Simple models of the hydrofracture process

Hydrofracturing to recover natural gas and oil relies on the creation of a fracture network with pressurized water. We analyze the creation of the network in two ways. First, we assemble a collection of analytical estimates for pressure-driven crack motion in simple geometries, including crack speed as a function of length, energy dissipated by fluid viscosity and used to break rock, and the conditions under which a second crack will initiate while a first is running. We develop a pseudo-three-dimensional numerical model that couples fluid motion with solid mechanics and can generate branching crack structures not specified in advance. One of our main conclusions is that the typical spacing between fractures must be on the order of a meter, and this conclusion arises in two separate ways. First, it arises from analysis of gas production rates, given the diffusion constants for gas in the rock. Second, it arises from the number of fractures that should be generated given the scale of the affected region and the amounts of water pumped into the rock.Shell UTNational Science FoundationPhysic

Onset of Mobilization and the Fraction of Trapped Foam in Porous Media

The dynamic behavior of foam trapped in porous media is modeled here with a pore network simulator. We predict the magnitude of the pressure drop leading to the onset of flow of foam lamellae in the region containing trapped foam. This mobilization pressure drop depends only on the number of lamellae in the flow path and on the geometry of the pores that make up this path. The principles learned in this study allow us to predict the fraction of foam that is trapped in a porous medium under given flow conditions. We present here the first analytic expression for the trapped foam fraction as a function of the pressure gradient, and of the mean and standard deviation of the pore size distribution. This expression provides a missing piece for the continuum foam flow models based on the moments of the volume-averaged population balance of foam bubbles

Pore-scale Modeling of Viscous Flow and Induced Forces in Dense Sphere Packings

We propose a method for effectively upscaling incompressible viscous flow in large random polydispersed sphere packings: the emphasis of this method is on the determination of the forces applied on the solid particles by the fluid. Pore bodies and their connections are defined locally through a regular Delaunay triangulation of the packings. Viscous flow equations are upscaled at the pore level, and approximated with a finite volume numerical scheme. We compare numerical simulations of the proposed method to detailed finite element (FEM) simulations of the Stokes equations for assemblies of 8 to 200 spheres. A good agreement is found both in terms of forces exerted on the solid particles and effective permeability coefficients

A review of physical supply and EROI of fossil fuels in China

This paper reviews China’s future fossil fuel supply from the perspectives of physical output and net energy output. Comprehensive analyses of physical output of fossil fuels suggest that China’s total oil production will likely reach its peak, at about 230 Mt/year (or 9.6 EJ/year), in 2018; its total gas production will peak at around 350 Bcm/year (or 13.6 EJ/year) in 2040, while coal production will peak at about 4400 Mt/year (or 91.9 EJ/year) around 2020 or so. In terms of the forecast production of these fuels, there are significant differences among current studies. These differences can be mainly explained by different ultimately recoverable resources assumptions, the nature of the models used, and differences in the historical production data. Due to the future constraints on fossil fuels production, a large gap is projected to grow between domestic supply and demand, which will need to be met by increasing imports. Net energy analyses show that both coal and oil and gas production show a steady declining trend of EROI (energy return on investment) due to the depletion of shallow-buried coal resources and conventional oil and gas resources, which is generally consistent with the approaching peaks of physical production of fossil fuels. The peaks of fossil fuels production, coupled with the decline in EROI ratios, are likely to challenge the sustainable development of Chinese society unless new abundant energy resources with high EROI values can be found

Modelling India’s coal production with a negatively skewed curve-fitting model

India’s coal demand is forecast to increase at a rapid pace in the future due to the country’s economic and population growth. Analyzing the scope for future production of India’s domestic coal resources, therefore, plays a vital role in the country’s development of sound energy policies. This paper presents a quantitative scenario analysis of India’s potential future coal production by using a negatively skewed curve-fitting model and a range of estimates of the country’s ultimately recoverable resources (URR) of coal. The results show that the resource base is sufficient for India’s coal production to keep increasing over the next few decades, to reach between 2400 and 3200 Mt/y at 2050, depending on the assumed value of URR. A further analysis shows that the high end of this range, which corresponds to our ‘GSI’ scenario, can be considered as the probable upper-bound to India’s domestic coal production. Comparison of production based on the ‘GSI’ scenario with India’s predicted demand shows that the domestic production of coal will be insufficient to meet the country’s rising coal demand, with the gap between demand and production increasing from its current value of about 268 Mt/y to reach 300 Mt/y in 2035, and 700 Mt/y by 2050. This increasing gap will be challenging for the energy security of India