A mathematical model for Biogrout

We present a mathematical model for Biogrout, which is a technique for soil reinforcement that is based on microbially induced carbonate precipitation. The model deals with the entire process, consisting of fixation of bacteria, as well as of the subsequent soil reinforcement. The paper deals with the coupling of two earlier models for bacterial placement and reinforcement, where the construction of the model is discussed, as well as numerical results. Further, we present analytical solutions for the constant flow velocity case. The model is based on the assumption that the porous medium is stiff.     

A mathematical model of spheroidal weathering

A mathematical model is developed to explain the geometrical patterns of spheroidal weathering. The model is then analyzed, and results of computer simulations for the weathering of spherical and ellipsoidal surfaces are presented. Ellipsoids weather initially into ellipsoids of greater or lesser eccentricity, depending on boundary conditions, and finally into spheres. This is in qualitative agreement with the geometry of observed weathering patterns. Some of these features would be difficult to explain by a diffusion model. The weathering of rectangles also is simulated, and they weather into ellipses or circles. These are also in qualitative agreement with observed weathering patterns.     

面向井周高陡构造的VSP地震干涉成像方法研究

随着我国油气勘探的不断深入,复杂高陡构造区越来越成为当今油气勘探的重点,现有成像方法无法满足井周高陡构造的成像需求。针对井中高陡构造,地震干涉法基于源检互易定理,对不同检波点处VSP资料进行相关/褶积处理,重构虚拟震源数据,得到以某一检波点为虚拟震源,另一检波点处接收到的虚拟SWP地震记录。根据地震干涉原理,将VSP资料的不同波场成分进行分离,并对不同波场成分进行数学运算来生成干涉道集。通过地震干涉法能够使虚拟观测系统更靠近目标区域,提高对高陡界面的成像分辨率,实现面向井周高陡构造的高精度成像。笔者等先是对地震干涉原理进行理论推导,基于扰动理论对VSP干涉道集的波场成分进行分析,验证了不同波场成分在地震干涉中的作用及虚假同相轴产生原因。引入窗函数滤波器,对远离虚拟源和虚拟检波器的记录进行衰减,压制干涉过程中生成的虚假同相轴。最后利用干涉成像条件对处理后的地震资料进行成像,并用盐丘模型进行数值试算,得到其高精度成像结果。     

煤基质膨胀收缩对储层渗透率影响的新数学模型

煤层渗透率变化受多种因素制约,其中有效应力和煤吸附–解吸过程中煤基质的膨胀/收缩是两个主要因素。基于这两方面影响因素,采用体积不变原理和MATCHSTICK模型,提出新的预测渗透率变化的模型,有效回避了经典模型中使用不确定参数引起的渗透率模拟误差问题。研究结果表明,渗透率随煤层压力的变化存在3种理论模型,煤层气排采过程中,应尽可能使得渗透率变化曲线呈现下降缓慢、抬升稳定快速且增幅较大的趋势。最后,通过与经典的Palmer-Mansoori模型和Shi-Durucan模型的模拟对比,并利用现场实测数据进行验证,证明了本文推导模型的正确性和实用性。     

A mathematical model of submarine platform development

Considering (1)the wave-induced cliff recession and (2)the wave dynamics in shallow water, the present study attempted to evolve a model of the temporal development of submarine platform with static sea level. The model, expressed in terms of an exponential function of time, shows that the platform development approaches equilibrium with time.     

A mathematical model of the brown tide

A differential equation model is proposed for “brown tide” algae blooms in the coastal waters of Long Island which provides a plausible mechanisms for the underlying dynamics. Growth rates depend on annual variations in temperature and salinity. The maximum population density is effectively limited by the availability of a favorable concentration of nutrients, together with zooplankton grazing. Salinity depends on rainfall while nutrient concentration is influenced by tidal flushing. The first of these factors is aperiodic, the second periodic, in time. The resulting nonlinear model distinguishes between ‘fast’ algae growth and ‘slow’ long-term changes in nutrients and salinity. Because of this one can show that explosive increases of algae densities will occur infrenquently at sporadic intervals. Computer trials with the model appear to replicate many, if not all, the essential features of the observed bloom.     

