Dmj David Smeulders

Dynamic permeability: reformulation of theory and new experimental and numerical data

The dynamic interaction between a rigid porous structure (porosity ϕ) and its saturating fluid is studied. From the microscopic conservation laws and constitutive relations, macroscopic equations are derived. An averaging technique proposed and discussed by for example Levy, Auriault and Burridge & Keller is used, from which we reformulate the theory by Johnson, Koplik & Dashen. The macroscopic equations then serve to describe the high-frequency behaviour of an oscillating fluid within a porous sample. This behaviour may be characterized by the length parameter Λ and by the tortuosity parameter α ∞ . It is shown that Λ and α ∞ , which describe an oscillatory flow behaviour, may be evaluated on the basis of steady potential flow theory. Numerical results are then presented for several pore geometries, and for these geometries, the steady-state permeability k 0 is computed numerically also. The parameter 8α ∞ k 0 /ϕΛ 2 , first introduced by Johnson et al. , is then evaluated and appears to be weakly dependent on pore geometry. This implies that for many porous media the dynamic interaction is described by an approximate scaling function. New experimental data, concerning oscillating flows through several porous media, are presented. Within limits of accuracy, these data are in agreement with the approximate scaling function.

Guided wave modes in porous cylinders: Experimental results

In this paper guided wave modes in porous media are investigated. A water-saturated porous cylinder is mounted in the test section of a shock tube. Between the porous sample and the wall of the shock tube a water-filled annulus exists. For very small annulus width, bulk waves are generated and one-dimensional modeling is sufficient. Otherwise two-dimensional effects become important and multiple guided wave modes occur. Using a newly developed traversable positioning system in the shock tube, the frequency-dependent phase velocities and damping coefficients in the 1-120 kHz frequency range were measured. Pronys method was used for data processing. Agreement was found between the experimental data and the two-dimensional modeling of the shock tube which was based on Biots theory.

Shock-induced borehole waves in porous formations: Theory and experiments

The characteristics of the pseudo-Stoneley wave along boreholes in porous formations are studied in a broad band of frequencies (100 Hz–200 kHz). Experiments are performed using a shock tube technique to excite the pseudo-Stoneley wave in a water saturated confined reservoir. The formation is a natural Berea sandstone. Frequency-dependent phase velocities and damping coefficients are measured using this technique. Quantitative agreement between the experimental results and the theoretical predictions is found for the phase velocity in the frequency range from 10 to 50 kHz. Theoretically, the influence of the permeability on the phase velocity, attenuation, radial displacement, and pore pressure is studied on the basis of the Biot theory and the contribution of the different bulk modes to the average radial displacement is analyzed in the frequency domain. The numerical results indicate that the permeability dependence at low frequencies is caused by the Biot slow wave.

Dispersive surface waves along partially saturated porous media

Numerical results for the velocity and attenuation of surface wave modes in fully permeable liquid/partially saturated porous solid plane interfaces are reported in a broadband of frequencies (100?Hz–1?MHz). A modified Biot theory of poromechanics is implemented which takes into account the interaction between the gas bubbles and both the liquid and the solid phases of the porous material through acoustic radiation and viscous and thermal dissipation. This model was previously verified by shock wave experiments. In the present paper this formulation is extended to account for grain compressibility. The dependence of the frequency-dependent velocities and attenuation coefficients of the surface modes on the gas saturation is studied. The results show a significant dependence of the velocities and attenuation of the pseudo-Stoneley wave and the pseudo-Rayleigh wave on the liquid saturation in the pores. Maximum values in the attenuation coefficient of the pseudo-Stoneley wave are obtained in the 10–20?kHz range of frequencies. The attenuation value and the characteristic frequency of this maximum depend on the liquid saturation. In the high-frequency limit, a transition is found between the pseudo-Stoneley wave and a true Stoneley mode. This transition occurs at a typical saturation below which the slow compressional wave propagates faster than the pseudo-Stoneley wave.

