The mechanical behaviour and shape memory effects were studied in the porous Ti-45.0 at. % Ni alloy produced by self-propagating high-temperature synthesis. It is shown that the porous Ti-45.0 at % Ni alloy is deformed by the same mechanisms as a cast Ti 50 Ni 50 alloy. At low temperatures, the deformation of the porous alloy is realised via martensite reorientation at a low yield limit and by dislocation slip at a high yield limit. At high temperatures (in the austenite B2 phase) the porous Ti-45.0 at % Ni alloy is deformed by the stress-induced martensite at a low yield limit and by dislocation slip at a high yield limit. The pseudoelasticity effect is not found in this alloy, while the transformation plasticity and the shape memory effects are observed on cooling and heating under a constant load. The values of the transformation plasticity, and the shape memory effects, depend linearly on the stress acting on cooling and heating. The temperatures of the martensitic transformation increase linearly when the stress rises up to 80 MPa. The porous Ti-45.0 at % Ni alloy accumulates an irreversible strain on cooling and heating and demonstrates unstable functional behaviour during thermal cycling.
The Unified Fracture Design (UFD) or constant proppant volume technique introduced by Valko and Economides1,2 was originally developed for pseudo-steady state flow conditions and oil industry has been applying this technique even for low permeability reservoirs where the transient conditions last considerable time. There is nothing in the literature that shows that optimum fracture design using constant-proppant volume concept for pseudo-steady state flow is the same or different than the optimum one for transient flow conditions.
This paper will present an extension of UFD technique (fixed proppant volume technique) to cover not only pseudo-steady conditions but also transient flow regime. Results have shown that each "dimensionless time snap shot" presents a similar J[D] type curve[3] with different optimum design curve. Therefore, the optimum fracture design is time dependant until pseudo-steady state condition is reached. Additionally, this paper presents a equivalent pseudo-steady state equation to calculate the dimensionless productivity index (J[D]) of finite-conductivity fractured wells producing at either transient or pseudo-steady state conditions. The pseudosteady state equation uses the definition of equivalent wellbore radius presented by Rueda[3], to take into account the finite conductivity, fracture penetration and time dependency of the solution. Following pseudo-steady state equation concept, new correlations (from 1500 numerical simulation runs) to calculate shape factors and f-functions for a fractured well were developed, where the f-function is an extension of the original Cinco-Ley's function for transient and pseudo-steady state flow period. These correlations are functions of dimensionless fracture conductivity (C[FD]), fracture penetration ratio (I[x]), and dimensionless time (t[A]). This pseudo-steady state equivalent equation can be used to generate a series of new J[D] type curves of a finite-conductivity fractured well for different dimensionless times t[DA]. Having this equation, a new approach to get the optimum fracture geometry for a specific proppant number (N[prop]) for a "fixed period of time" was also developed and presented in this paper.
INTRODUCTION
For unfractured well, Ramey and Cobb[4] presented the constant rate solution of the diffusivity equation at pseudo-steady state for any closed reservoir of any shape:
(1)
Where t[DA] is dimensionless time, A is the drainage area; C[A] is the Dietz shape factor as function of the drainage area shape and well location.
Rueda[3] presented that the average dimensionless pressure for fractured well in square drainage area can be written as follows:
(2)
The production of piston rings, the main failure of which is wearing of working surfaces, takes a considerable place during various parts producing. Therefore, large attention is payed to the problems of wear resistance improvement of pairs of friction of piston rings surfaces. The creation of combination of high hardness with high plasticity is real in a heterogeneous alloy. The problem of developing a method for increasing the wear resistance of piston rings seems to be a topical issue.
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