy of the tip asymptotic expansion as well as the O(h 4 ) error due to the Hermite cubic interpolation. The errors due to these two approximations need to be matched in order to achieve optimal convergence. Backward Euler time-stepping yields a robust algorithm that, along with geometric increments in the time-step, can be used to explore the transition between propagation regimes over many orders of magnitude in time.

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Computer Methods in Applied Mechanics and Engineering

This paper reviews recent results of a research program aimed at developing a theoretical framework to understand and predict the different modes of propagation of a fluid-driven fracture. The research effort involves constructing detailed solutions of the crack tip region, developing global models of hydraulic fractures for plane strain and radial geometry, and identifying the parameters controlling the fracture growth. The paper focuses on the propagation of hydraulic fractures in impermeable rocks. The controlling parameters are identified from scaling laws that recognize the existence of two dissipative processes: fracturing of the rock (toughness) and dissipation in the fracturing fluid (viscosity). It is shown that the two limit solutions (corresponding to zero toughness and zero viscosity) are characterized by a power law dependence on time and that the transition between these two asymptotic solutions depends on a single number, which can be chosen to be either a dimensionless toughness or a dimen...

Propagation Regimes of Fluid-Driven Fractures in Impermeable Rocks

Poroelastic response of a borehole in a non-hydrostatic stress field

A phenomenological model for the drilling action of drag bits

Hydraulic fractures represent a particular class of tensile fractures that propagate in solid media under pre-existing compressive stresses as a result of internal pressurization by an injected viscous fluid. The main application of engineered hydraulic fractures is the stimulation of oil and gas wells to increase production. Several physical processes affect the propagation of these fractures, including the flow of viscous fluid, creation of solid surfaces, and leak-off of fracturing fluid. The interplay and the competition between these processes lead to multiple length scales and timescales in the system, which reveal the shifting influence of the far-field stress, viscous dissipation, fracture energy, and leak-off as the fracture propagates.

Emmanuel Detournay

Papers

Fundamentals of Poroelasticity

Propagation Regimes of Fluid-Driven Fractures in Impermeable Rocks

Poroelastic response of a borehole in a non-hydrostatic stress field

A phenomenological model for the drilling action of drag bits

Mechanics of Hydraulic Fractures