Guided wave modes in porous cylinders: Theory

The classical theory of wave propagation in elastic cylinders is extended to poro-elastic mandrel modes. The classical theory predicts the existence of undamped L modes and damped C, I, and Z modes. These waves also appear in poro-elastic mandrels, but all of them become damped because of viscous effects. The presence of the Biot slow bulk wave in the poro-elastic material is responsible for the generation of additional mandrel modes. One of them was already discussed by Feng and Johnson, and the others can be grouped together as so-called D modes. The damping of these D modes is at least as high as the damping of the free-field slow wave.

Pressure wave propagation in a partially water‐saturated porous medium

Reflection and transmission of a stepwise pressure wave incident to a partially water‐saturated porous medium is investigated. The strongly dispersive character of the phase velocities and damping due to air bubble resonance causes pressure over‐ and undershoot in reflection and a fast oscillatory disturbance propagating into the porous medium. Theoretical results are compared with new results from shock tube experiments. A qualitative agreement is found.

A Partition of Unity-Based Model for Crack Nucleation and Propagation in Porous Media, Including Orthotropic Materials

In this paper, we present a general partition of unity-based cohesive zone model for fracture propagation and nucleation in saturated porous materials. We consider both two-dimensional isotropic and orthotropic media based on the general Biot theory. Fluid flow from the bulk formation into the fracture is accounted for. The fracture propagation is based on an average stress approach. This approach is adjusted to be directionally depended for orthotropic materials. The accuracy of the continuous part of the model is addressed by performing Mandel’s problem for isotropic and orthotropic materials. The performance of the model is investigated with a propagating fracture in an orthotropic material and by considering fracture nucleation and propagation in an isotropic mixed-mode fracture problem. In the latter example we also investigated the influence of the bulk permeability on the numerical results.

Similarity of sharp-edged porous media

Abstract The dynamic interaction between a rigid porous structure (porosity φ) and its saturating fluid is studied. From the microscopic conservation laws and constitutive relations, macroscopic equations are derived. An averaging technique proposed and discussed by authors like Levy, Auriault and Burridge and Keller is used. The macroscopic equations are studied in the high-frequency limit. The high-frequency behaviour is characterized by the tortuosity parameter α∝ and by an effective pore radius Λ, denned previously by Johnson et al. The low frequency behaviour is characterized by the ratio of the steady-state permeability K0 and the porosity φ. A similarity parameter M = 8α ∝ K 0 φΛ 2 (in the two-dimensional case M = 12α ∝ K 0 φΛ 2 ) is defined, which is approximately equal to 1 for configurations that have smooth microscopic geometries. For sharp-edged pore geometries, however, M is no longer found equal to one. Numerical computations are performed using a Schwartz-Christoffel transformation.

A Spectroscopic Technique for Local Temperature Measurement in a Micro-Optofluidic System

We present a spectroscopy technique to measure temperature locally in a polydimethylsiloxane micro-optofluidic chip with integrated optical fibers and minimal optical components. The device was fabricated in one step with fiber coupler grooves followed by the manual integration of the optical fibers. The experimental setup consists of a micro-optofluidic chip with a pair of optical fibers for excitation and fluorescence collection, a laser module, and a spectrometer. The laser module is coupled to one of the optical fibers to guide the light into the microchannel. The fluorescence signal is collected by a second integrated optical fiber placed orthogonally. A spectroscopy technique is used to measure the local temperature in a microchannel (500 μm wide and 125 μm in height) using Rhodamine B as a temperature indicator. It is shown that for a flow rate between 200 and 400 μL/min, the local temperature can be determined.

A DFT based equilibrium study of a chemical mixture Tachyhydrite and their lower hydrates for long term heat storage

Chloride based salt hydrates are promising materials for seasonal heat storage. However, hydrolysis, a side reaction, deteriorates, their cycle stability. To improve the kinetics and durability, we have investigated the optimum operating conditions of a chemical mixture of CaCl2 and MgCl2 hydrates. In this study, we apply a GGA-DFT to gain insight into the various hydrates of CaMg2Cl6. We have obtained the structural properties, atomic charges and vibrational frequencies of CaMg2Cl6 hydrates. The entropic contribution and the enthalpy change are quantified from ground state energy and harmonic frequencies. Subsequently, the change in the Gibbs free energy of thermolysis was obtained under a wide range of temperature and pressure. The equilibrium product concentration of thermolysis can be used to design the seasonal heat storage system under different operating conditions.