Temporal alteration of fracture permeability in granite under hydrothermal conditions and its interpretation by coupled chemo-mechanical model

Examining the evolution of fracture permeability under stressed and temperature-elevated conditions, a series of flow-through experiments on a single rock fracture in granite has been conducted under confining pressures of 5 and 10 MPa, under differential water pressures ranging from 0.04 to 0.5 MPa, and at temperatures of 20–90 °C, for several hundred hours in each experiment. Measurements of fluid and dissolved mass fluxes, and post-experimental microscopy, were conducted to constrain the progress of mineral dissolution and/or precipitation and to examine its effect on transport properties. Generally, the fracture aperture monotonically decreased with time at room temperature, and reached a steady state in relatively short periods (i.e., <400 h). However, once the temperature was elevated to 90 °C, the aperture resumed decreasing and kept decreasing throughout the rest of the experimental periods. This reduction may result from the removal of the mineral mass from the bridging asperities within the fracture. Post-experimental observations by scanning electron microscopy, coupled with energy dispersive X-ray spectroscopy (SEM-EDX), revealed the formation of several kinds of secondary minerals such as silica and calcite. However, the precipitated minerals seemed to have had little influence on the flow characteristics within the fracture, because the precipitation was limited to quite local and small areas. The evolving rates and ultimate magnitudes of the fracture aperture are likely to be controlled by the stress exerted over the contacting asperities and temperatures, and by the prescribed flow conditions. Thus, this complex behavior should be attributed to the coupled chemically- and mechanically-induced effect. A coupled chemo–mechano conceptual model, accounting for pressure and free-face dissolutions, is presented in this paper to follow the evolution of the fracture permeability observed in the flow-through experiments. This model addresses the two dissolution processes at the contacting asperities and the free walls within the fractures, and is also capable of describing multi-mineral dissolution behavior. The model shows that the evolution of a fracture aperture (or related permeability) and of element concentrations may be followed with time under arbitrary temperature and pressure conditions. The model predictions for the evolving fracture aperture and elements concentrations show a relatively good agreement with the experimental measurements, although it is not possible to replicate the abrupt reduction observed in the early periods of the experiments, which is likely to be due to an unaccounted mechanism of more stress-mediated fracture compaction driven by the fracturing of the propping asperities.     

A general mathematical model for balanced global isostasy

A general mathematical model of balanced global isostasy is presented that describes the geometrical relationships among atmospheric, oceanic, lithospheric, and asthenospheric components relative to a fixed, external frame of reference in terms of 19 parameters of mass, density, area, and thickness in five basic equations and various corollaries. The model is applicable and necessary for evaluating lithospheric processes that operate on a global scale or that affect globally oriented parameters such as sea level, freeboard, and ocean basin depth. It also provides a means of testing the internal consistency of a given set of mass, density, volume, and area parameters relative to present crustal geometry by showing how well they combine to predict present continental free-board. With modification, the basic model can be used to examine more complex questions involving glacially induced sea level fluctuations and long-term crustal evolution resulting from differential energy flux to Earth, short-term modulation of heat flux from the asthenosphere, and long-term monotonic cooling.     

Hydrothermal alteration and the formation of aluminous haloes around sulfide deposits

