# Bibliography - Zhong Zheng

- Zheng, Zhong, Bo Guo, Ivan C. Christov, Michael Celia, and Howard Stone, 2015:
**Flow regimes for fluid injection into a confined porous medium** In , Cambridge University Press, **767**, doi:10.1017/jfm.2015.68 881–909

[ Abstract ]We report theoretical and numerical studies of the flow behavior when a fluid is injected into a confined porous medium saturated with another fluid of different density and viscosity. For a two-dimensional configuration with point source injection,
a nonlinear convection–diffusion equation is derived to describe the time evolution of the fluid–fluid interface. In the early time period, the fluid motion is mainly driven by the buoyancy force and the governing equation is reduced to a nonlinear diffusion equation with a well-known self-similar solution. In the late time period, the fluid
flow is mainly driven by the injection, and the governing equation is approximated by a nonlinear hyperbolic equation that determines the global spreading rate; a shock solution is obtained when the injected fluid is more viscous than the displaced fluid, whereas a rarefaction wave solution is found when the injected fluid is less viscous.
In the late time period, we also obtain analytical solutions including the diffusive term associated with the buoyancy effects (for an injected fluid with a viscosity higher than or equal to that of the displaced fluid), which provide the structure of the moving front. Numerical simulations of the convection–diffusion equation are
performed; the various analytical solutions are verified as appropriate asymptotic limits, and the transition processes between the individual limits are demonstrated. The flow behavior is summarized in a diagram with five distinct dynamical regimes:
a nonlinear diffusion regime, a transition regime, a travelling wave regime, an equal-viscosity regime, and a rarefaction regime.

- Zheng, Zhong, Ivan C. Christov, and Howard Stone, 2014:
**Influence of heterogeneity on second-kind self-similar solutions for viscous gravity currents**. *Journal of Fluid Mechanics*, Cambridge University Press, **747**, doi:10.1017/jfm.2014.148 218–246

[ Abstract ]We report experimental, theoretical and numerical results on the effects of horizontal heterogeneities on the propagation of viscous gravity currents. We use two geometries to highlight these effects: (a) a horizontal channel (or crack) whose gap thickness
varies as a power-law function of the streamwise coordinate; (b) a heterogeneous porous medium whose permeability and porosity have power-law variations. We demonstrate that two types of self-similar behaviours emerge as a result of horizontal
heterogeneity: (a) a first-kind self-similar solution is found using dimensional analysis (scaling) for viscous gravity currents that propagate away from the origin (a point of zero permeability); (b) a second-kind self-similar solution is found using a phase-plane
analysis for viscous gravity currents that propagate toward the origin. These theoretical predictions, obtained using the ideas of self-similar intermediate asymptotics, are compared with experimental results and numerical solutions of the governing partial
differential equation developed under the lubrication approximation. All three results are found to be in good agreement.

- Zheng, Zhong, B. Soh, H.E. Huppert, and Howard Stone, February 2013:
**Fluid drainage from the edge of a porous reservoir** In , Cambridge University Press, **718**, doi:10.1017/jfm.2012.630 558-568

[ Abstract ]We report theoretical and experimental studies to describe buoyancy-driven fluid drainage from a porous medium for configurations where the fluid drains from an edge. We first study homogeneous porous systems. To investigate the influence of
heterogeneities, we consider the case where the permeability varies transverse to the flow direction, exemplified by a V-shaped Hele-Shaw cell. Finally, we analyse a model where both the permeability and the porosity vary transverse to the flow direction. In each case, a self-similar solution for the shape of these gravity currents is found and a power-law behaviour in time is derived for the mass remaining in the system. Laboratory experiments are conducted in homogeneous and V-shaped Hele-Shaw cells, and the measured profile shapes and the mass remaining in the cells agree well with our model predictions. Our study provides new insights into drainage processes such as may occur in a variety of natural and industrial activities, including the geological storage of carbon dioxide.

- Al-Housseiny, Talal, Peichun Tsai, Zhong Zheng, and Howard Stone, 2011:
**The effect of permeability gradients on immiscible displacement in Hele-Shaw flows**. *American Physical Society*,

[ Abstract ]In heterogeneous media, it is well known that when a fluid of high viscosity displaces a less viscous fluid, the interface can still be unstable and exhibit finger-like patterns due to capillary fingering. Motivated by porous media flows in natural geological formations, we consider homogeneous displacement in a Hele-Shaw cell subjected to a permeability gradient. The permeability gradient is introduced by linearly varying the Hele-Shaw cell depth. We study how capillary forces can affect interfacial stability in the presence of the gradient via linear stability analysis. Depending on the system, we find that surface tension can either have a stabilizing or a destabilizing role. We report the emergence of an important dimensionless parameter--the ratio of the permeability gradient to the capillary number--that determines the stability of the interface along with the well-studied viscosity ratio. Experiments testing the theoretical findings will also be presented.

- Zheng, Zhong, Eric Larson, Z. Li, Guangjian Liu, and Robert H. Williams, 2010:
**Near-term mega-scale CO**_{2} capture and storage demonstration opportunities in China. *Energy and Environmental Science*, The Royal Society of Chemistry, **3(9)**, doi:10.1039/B924243K 1153-1169

[ Abstract ]China is unique in the large number (nearly 400) of existing and planned projects for making ammonia,
methanol, and other fuels and chemicals from coal. A natural by-product of these processes is a nearly
pure CO_{2} stream. Collectively, these facilities will emit (once all are operating) some 270 million tonnes
of CO_{2} per year. Taking advantage of the relatively low cost of capturing these CO_{2} streams (as
compared with capturing CO_{2} from power plant flue gases), some of the 20 large-scale CO_{2} capture and
storage (CCS) demonstration projects called for by the leaders from the G8 to be deployed during the
next decade might be expeditiously located in China. Our analysis identifies 18 coal-chemicals/fuels
facilities, each emitting one million tonnes/year or more of CO_{2}, that are within 10 km of prospective
deep saline aquifer CO_{2} storage sites and an additional 8 facilities within 100 km. The potential CO_{2}
storage basins are identified based on work by others. We adapted two published cost models for CO_{2}
compression and transport to develop preliminary estimates of prospective costs for potential CCS
projects in China. Our "N^{th} plant" cost estimates for the 18 projects where the CO_{2} source is within
10 km of a sink, are between $9 and $13/tonne of CO_{2}. (The highest cost estimate among all evaluated
projects was less than $21/tonne of CO_{2}.) The 10-year net-present value cost for projects ranged from
$89 million to $1.15 billion, with more than 75% of the projects having net present value costs of $200
million or less. These relatively modest CCS costs suggest that there would be mutual value in
international cooperation to support CCS demonstrations in China.

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