A mass transfer model of bauxite formation

The formation of bauxite due to weathering of a granitic protolith has been simulated by means of a one-dimensional flow and reaction model based on the mass transfer principle. The model couples mineral dissolution and precipitation reactions, speciation in solution, and advective solute transport in a porous medium. A very important aspect of the modeling study is the use of mineral reaction rates determined experimentally in the laboratory. The important effects of solution saturation state and pH have been incorporated into the kinetic rate laws governing the heterogeneous reactions. The values of these parameters have been obtained from the scientific literature to guarantee that realistic reaction rates are used in the simulations. Albite and quartz are the minerals that make up the parent rock in the model. Gibbsite, kaolinite, and a Na-mica (as a surrogate for smectite) are the secondary minerals that have been taken into account. Long-term simulations (>1 Ma) have been run, and the formation of a bauxitic profile, with an upper gibbsite-rich and a lower kaolinite-rich zone, is predicted. In early stages of the process (up to a few hundreds of thousands of years), both gibbsite and kaolinite precipitate directly from solution as a consequence of albite dissolution. In later stages, the bulk of gibbsite precipitation derives from the incongruent dissolution of kaolinite, while kaolinite precipitation is still caused by the dissolution of albite. This is also reflected by the formation of two reaction fronts in the profile. These results are compared with weathering sequences from the Los Pijiguaos bauxite deposit, Venezuela. The overlap between the gibbsite and kaolinite zones and the replacement of kaolinite by gibbsite are consistent with model calculations. Mechanical denudation has to be called upon to explain the limited thicknesses of the weathering profiles in the field. The role of mechanical erosion is supported by the presence of microsedimentary structures in the bauxite and the balance between dissolved and suspended loads in the streams draining the area.     

A study of a plug-flow model for flotation froth behaviour

The importance of the cleaning action of the froth has been recognised. In order to observe the effect of various mechanisms on the gradients of mineral concentration in the froth, experiments were performed in a flotation cell using a deep froth phase where transverse motion of the froth was reduced to a minimum. The variables chosen for study include gas rate, baffling of the froth and product removal rate. The mineral studied comprised a mixed Cu, Zn and Fe sulphide with a siliceous gangue. A model based on counter-current plug-flow assumptions is advanced to describe some of the effects observed. A number of these effects are simulated using this model, leading to a better understanding of some of the processes occurring in the froth.     

A modified laboratory cell for the flotation of coal

The need to obtain accurate, operator-independent data from small-scale laboratory flotation tests has become particularly apparent in the treatment of fine coal. The work described suggests a method for reducing operator dependency by removing the flotation froth uniformly. This is achieved using a perspex insert to change the geometry of the cell, by maintaining a constant pulp level height and by removing froth from the full width of the cell and at a fixed depth.A comparison is made between the modified cell and a conventional Denver cell by obtaining equilibrium and kinetic data for each cell from two independent operators.The comparison shows a reduction in the variability of the results obtained from the modified cell.     

裂隙岩体渗流-传热耦合的复合单元模型

基于复合单元法建立了裂隙岩体渗流-传热耦合的复合单元模型。该模型前处理简便快捷,网格剖分不受限制,可依据裂隙的真实信息自动将其离散在单元内。其次,采用交叉迭代算法,对裂隙岩体的渗流场和温度场进行耦合分析,耦合算法不仅考虑了温度对流体运动黏度的影响,而且可计算裂隙中流体与相邻岩块间渗流-传热过程以及两者间的渗流量和热量交换。通过与已有近似解析解相比较,验证了复合单元耦合算法的可靠性。算例分析表明,渗流-传热耦合作用对裂隙岩体的渗流场和温度场均有一定的影响。分析了不同岩块热传导系数和裂隙开度对热能提取效率的影响,结果显示,岩块热传导系数越大、裂隙开度越大,低温流体从高温岩块中吸取的热能会较多,出口处流体温度下降得较快。     

A recycle flow flotation machine model

Residence time measurements were made on a Denver laboratory flotation machine with and without the DR ring assembly. Soluble and insoluble tracers were used (a dye and fine quartz, respectively), and the variables studied were tank liquid volume, $\text{V}$, water and air volumetric flow rates, Q and Q_A respectively, and some geometric and design variables.By analogy with nominal residence time, $\text{t}{}_{\mathrm{<mtext>N</mtext>}}\text{(=}\text{V}\text{Q}\text{)}$, a term “effective residence time” $\text{t}{}_{\mathrm{<mtext>E</mtext>}}$ is defined by:

$\text{f}\text{(t)=}\text{exp}\text{[?}\text{t}\text{t}{}_{\mathrm{E}}$

where f(t) is the fraction of tracer remaining in the tank at time t. Perfect mixing is indicated if and only if: (i) data satisfies the exponential relationship; and (ii) $\text{t}{}_{\mathrm{<mtext>E</mtext>}}\text{t}{}_{\mathrm{<mtext>N</mtext>}}\text{= 1}$.Using the soluble tracer the machine behaved substantially as a perfect mixer under all operating conditions, except with the DR ring at values of Q_A nearly double the natural aeration capacity of the machine; condition (i) above was satisfied, but $\text{t}{}_{\mathrm{<mtext>E</mtext>}}\text{t}{}_{\mathrm{<mtext>N</mtext>}}\text{～ 1.1}$.With the insoluble tracer the machine behaved as a perfect mixer only without air. As Q_A increased, $\text{t}{}_{\mathrm{<mtext>E</mtext>}}\text{t}{}_{\mathrm{<mtext>N</mtext>}}$ increased from unity to about 1.2, and the effect was emphasized by the DR ring. In all cases condition (i) above was satisfied.A model in which the flow pattern in the tank includes a large component of pulp recirculation through the impeller region is developed. This model can account for the experimental findings but the details remain to be elucidated.     

Dynamic model of flotation cell banks — circuit analysis

While all mineral industry flotation circuits are stable, they are sensitive to low-frequency perturbations in the feedrate. In both countercurrent and cocurrent circuits, the lead cell is more sensitive to feed variations. The frequency response predicts the amount of extra cell capacity needed to handle the maximum feed due to a sinusoidal forcing function. Feedback loops are more significant than sump delays. The countercurrent $\text{4 × 4}$ circuit floating quartz, with a 200-sec retention time, requires 75 minutes for the concentration of quartz in the input to the first cell to reach 95% of its steady-state value. Countercurrent circuits were found superior to cocurrent circuits in all respects.     

A model for the emplacement of the eastern compartment of the bushveld complex

The stratigraphy and geological position of the eastern compartment of the Bushveld Complex are described. A mechanical model for the initiation and growth of the eastern compartment of the Bushveld intrusion has been developed using thin elastic plate theory, assuming linked conical magma chambers. It is shown that the contribution to the pressure at the base of a cell by the restitutional force exerted by the roof of Rooiberg felsites is 10⁴ times as great as that of the layers of host in the cone. Both are minimal compared to the lithostatic pressure exerted by the magma pile. Roof deformation is therefore seen to be a more important process than sagging of the floor during intrusion—a feature which probably occurred during cooling, solidification and isostatic readjustment of the area.A stratigraphie model is proposed in which the intrusion of basic rocks into the Transvaal sequence is discussed in the light of continuous basin subsidence. Early submarine sedimentation in an irregularly-floored basin some 620 km in diameter situated on the Archaean craton gave rise to a 7.7 km thick sedimentary pile, to which was added some 7 km of subaerial basalts and felsites. Depression of the floor of the basin into the regime of maximum horizontal compression induced favourable conditions for the intrusion of a total of 2.5 km of diabase sills which further assisted the subsidence. The 9 km thick Bushveld Complex was intruded into the basal sections at points along a 010° trend in a regime characterised by shear failure. Early magma influxes gave rise to a laminated marginal zone forming a shallow cone, with associated sill activity, whilst continued later influxes filled the conical cell, transgressed the floor and uparched the roof. Partial melting in the regions beneath the Complex, exacerbated by continued crustal depression, gave rise to the late Bushveld granites.     

A numerical model for porosity modification at a sandstone-mudstone boundary by quartz pressure dissolution and diffusive mass transfer

In many sandstones quartz cements significantly reduce porosity. The origin of these cements is often unclear. This paper investigates a possible mechanism for the generation of silica for quartz cement by pressure dissolution in interbedded mudstones. Theoretical models of quartz pressure dissolution, including the effects of silica precipitation kinetics, show that the concentration of dissolved silica in the pore fluids of a compacting sediment increases with decreasing grain size and silica precipitation constant. Quartz precipitation is strongly inhibited by the presence of small amounts of clay within a sediment, suggesting that siltstones and quartz-rich mudstones which are undergoing pressure dissolution may act as a source of dissolved silica for export to nearby, coarser sediments. A computational model for the diagenetic modification of a sandstone-mudstone interface due to pressure dissolution is described. Both sandstone and mudstone layers are assumed to be actively compacting by pressure dissolution, and mass transport by molecular diffusion is considered. As quartz precipitation in the mudstone layer is relatively slow compared to that in the sandstone, significant amounts of dissolved silica become available in the mudstone, and may be exported into the adjacent sandstone. In the absence of pore-fluid advection, this may result in the formation of extensive secondary quartz within the sandstone, close to the interface. The volume of silica exported from the mudstone is limited by the length scale over which diffusion through the mudstone is effective. This is typically 3–5 m. The volume of silica available therefore suggests that extensive porosity modification within the adjacent sandstone can only occur close to the mudstone. Thus it is possible that thin sandstones could become cemented by slow diffusive transfer of silica, but that in thicker sandstones the silica may become dispersed by pore-fluid advection.     

