Computational sciences in the upstream oil and gas industry.

The predominant technical challenge of the upstream oil and gas industry has always been the fundamental uncertainty of the subsurface from which it produces hydrocarbon fluids. The subsurface can be detected remotely by, for example, seismic waves, or it can be penetrated and studied in the extremely limited vicinity of wells. Inevitably, a great deal of uncertainty remains. Computational sciences have been a key avenue to reduce and manage this uncertainty. In this review, we discuss at a relatively non-technical level the current state of three applications of computational sciences in the industry. The first of these is seismic imaging, which is currently being revolutionized by the emergence of full wavefield inversion, enabled by algorithmic advances and petascale computing. The second is reservoir simulation, also being advanced through the use of modern highly parallel computing architectures. Finally, we comment on the role of data analytics in the upstream industry.This article is part of the themed issue 'Energy and the subsurface'.

Motion of packings of frictional grains.

Friction plays a key role in controlling the rheology of dense granular flows. Counting the number of constraints vs the number of variables indicates that critical coordination numbers Zc=3 (in D=2) and Zc=4 (in D=3) are special, in that states in which all contacts roll without frictional sliding are naively possible at and below these average coordination numbers. We construct an explicit example of such a state in D=2 based on a honeycomb lattice. This state has surprisingly large values for the typical angular velocities of the particles. Solving for the forces in such a state, we conclude that organized shear can exist in this state only on scales l

Avalanche dynamics on a rough inclined plane.

The avalanche behavior of gravitationally forced granular layers on a rough inclined plane is investigated experimentally for different materials and for a variety of grain shapes ranging from spherical beads to highly anisotropic particles with dendritic shape. We measure the front velocity, area, and height of many avalanches and correlate the motion with the area and height. We also measure the avalanche profiles for several example cases. As the shape irregularity of the grains is increased, there is a dramatic qualitative change in avalanche properties. For rough nonspherical grains, avalanches are faster, bigger, and overturning in the sense that individual particles have down-slope speeds u p that exceed the front speed uf as compared with avalanches of spherical glass beads that are quantitatively slower and smaller and where particles always travel slower than the front speed. There is a linear increase of three quantities: (i) dimensionless avalanche height, (ii) ratio of particle to front speed, and (iii) the growth rate of avalanche speed with increasing avalanche size with increasing tan theta r where theta r is the bulk angle of repose, or with increasing beta P, the slope of the depth averaged flow rule, where both theta r and beta P reflect the grain shape irregularity. These relations provide a tool for predicting important dynamical properties of avalanches as a function of grain shape irregularity. A relatively simple depth-averaged theoretical description captures some important elements of the avalanche motion, notably the existence of two regimes of this motion.

Velocity correlations in dense gravity-driven granular chute flow.

We report numerical results for velocity correlations in dense, gravity-driven granular flow down an inclined plane. For the grains on the surface layer, our results are consistent with experimental measurements reported by Pouliquen. We show that the correlation structure within planes parallel to the surface persists in the bulk. The two-point velocity correlation function exhibits exponential decay for small to intermediate values of the separation between spheres. The correlation lengths identified by exponential fits to the data show nontrivial dependence on the averaging time Deltat used to determine grain velocities. We discuss the correlation length dependence on averaging time, incline angle, pile height, depth of the layer, system size, and grain stiffness and relate the results to other length scales associated with the rheology of the system. We find that correlation lengths are typically quite small, of the order of a particle diameter, and increase approximately logarithmically with a minimum pile height for which flow is possible, hstop, contrary to the theoretical expectation of a proportional relationship between the two length scales.

Two scenarios for avalanche dynamics in inclined granular layers.

We report experimental measurements of avalanche behavior of thin granular layers on an inclined plane for low volume flow rate. The dynamical properties of avalanches were quantitatively and qualitatively different for smooth glass beads compared to irregular granular materials such as sand. Two scenarios for granular avalanches on an incline are identified, and a theoretical explanation for these different scenarios is developed based on a depth-averaged approach that takes into account the differing rheologies of the granular materials.

Ripening of porous media.

We address the surface-tension-driven dynamics of porous media in nearly saturated pore-space solutions. We linearize this dynamics in the reaction-limited regime near its fixed points--surfaces of constant mean curvature (CMC surfaces). We prove that the only stable interface for this dynamics is the plane and estimate the time scale for a CMC surface to become unstable. We also discuss the differences between dynamics in open and closed environments, pointing out the unlikelihood that CMC surfaces are ever realized in such environments on any time scale.

Analogies between granular jamming and the liquid-glass transition.

Based on large-scale, three-dimensional chute flow simulations of granular systems, we uncover strong analogies between the jamming of the grains and the liquid-glass transition. The angle of inclination theta in the former transition appears as an analog of temperature T in the latter. The transition is manifested in the development of a plateau in the contact normal force distribution P(f) at small forces, the splitting of the second peak in the pair-correlation function g(r), and increased fluctuations of the system energy. The static state also exhibits history dependence, akin to the quench-rate dependence of structural properties of glasses, due to the hyperstaticity of the contact network.

Geometry of frictionless and frictional sphere packings.

We study static packings of frictionless and frictional spheres in three dimensions, obtained via molecular dynamics simulations, in which we vary particle hardness, friction coefficient, and coefficient of restitution. Although frictionless packings of hard spheres are always isostatic (with six contacts) regardless of construction history and restitution coefficient, frictional packings achieve a multitude of hyperstatic packings that depend on system parameters and construction history. Instead of immediately dropping to four, the coordination number reduces smoothly from z=6 as the friction coefficient mu between two particles is increased.

Branched growth with eta approximately 4 walkers.

Diffusion-limited aggregation has a natural generalization to the "eta models," in which eta random walkers must arrive at a point on the cluster surface in order for growth to occur. It has recently been proposed that in spatial dimensionality d=2, there is an upper critical eta(c)=4 above which the fractal dimensionality of the clusters is D=1. I compute the first-order correction to D for eta<4, obtaining D=1 + 1/2 (4-eta). The methods used can also determine multifractal dimensions to first order in 4-eta.

Stability of monomer-dimer piles.

We present an experimental and theoretical study of piles consisting of monodisperse spherical grains mixed with a weight fraction nu(d) of dimer grains made by the rigid bonding of two such spherical grains. The maximum static angle of stability tantheta(c) of the pile increases from 0.45 to 1.1 and the grain packing fraction Phi decreases from 0.58 to 0.52 as nu(d) is increased from 0 to 1. The stability of these piles appears to be controlled by the grains sitting on the surface, which roll out of their local "traps" as the tilt angle is increased. We attribute the increase in tan theta(c)(nu(d)) to the enhanced stability of dimers on the surface, such that at higher tilt angles, there are sufficiently many stable surface traps available to accommodate the reduced density of monomers on the surface. A full characterization of the grain-scale roughness of the surface is required to quantitatively account for the changes in theta(c) with nu(d).