Three-dimensional imaging of porous media using confocal laser scanning microscopy.

In the last decade, imaging techniques capable of reconstructing three-dimensional (3-D) pore-scale model have played a pivotal role in the study of fluid flow through complex porous media. In this study, we present advances in the application of confocal laser scanning microscopy (CLSM) to image, reconstruct and characterize complex porous geological materials with hydrocarbon reservoir and CO2 storage potential. CLSM has a unique capability of producing 3-D thin optical sections of a material, with a wide field of view and submicron resolution in the lateral and axial planes. However, CLSM is limited in the depth (z-dimension) that can be imaged in porous materials. In this study, we introduce a 'grind and slice' technique to overcome this limitation. We discuss the practical and technical aspects of the confocal imaging technique with application to complex rock samples including Mt. Gambier and Ketton carbonates. We then describe the complete workflow of image processing to filtering and segmenting the raw 3-D confocal volumetric data into pores and grains. Finally, we use the resulting 3-D pore-scale binarized confocal data obtained to quantitatively determine petrophysical pore-scale properties such as total porosity, macro- and microporosity and single-phase permeability using lattice Boltzmann (LB) simulations, validated by experiments.

Dynamics and rheology of wormlike micelles emerging from particulate computer simulations.

We perform coarse-grained computer simulations of solutions of semidilute wormlike micelles and study their dynamic and rheological properties, both in equilibrium and under shear flow. The simulation model is tailored to the study of relatively large time and length scales (micrometers and several milliseconds), while it still retains the specific mechanical properties of the individual wormlike micelles. The majority of the mechanical properties (persistence length, diameter, and elastic modulus of a single worm) is determined from more detailed atomistic molecular dynamics simulations, providing the link with the chemistry of the surfactants. The method is applied to the case of a solution containing 8% (by weight) erucyl bis(hydroxymethyl)methylammonium chloride (EHAC). Different scission energies ranging from 15.5k(b)T to 19.1k(B)T are studied, leading to both unentangled and entangled wormlike micelles. We find a decrease in the average contour length and an increase in the average breaking rate with increasing shear rate. In equilibrium, the decay of the shear relaxation modulus of the unentangled samples agrees with predictions based on a theory of breakable Rouse chains. Under shear flow, transient over- and undershoots are measured in the stress tensor components. At high shear rates we observe a steady-state shear stress proportional to gamma(1/3), where gamma is the shear rate. This is confirmed by our high shear rate experiments of real EHAC in a parallel-plate geometry.

Simulation of dissolution in porous media in three dimensions with lattice Boltzmann, finite-volume, and surface-rescaling methods.

We present a pore-scale dissolution model for the simulation of reactive transport in complex porous media such as those encountered in carbon-storage injection processes. We couple a lattice Boltzmann model for flow calculation with a finite-volume method for solving chemical transport equations, and allow the computational grid to change as mineral surfaces are dissolved according to first-order reaction kinetics. We appraise this scheme for use with high Péclet number flows in three-dimensional geometries and show how the popular first-order convection scheme is affected by severe numerical diffusion when grid Péclet numbers exceed unity, and confirm that this can be overcome relatively easily by using a second-order method in conjunction with a flux-limiter function. We then propose a surface rescaling method which uses parabolic elements to counteract errors in surface area exposed by the Cartesian grid and avoid the use of more complex embedded surface methods when surface reaction kinetics are incorporated. Finally, we compute dissolution in an image of a real porous limestone rock sample injected with HCl for different Péclet numbers and obtain dissolution patterns in concordance with theory and experimental observation. A low injection flow rate was shown to lead to erosion of the pore space concentrated at the face of the rock, whereas a high flow rate leads to wormhole formation.

Mechanical properties of surfactant bilayer membranes from atomistic and coarse-grained molecular dynamics simulations.

We use simulations to predict the stability and mechanical properties of two amphiphilic bilayer membranes. We carry out atomistic MD simulations and investigate whether it is possible to use an existing coarse-grained (CG) surfactant model to map the membrane properties. We find that certain membranes can be represented well by the CG model, whereas others cannot. Atomistic MD simulations of the erucate membrane yield a headgroup area per surfactant a(0) of 0.26 nm(2), an elastic modulus K(A) of 1.7 N/m, and a bending rigidity kappa of 5 k(B)T. We find that the CG model, with the right choice for the size and potential well depth of the head, correctly reproduces a(0), kappa, as well as the fluctuation spectrum over the whole range of q values. Atomistic MD simulations of EHAC, on the other hand, suggest that this membrane is unstable. This is indicated by the fact that kappa is of the order of k(B)T, which means that the interface is extremely flexible and diffuse, and K(A) is close to zero, which means that the surface tension is zero. We argue that the CG model can be used if the headgroups are uncharged, dipolar, or effectively dipolar due to headgroup charge screening induced by counterion condensation.

Influence of shear flow on the formation of rings in wormlike micelles: a nonequilibrium molecular dynamics study.

We study the influence of shear flow on the formation of rings in a generic reversible polymer (FENE-C) model, representative for wormlike micelles. Under equilibrium conditions, rings are dominating in dilute solutions, while linear chains are dominating in strongly overlapping and concentrated solutions. We find that shear flow induces a net shift of micellar mass from linear chains to rings. At the same time, the average aggregation size of linear chains is decreasing, while the average aggregation size of rings is increasing. We hypothesize that the increased abundance and size of rings are caused by a decreased entropy gain associated with ring opening under shear flow. Linear chains and rings are elongated in the flow direction and contracted in the gradient direction. This leaves an essentially two-dimensional free volume, which two newly created chain ends can explore after being disconnected. We study the ratio of ring and linear chain distribution functions to substantiate this hypothesis. Finally, we study the rheology and discuss how the observed increase of ring abundance can provide a positive feedback between strain and ring connectivity. Such a positive feedback can contribute to shear thickening behavior, observed in micellar solutions near the overlap concentration.

Influence of system size and solvent flow on the distribution of wormlike micelles in a contraction-expansion geometry.

Viscoelastic wormlike micelles are formed by surfactants assembling into elongated cylindrical structures. These structures respond to flow by aligning, breaking and reforming. Their response to the complex flow fields encountered in porous media is particularly rich. Here we use a realistic mesoscopic Brownian Dynamics model to investigate the flow of a viscoelastic surfactant (VES) fluid through individual pores idealized as a step expansion-contraction of size around one micron. In a previous study, we assumed the flow field to be Newtonian. Here we extend the work to include the non-Newtonian flow field previously obtained by experiment. The size of the simulations is also increased so that the pore is much larger than the radius of gyration of the micelles. For the non-Newtonian flow field at the higher flow rates in relatively large pores, the density of the micelles becomes markedly non-uniform. In this case, we find that the density in the large, slowly moving entry corner regions is substantially increased.

Molecular-dynamics simulation of amphiphilic bilayer membranes and wormlike micelles: a multi-scale modelling approach to the design of viscoelastic surfactant solutions.

Bilayer membranes and wormlike micelles have been studied using molecular-dynamics simulations. The structure of the worm is analysed in terms of radial density distribution functions, and mechanical properties such as the elastic modulus are calculated. From an analysis of the fluctuation spectra of the tensionless states, we have calculated bending rigidities. Micelles consisting of coarse-grained (CG) model surfactants are studied in order to map the properties of the atomistic micelle. We optimize the CG model with respect to the structure factor of the atomistic micelle. The mechanical properties thus obtained will be used as input for a mesoscopic model of wormlike micelles where the persistence length is the smallest length-scale.