The sulfide deposits of Chizeuil (Saone et Loire) occur in a Late Devonian volcano-sedimentary sequence within an acid volcanic unit and close to a Carboniferous granite batholith. Sulfide bodies, mainly pyrite, are enclosed in andalusite-bearing siliceous rocks lacking primary textures and recrystallized by the granitic thermal metamorphism.Several genetic interpretations were proposed for these siliceous rocks and the associated mineralization, i.e., as either being related to the granite intrusion or of volcanogenic derivation. Detailed studies led to their identification as hydrothermal alterites.A petrographic study of these siliceous alterites reveals that the main mineral phases are only constituted of silica and alumina: quartz, andalusite, kaolinite and minor contents of muscovite, diaspore and corundum. Neither K-feldspar or biotite are present with andalusite. This implies that thermal metamorphism occurred on an already alkali-, calcium- and magnesium-depleted rock.These siliceous alterites show less mobile-element (Al, Ti, V, Zr, Nb) concentration ranges similar to those of acid volcanic host rocks. A metasomatic model is computed from chemical data on surrounding soda dacites, assuming that acid hydrolysis was the only phenomenon involved, and that Al was stable in this process.Although altered rock types grading to soda dacites do not crop out, their existence may be deduced from surficial bedrock multielement geochemical data. The zoned distribution of elements agrees with that deduced from reactions and experimental phase diagrams.The pyrite bodies are surrounded by two distinct concentric alteration zones; the inner one is advanced argillic and the outer one is sericitic. Such a pattern is unusual for volcanogenic sulfide deposits but commonly associated with porphyry deposits. It may be related to the strong acidity (pH3) of hydrothermal solutions.These siliceous rocks were produced by an in-situ alteration of brecciated dacitic lavas, inside which a stockwork-type pyritic mineralization was deposited.     

A catastrophe mathematical model for uranium mineralization of hot-water origin

Presented in this paper are some primary data on the temperature, stratigraphical altitude and thickness of a certain uranium ore deposit. Taking these data as the parameters for the temperature, pressure and geochemical conditions of uranium mineralization under ideal geological conditions which constitute a finite variable series, in conjunction with the catastrophe theory developed by Rene Thom (1968), we have proposed a swallow-tail model fit to uranium mineralization. This model provides insight into the mechanism of uranium mineralization. Our study shows that the process of uranium mineralization is a discontinuous or catastrophic event. Temperature and pressure are considered important thermodynamic conditions which control the distribution pattern of uranium mineralization, and the principle of temperature-pressure correspondence for uranium mineralization has been also derived. Geological bodies of minerogenetic importance serve as favourable geochemical media for capturing ore-forming materials. Uranium mineralization of commercial importance depends on a delicate coupling between temperature,pressure, and geochemical condition. The loci of uranium mineralization in the model constitute the surfaceK, referred to as the surface of enrichment-mineralization, on which minerogenetic domain is expected. The model provides quantitatively clues to the process of uranium mineralization, i.e., a process from quantitative to qualitative changes.     

A mathematical model for orientation data from macroscopic conical folds

Statistical techniques are developed to classify folds into one of three classes: cylindrical, conical, or neither. A translated version of Bingham's distribution on the sphere is applied to orientation data fron conical folds. Iterative least-squares techniques are used to determine the best-fitting small circle (or cone), and confidence intervals for the cone axis and half apical angle are developed. Examples of a cylindrical and a conical fold are given. Another fold is neither cylindrical nor conical and is classified as pseudoconical. Relationships between the Bingham and Fisher distributions are presented.     

A mathematical and numerical model for reactive fluid flow systems

We formulate mathematical and numerical models for multispecies, multi-phase and non-isothermal reactive fluid flow in porous media focusing on the chemical reactions and the transport of solutes. Mass conservation and stability in the time integration are emphasized. We use cell-centered finite volume differencing in space and an implicit Runge-Kutta method in time. Assuming two space dimensions, we introduce flux approximation for arbitrarily shaped convex quadrilaterals. On equidistant and variable sized rectangular grids we choose limited κ= related schemes to approximate the advective flux and the central difference scheme for the diffusive flux. On non-rectangular grids we recommend the VF9 scheme for the estimation of the diffusive flux. Our model exists as a code. This revised version was published online in July 2006 with corrections to the Cover Date.     

泥石流的二维数学模型

泥石流是在重力作用下,由砂粒石块和水等组成的固液混合物,是一种发生于山区的复杂的地质灾害现象。泥石流主要是由暴雨诱发引起的,它沿着复杂的三维地形高速流动,具有流体流动的特性。为了模拟泥石流的运动规律,预测降雨诱发的泥石流的到达距离和泛滥范围,减少和避免泥石流引起的灾害,把泥石和雨水组成的固液混合物假定为遵循均匀、连续、不可压缩的、非定常的牛顿流体运动规律。基于质量守恒方程和Naiver-stokes方程,采用深度积分方法,推导出了一个模拟泥石流运动的二维数学模型。所有方程式可用有限差分法来求解。结合GIS,该模型可用于预测泥石流的流动距离和泛滥范围,以及泛滥范围内的危险房屋和路段,也可以用于泥石流灾害的风险性分析。     

