Numerical modelling of hydraulic fracturing

In this paper we present a numerical model for hydraulic fracturing purposes. The rock formation is modelled as a poroelastic material based on Biot’s Theory. A fracture is represented in a discrete manner using the eXtended Finite Element Method (X-FEM). The fluid flow is governed by a local mass balance. This means that there is an equilibrium between the opening of the fracture, the tangential fluid flow, and the fluid leakage. The mass balance in the fracture is solved with a separate equation by including an additional degree of freedom for the pressure in the fracture. The fracture can grow in arbitrary directions by using an average stress criterion. We show a result of hydraulic fracture propagation for a 2D circular borehole. The fracture direction is consistent with the expected direction

The enhanced local pressure model for the accurate analysis of fluid pressure driven fracture in porous materials

In this paper, we present an enhanced local pressure model for modelling fluid pressure driven fractures in porous saturated materials. Using the partition-of-unity property of finite element shape functions, we describe the displacement and pressure fields across the fracture as a strong discontinuity. We enhance the pressure in the fracture by including an additional degree of freedom. The pressure gradient due to fluid leakage near the fracture surface is reconstructed based on Terzaghi’s consolidation solution. With this numerical formulation we ensure that all fluid flow goes exclusively in the fracture and it is not necessary to use a dense mesh near the fracture to capture the pressure gradient. Fluid flow in the rock formation is described by Darcy’s law. The fracture process is governed by a cohesive traction separation law. The performance of the numerical model for fluid driven fractures is shown in three numerical examples

Development of a micro-optofluidic temperature sensor

A fluorescent micro-optofluidic temperature sensor is developed using a temperature sensitive dye. The sensor can measure temperatures in microregions up to 70 ºC and is applicable in lab-on-a chip devices. It is fabricated using soft lithography method and uses Rhodamine B dissolved in water as a temperature indicator

Development of a micro-optofluidic temperature sensor

A fluorescent micro-optofluidic temperature sensor is developed using a temperature sensitive dye. The sensor can measure temperatures in microregions up to 70 ºC and is applicable in lab-on-a chip devices. It is fabricated using soft lithography method and uses Rhodamine B dissolved in water as a temperature indicator

Experimental Observation of Differences in the Dynamic Response of Newtonian and Viscoelastic Fluids

In this paper we present an experimental study of the dynamic responses of a Newtonian fluid and a Maxwellian fluid under an oscillating pressure gradient. We use laser Doppler anemometry in order to determine the velocity of each fluid inside a cylindrical tube. In the case of the Newtonian fluid, the dissipative nature is observed and the response obeys the Zhou and Sheng universality (PRB 39, 12027 (1989)). In the dynamic response of the Maxwellian fluid an enhancement at the frequencies predicted by the corresponding theory (PRE 58, 6323 (1998)) is observed.Comment: 5 pages, 4 Figures, paper to be published in Phys. Rev.