Computational modelling and design of responsive industrial fluids (wormlike micelles)

Introduction

In this project we work together with scientists at Schlumberger Cambridge Research and focus on the design of new generation fracturing fluids. The production of oilwells is sometimes limited by low natural reservoir permeability. The creation of hydraulic fractures is one major stimulation commonly used to overcome these limitations. This is usually done by injecting polymer gels, which transmit hydraulic pressure to the rock to induce fractures, into which proppants are transported to keep the fractures open on removal of the fluid pressure. Once the proppant is in place, delayed oxidative or enzymatic breakers are used to degrade the gel retained within the fracture. A disadvantage of many of these polymeric fluids is that, despite the gel-breaking step, small cross-linked fragments comparable in size to the proppant pore throats reduce the hydraulic conductivity significantly. An important new generation of fracturing fluids based upon wormlike micelles, forming viscoelastic surfactants (VES), has recently been introduced which attempts to overcome this problem. Similarly to polymer gels, entanglements between these micelles impart viscoelastic properties to the solution, i.e. the wormlike micelles function as thickening and rheology-control agents. However, once the wormlike micelles come into contact with hydrocarbon produced from the fracture through the proppant pack, the VES revert to small spherical micelles or micro-emulsions, the fluid viscosity/elasticity falls by orders of magnitude, and the fluid residues flow easily out of the pack.

Importance of coarse-graining techniques

It is impossible to reach the sufficiently long length and time-scales to study the most interesting rheological phenomena by direct atomistic molecular dynamics simulations. Coarse-graining techniques are therefore critical to the advancement of understanding of VES fluids, and have been extensively studied in the literature. In our research we simplify the extended hierarchy to two levels of coarse-graining:

1. From microscopic atomistic models to particle based mesoscopic models. Here the emphasis is on how microscopic chemical details of the individual surfactant molecules lead to specific properties, like the bending rigidity and persistence lengths of amphiphilic bilayers and worms.
2. From mesoscopic models to rheological properties. At this level, properties like the persistence length, bending rigidities, and mesoscale objects such as micellar entanglements and junctions are linked to rheological behaviour.

Future plans

We will investigate both level 1 and level 2 type coarse-graining schemes. In the case of the polymer melts, a direct coarse-graining from an atomic level to a mesoscopic "soft blob" model was possible. For these surfactant systems we think this will be too large a step to begin with. The smallest length-scale of a worm-like micelle, which is of relevance for its rheological behaviour, is the persistence length. In a first instance we will describe long worms by means of bead-spring models whose springs have equilibrium length of the order of roughly one persistence length. In order to detect and process possible entanglements the TWENTANGLEMENT program, which has been written to perform simulations of coarse-grained polymer melts, will be adapted to these new systems. A mechanism has to be added by which bonds can break or merge at entanglements, to emerge again as unentangled bonds or T-junctions plus one detached chain. T-junctions should also be able to slide along one of the partaking legs. Brownian Dynamics (BD) simulations will be performed with the above model under various conditions of flow. Because of the high worm concentration, we expect hydrodynamic interactions to be largely screened, so that they can be ignored in a first instance, or else taken into account in a heuristic way. The relative importance of the above processes of break-up and merging at entanglements will be studied by varying the corresponding thresholds.

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