A new mathematical model for soil-column experiment and parameter identification

In this paper, one-dimensional soil-column experiment and its mathematical models were discussed. Due to nonlinear behaviors of solute transport in soil and groundwater, the ordinary retardation factor could be a nonlinear function of solute concentration, and the zero production term could be modified to a nonlinear term related with solute concentration, and then a new mathematical model with nonlinear terms was put forward. Furthermore, an inverse problem of identifying nonlinear source parameters was put forward according to the additional data of breakthrough curves （BTCs）. Numerical simulations for the inverse problem here were carried out by applying gradient regularization （GR） method. Finally, the method was successfully used to explore an actual soil-column experiment in Zhangdian, Zibo, Shandong Province.     

A mathematical model for orientation data from macroscopic cylindrical folds

An asymptotic form of Bingham's distribution on the sphere is applied to orientation data from cylindrical folds. Data from cylindrical folds typically form two clusters, one cluster for each fold limb. A bimodal distribution is obtained by fitting a unimodal distribution to each cluster. One parameter of the distribution gives the fold axis, another parameter is directly related to the curvature of the fold limb. Certain tests of hypotheses based on this distribution are the same as tests based on the Dimroth—Watson (symmetric girdle)distribution. One such is the test of whether two folds have the same fold axis.     

Effects of human-induced alteration of groundwater flow on concentrations of naturally-occurring trace elements at water-supply wells

The effects of human-induced alteration of groundwater flow patterns on concentrations of naturally-occurring trace elements were examined in five hydrologically distinct aquifer systems in the USA. Although naturally occurring, these trace elements can exceed concentrations that are considered harmful to human health. The results show that pumping-induced hydraulic gradient changes and artificial connection of aquifers by well screens can mix chemically distinct groundwater. Chemical reactions between these mixed groundwaters and solid aquifer materials can result in the mobilization of trace elements such as U, As and Ra, with subsequent transport to water-supply wells. For example, in the High Plains aquifer near York, Nebraska, mixing of shallow, oxygenated, lower-pH water from an unconfined aquifer with deeper, confined, anoxic, higher-pH water is facilitated by wells screened across both aquifers. The resulting higher-O₂, lower-pH mixed groundwater facilitated the mobilization of U from solid aquifer materials, and dissolved U concentrations were observed to increase significantly in nearby supply wells. Similar instances of trace element mobilization due to human-induced mixing of groundwaters were documented in: (1) the Floridan aquifer system near Tampa, Florida (As and U), (2) Paleozoic sedimentary aquifers in eastern Wisconsin (As), (3) the basin-fill aquifer underlying the California Central Valley near Modesto (U), and (4) Coastal Plain aquifers of New Jersey (Ra). Adverse water-quality impacts attributed to human activities are commonly assumed to be related solely to the release of the various anthropogenic contaminants to the environment. The results show that human activities including various land uses, well drilling, and pumping rates and volumes can adversely impact the quality of water in supply wells, when associated with naturally-occurring trace elements in aquifer materials. This occurs by causing subtle but significant changes in geochemistry and associated trace element mobilization as well as enhancing advective transport processes.     

A probabilistic permeability model and the pore size density function

Mathematical interpretation of the pore size disribution (PSD) data as measured by mercury intrusion porosimetry was revealed in detail. The PSD data were commonly presented as cumulative intruded volume per gram of specimen versus pore size. In this paper, however, they were expressed in a dimensionless term for convenient mathematical operations. The pore size density function was deduced from the PSD data using the finite difference approximation and curve-fitting technique. For the prediction of permeability, first the published correlations between permeability and pore geometry were critically reviewed. A probabilistic permeability model based on the pore size density function was then developed, which can be thought of as a generalization of Childs and Collis-George's model. Predictions of permeability of the compacted soils studied using the developed model were very good for a wide range of permeabilities.