Entry Date:
March 4, 2010

Numerical Simulation Technologies: Smooth Particle Hydrodynamics

Principal Investigator John Williams


Smooth Particle Hydrodynamics (SPH) is a meshfree Lagrangian particle method first proposed for astrophysical problems and now widely applied to fluid mechanics problems, and continuum problems involving large deformation or brittle fracture. While SPH is a computationally expensive numerical method, in many circumstances the expense can be justified by the versatility of the method and its ability to easily handle multi-physics phenomena.

We have developed a 3D, multi-phase SPH simulator including surface tension effects such as contact angle and surface wettability. The simulator is programmed within a multi-core numerical framework which allows efficient, scalable parallel execution. Several results from the simulator are provided in what follows.

2D Single Phase Permeability Verification -- While the ability to simulate a diverse range of complex phenomena with SPH represents a key advantage over alternate methods, the accuracy of such a method must be supported by verifying tests on more simple, single-phase benchmark problems. The performance of SPH in the reproduction of one-dimensional flow characteristics have been well defined in the literature. Additionally, two-dimensional flows past systems such as periodic arrays of cylinders and more complex flow obstructions have demonstrated good agreement with conventional numerical and analytical solutions to the same problems.

The image to the left shows permeability results from the SPH simulator for single-phase flow through a 2D periodic array of cylinders. Permeability is plot aganst a range of solid volume fractions (1 - porosity) and compared with widely accepted stokes solver results. SPH results were within less than one percent of the stokes solver benchmark.

For the simulation a new technique for enforcing no-slip boundary conditions for low Reynolds number flows was used, which has been developed by the MIT Geonumerics group. This is one of the most numerically efficient and accurate SPH no-slip boundary methods available, details can be found in the Publications section.

3D Single Phase Permeability Verification -- While the two-dimensional flow verification is a reproduction of existing work publishied on SPH, verification of three-dimensional flow remains largely untreated within the published literature. Ordered sphere packs are an idealized three-dimensional porous media and modeling flow through such media has commonly been used as a standard test problem to verify the three-dimensional accuracy of a numerical method. The simulation of such a system using SPH goses a long way towards verifying the method for all flow and validating its more advanced capabilities.

The image to the left shows permeability results from the SPH simulator for single-phase flow through a 3D ordered packing of spheres. Permeability is again plot against a range of solid volume fractions (1 - porosity) up to levels indicative of actual permeable reservoir rock (~ 10% porosity). Results are compared with the widely cited 3D stokes solver results and again compare accurately with the benchmark (a deviation of less than 3% in the worst case).

Once again, no-slip boundaries have been enforced resulting in the high level of accruacy observed.

Falling Drop Simulation -- The example of a droplet of water falling on a flat surface of water is commonly used to demonstrate the free surface response of a simulator. The animation shows clearly the disturbance and splash-back resulting from the water droplet impacting on the flat water surface. Surface tension has been included in the simulation with the effects clearly seen in the behavior of splash droplets on the water surface.

Rayleigh-Taylor Instability -- The Rayleigh-Taylor instability is a well known experimentally observed multi-phase fluid phenomenon which is commonly used to demonstrate the ability of a simulation code to handle several fluid phases. The Rayleigh-Taylor instability results between two layers of fluid when the upper layer has a higher density, forcing it to flow to the bottom of the container due to gravity. The shape of the fluid interfaces as the heavier fluid displaces the lighter is what is referred to as the Rayleigh-Taylor instability.

The animation shows a 2D simulation of a light bottom layer of fluid being displaced by a heavier top layer of fluid within a container. The simulation includes effects from surface tension.

Three-Dimensional Rayleigh-Taylor Instability -- The Rayleigh-Taylor instability can also be observed in 3D resulting in a very large number of phase interfacial surfaces. Once again, the phenomena results from a layer of high density fluid dropping under gravity through a layer of lower density.

This animation shows the 3D Rayleigh-Taylor Instability, again solved using SPH. This result demonstrates the ability of the developed numerical algorithms to handle complex multi-phase surfaces, i.e. air-water-oil-wall. Again surface tension effects are important for the formation of fluid droplets and their subsequent return to the fluid mass.

Non-Wetting Water Invasion -- A key technique used in industry to increase the yield of an oil field is water invasion or water flooding. The rather straight forward premise behind this technique is that water (or some other fluid) is flooded into a reservoir from specific positions to invade the porous rock and displace oil which may not have otherwise been able to be recovered. By changing or “designing” the chemical properties of the invasion fluid there is great potential to improve the effectiveness of the invasion. The wettability of the fluid is one property which has significant effect on the effectiveness of an invasion process.

In the animation, a non-wetting water phase (blue) is flooded into a rigid granular media (black) containing a wetting oil phase (red). The non-wetting nature of the invading phase clearly causes fingering and, as a consequence, little oil is displaced.

Wetting Water Invasion -- By modifying the phase properties of the previous example such that a wetting water phase (blue) is flooded into a rigid granular media (black) containing a non-wetting oil phase (red), the penetration of the invading phase is greatly increased. The animation shows the significant increase in oil which is recovered as a result of changing the wettability of the invading phase.

These simulations demonstrate both the performance of the SPH simulator to handle complex surface tension phenomena such as wettability and contact angle, and the potential of such simulators to allow “design” of invading fluids to optimize the amount of oil recovered.

Three-Dimensional Wetting Water Invasion -- In this example, a 3D version of the water invasion experiment is carried out. As with the last example, a wetting water phase is flooded into a rigid granular media (black) containing a non-wetting oil phase. Owing to the high porosity of the grains in the problem, the majority of the oil in the example is displaced by the invading water.

Simulation tools such as these have a wide range of applications for the design and testing of chemical treatments such as surfactants which alter the wettability of fluid phases in oil reservoir rock.