Inversely-Mapped Analytical Solutions for Flow Patterns around and within Inclined Elliptic Inclusions in Fluid-Saturated Rocks   总被引：1，自引：0，他引：1  

Chongbin Zhao  Bruce E. Hobbs  Alison Ord  Shenglin Peng  Liangming Liu 《Mathematical Geosciences》2008,40(2):179-197

In this paper, an inverse mapping is used to transform the previously-derived analytical solutions from a local elliptical coordinate system into a conventional Cartesian coordinate system. This enables a complete set of exact analytical solutions to be derived rigorously for the pore-fluid velocity, stream function, and excess pore-fluid pressure around and within buried inclined elliptic inclusions in pore-fluid-saturated porous rocks. To maximize the application range of the derived analytical solutions, the focal distance of an ellipse is used to represent the size of the ellipse, while the length ratio of the long axis to the short one is used to represent the geometrical shape of the ellipse. Since the present analytical solutions are expressed in a conventional Cartesian coordinate system, it is convenient to investigate, both qualitatively and quantitatively, the distribution patterns of the pore-fluid flow and excess pressure around and within many different families of buried inclined elliptic inclusions. The major advantage in using the present analytical solution is that they can be conveniently computed in a global Cartesian coordinate system, which is widely used in many scientific and engineering computations. As an application example, the present analytical solutions have been used to investigate how the dip angle of an inclined elliptic inclusion affects the distribution patterns of the pore-fluid flow and excess pore-fluid pressure when the permeability ratio of the elliptic inclusion is of finite but nonzero values.  相似文献   

Numerical Simulations of Convection Cells in Sedimentary Basins with Application to Geothermal Energy     

C. Detournay  B. Hobbs 《Rock Mechanics and Rock Engineering》2015,48(6):2631-2636

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Why asymptotic limit of the acid dissolution capacity can lead to a sharp dissolution front in chemical dissolution of porous rocks?          下载免费PDF全文

Chongbin Zhao  B.E. Hobbs  A. Ord 《国际地质力学数值与分析法杂志》2017,41(15):1590-1602

The use of the asymptotic limit can greatly simplify the theoretical analysis of chemical dissolution front instabilities in fluid‐saturated rocks and therefore make it possible to obtain mathematical solutions, which often play a crucial role in understanding the propagation behavior of chemical dissolution fronts in chemical dissolution systems. However, there has been a debate in recent years that the asymptotic limit of the acid dissolution capacity (i.e., the acid dissolution capacity number approaching zero) alone cannot lead to a sharp dissolution front of the Stefan type in the acidization dissolution system, in which the dissolvable minerals of carbonate rocks are chemically dissolved by the injected acid flow. The acid dissolution capacity number is commonly defined as the ratio of the volume of the carbonate rock dissolved by an acid to that of the acid. In this paper, we use four different proof methods, including (i) direct use of the fundamental concepts; (ii) use of the mathematical governing equations of an acidization dissolution system; (iii) use of the different time scaling approach; and (iv) use of a moving coordinate system approach, to demonstrate that the asymptotic limit of the acid dissolution capacity can indeed lead to sharp dissolution fronts of the Stefan type in acidization dissolution systems on a much larger time scale (than the dissolution time scale). Our new finding is that on the reaction time scale, the condition of the conventional time derivative of porosity approaching zero alone can ensure that the acidization dissolution front has a sharp shape of the Stefan type. Copyright © 2017 John Wiley & Sons, Ltd.  相似文献   

Geodynamic modelling of the Century deposit,Mt Isa Province,Queensland     

A. Ord  B. E. Hobbs  Y. Zhang  G. C. Broadbent  M. Brown  G. Willetts 《Australian Journal of Earth Sciences》2013,60(6):1011-1039

This paper is concerned with an example of quantitative modelling of orebody formation as a guide to reducing the risk for future mineral exploration. Specifically, the paper presents a detailed 3–D numerical model for the formation of the Century zinc deposit in northern Queensland. The model couples fluid flow with deformation, thermal transport and chemical reactions. The emphasis of the study is a systems approach where the holistic mineralising system is considered rather than concentrating solely on the mineral deposit. In so doing the complete plumbing system for mineralisation is considered with a view to specifying the critical conditions responsible for the ore deposit occurring where it does and having the size and metal grades that are observed. The numerical model is based on detailed geological, tectonic, isotopic and mineralogical data collected over the past 20 years. The conclusions are that the Century zinc deposit is located where it is because of the following factors: (i) a thermal anomaly is associated with the Termite Range Fault due to advection of heat from depth by fluid flow up the Termite Range Fault; (ii) bedding‐plane fissility in the shale rocks hosting the Century zinc deposit has controlled the wavelength and nature of D₁ folding in the vicinity of the deposit and has also controlled increases in permeability due to hydrofracture of the shales; such hydrofracture is also associated with the production of hydrocarbons as these shales passed through the ‘oil‐window’; (iii) Pb–Zn leached from crustal rocks in the stratigraphic column migrated up along faults normal to the Termite Range Fault driven by topographic relief associated with inversion at the end of the Isan Orogeny; these fluids mixed with H₂S derived at depth moving up the Termite Range Fault to mix with the crustal fluids to precipitate Pb–Zn in a plume downstream from the point of mixing. Critical factors to be used as exploration guides are high temperatures, carbonaceous fissile shales now folded into relatively tight D₁ folds, fault‐controlled plumbing systems that enable fluid mixing, depletion of metals upstream of the deposit and,in particular,a very wide Fe‐depletion halo upstream of the deposit.  相似文献   

Theoretical analyses of acidization dissolution front instability in fluid‐saturated carbonate rocks     

Chongbin Zhao  B. E. Hobbs  A. Ord 《国际地质力学数值与分析法杂志》2013,37(13):2084-2105

This paper presents an instability theory that can be used to understand the fundamental behavior of an acidization dissolution front when it propagates in fluid‐saturated carbonate rocks. The proposed theory includes two fundamental concepts, namely the intrinsic time and length of an acidization dissolution system, and a theoretical criterion that involves the comparison of the Zhao number and its critical value of the acidization dissolution system. The intrinsic time is used to determine the time scale at which the acidization dissolution front is formed, while the intrinsic length is used to determine the length scale at which the instability of the acidization dissolution front can be initiated. Under the assumption that the acidization dissolution reaction is a fast process, the critical Zhao number, which is used to assess the instability likelihood of an acidization dissolution front propagating in fluid‐saturated carbonate rocks, has been derived in a strictly mathematical manner. Based on the proposed instability theory of a propagating acidization dissolution front, it has been theoretically recognized that: (i) the increase of the mineral dissolution ratio can stabilize the acidization dissolution front in fluid‐saturated carbonate rocks; (ii) the increase of the final porosity of the carbonate rock can destabilize the acidization dissolution front, while the increase of the initial porosity can stabilize the acidization dissolution front in fluid‐saturated carbonate rocks; (iii) the increase of the mineral dissolution ratio can cause an increase in the dimensionless propagation speed of the acidization dissolution front; (iv) the increase of the initial porosity can enable the acidization dissolution front to propagate faster, while the increase of the final porosity can enable the acidization dissolution front to propagate slower in the acidization dissolution system. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

An iterative scheme for use in MT 2D forward modelling — to speed up production of the Jacobian and to improve accuracy of the inverse matrix     

A. J. Zhang  E. R. G. Hill  B. A. Hobbs 《Physics of the Earth and Planetary Interiors》1990,60(1-4):40-52

An important stage in two-dimensional magnetotelluric modelling is the calculation of the Earth's response functions for an assumed conductivity model and the calculation of the associated Jacobian relating those response functions to the model parameters. The efficiency of the calculation of the Jacobian will affect the efficiency of the inversion modelling. Rodi (1976) produced all the Jacobian elements by inverting a single matrix and using an approximate first-order algorithm. Since only one inverse matrix required calculation the procedure speeded up the inversion. An iterative scheme to improve the approximation to the Jacobian information is presented in this paper. While this scheme takes a little longer than Rodi's algorithm, it enables a more accurate determination of the Jacobian information. It is found that the Jacobian elements can be produced in 10% of the time required to calculate an inverse matrix or to calculate a 2D starting model. A modification of the algorithm can further be used to improve the accuracy of the original inverse matrix calculated in a 2D finite difference program and hence the solution this program produces. The convergence of the iteration scheme is found to be related both to the originally calculated inverse matrix and to the change in the newly formed matrix arising from perturbation of the model parameter. A ridge regression inverse algorithm is used in conjunction with the iterative scheme for forward modelling described in this paper to produce a 2D conductivity section from field data.  相似文献   

Arctic hazes in summer over Greenland and the North American Arctic: II. Nature and concentrations of accumulation-mode and giant particles     

Yutaka Ishizaka  Peter V. Hobbs  Lawrence F. Radke 《Journal of Atmospheric Chemistry》1989,9(1-3):149-159

Airborne measurements made during August 1985 over Greenland and its environs show that both accumulation-mode (0.1 m D2.0 m) and giant (D2 m) particles were present in relatively high concentrations in arctic haze layers and that the accumulation-mode particles dominated light scattering. Particles with diameters (D) between 1 and 4 m consisted predominately of mixed materials, small and dense inclusions, and probably organic compounds containing sulfur. Many of the particles from 0.1 to 1 m in diameter were also of mixed composition, with sulfuric acid, ammonium sulfate and organics probably the dominant constituents.  相似文献   

Development and propagation of precipitation cores on cold fronts     

J. D. Locatelli  J. E. Martin  P. V. Hobbs 《Atmospheric Research》1995,38(1-4)

The structure and propagation of precipitation cores on a variety of cold fronts are described. The shapes of the cores, and their orientations with respect to the synoptic-scale front, are not always uniform either between fronts or within the same front. Interactions between cores depend on their proximity and relative strength. Large gaps between precipitation cores move along the cold front at a slower speed than the cores and affect the evolution of the precipitation cores. The spacing of precipitation cores, the height of the head of the density current associated with the cold front, and the strength of the cold front are positively correlated with precipitation strength. This suggests that interactions between cores are strongly influenced by precipitation.Current theories for precipitation cores on narrow cold-frontal rainbands cannot account for these observations. A new mechanism is proposed based on a positive feedback between the diabatic cooling produced by the melting and evaporation of precipitation, the head of the density current, and the strength of the front.  相似文献   

Preface     

B. A. Hobbs  G. Fischer 《Surveys in Geophysics》1987,9(3-4):233-234

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Model formulation and model smoothing for 2-D magnetotelluric inversion     

A. J. Zhang  B. A. Hobbs 《Geophysical Journal International》1992,108(2):507-516

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