Fluid convection and mass transfer in porous sandstones—a theoretical model

When porous, fluid-saturated, bodies of geologic dimensions are subjected to temperature gradients on the order of the normal geothermal gradient (25°C/km) it is shown that large (km) scale eddy currents will spontaneously arise and persist in these bodies. The velocity of these fluid currents is on the order of 1 meter per year, but taken over a period of several million years, the mass flux accompanying the fluid flow is large enough to produce significant porosity changes. It is shown that diffusive mass transfer is generally a negligible component of the total mass flux when characteristic distances are greater than grain diameters and it is concluded that most post-depositional reservoir cementation is due to slowly circulating fluids. In terms of a broad perspective, reservoir diagenesis can be regarded as a low heat flow analogue of hydrothermal alteration, occupying the low fluid flow regime of the spectrum, and passing into the hydrothermal regime as the heat flow and fluid velocities increase.     

安徽兆吉口热液型铅锌矿区元素迁移量三维地球化学勘查模式

安徽兆吉口铅锌矿床位于长江中下游成矿带安庆-贵池矿集区南侧的东至县杨老尖-龙门尖地区,这一矿床的发现使皖西南地区地质找矿实现重大突破。文中利用Grant的Isocon图解法,研究活动元素的分布特征和迁移规律,以奠定兆吉口地区的地球化学勘查指标及成矿环境指标的研制基础,发现成矿元素Pb、Zn、Cu、Au、Ag、Mo及其伴生元素As、Bi、Sb和矿化剂元素S等从围岩向矿体部位带入程度增加,常量元素SiO2、Fe2O3、MgO、CaO、Na2O、K2O等在青白口系带出,于矿体部位带入。矿床系统的质量是净带入的,平均质量变化为4%;青白口系质量是净带出的,质量变化为-18%。依据元素迁移规律,试制元素迁移量三维地球化学图,认为研究区进一步找矿工作应当沿断裂带向北东和南西方向拓展,结合已有地质资料,对元素迁移进行了解释,并对矿床成因进行了讨论,认为试验矿床是由区域变质构造运动热液作用形成的,试验矿床只是区域变质构造运动热液活动共同形成的矿床(系列)的一部分,研究区具有良好的找矿前景。     

A rock mass classification model for caving roofs

Summary Evaluation of the caving behaviour of longwall roof rocks has thus far been based on a pot-pourri of classification systems, which ignore basic caving criteria. The paper outlines a new classification model of roof strata namely cavability using fuzzy set methodology and linguistic variables to assign ratings for individual roof beds. A microcomputer program has been developed to evaluate the decision ratings for cavability and the model applied to ten longwall case-histories from Indian coalfields. The classification model has excellent potential for being used as a standard tool for the evaluation of caving behaviour of longwall roof rocks.     

A recycle flow flotation machine model: Response of model to parameter changes

The fraction of solid tracer retained in a laboratory flotation machine is measured as a function of time, simulating semi-batch testing. Observed departures from ideal mixing in which the ratio mean retention time/mean residence time exceeds unity can be accounted for by a recycle model of pulp circulation around the impeller region.Solutions of the system differential equations are recast into forms allowing calculation of the system parameters from the retention time ratio and an initial value, both obtained from tracer experiment data. The effect of changing the parameter values on the model response is discussed. Some special cases, applications, and alternative models are mentioned, and an example is provided.The effects of experimental error on estimated parameter values, and relationships between tracer concentration in the exit stream and the fraction retained formulations, are discussed in appendices.     

An appreciation of galena concentration using a steady-state flotation model

A general-purpose computer program has been developed for the steady-state modelling of flotation plants. It permits simulation of flotation banks, made up of any number of cells, interconnected if necessary through a regrind unit. Specification of the fresh feed material in terms of the relative amounts and flotation-rate behaviour of its flotable components is necessary so that the program can then calculate the concentration of these components in all the plant streams.The use of the program for plant investigation is demonstrated using data for a lead concentration plant. The model was fitted to steady-state plant data and then tested by comparing the predictions of the model with actual plant measurements at a second feed condition. Full circuit simulation results are also presented to show how steady-state modelling can be used to give information on the likely response of the plant to other changes in feed material and the benefits which might result from rearrangements of the circuit.     

Potential use of model predictive control for optimizing the column flotation process

A constrained model predictive control (MPC) strategy is proposed to deal with the problem of optimizing flotation column operation using secondary variables. Froth depth, collection zone gas hold-up and bias rate are selected as secondary variables to be controlled whereas tailing, wash-water and gas flow rate are used as manipulated variables. The control problem was formulated in order to minimize the tracking error of the gas hold-up and bias rate by maintaining gas flow rate, wash-water flow rate and bias rate within their operational limits. In particular, a strategy was conceived to optimize the column flotation process based on establishing an unreachable high set point for the gas hold-up (which is equivalent to maximizing the bubble surface area available for particle collection at a given flotation reagent dosage and thus recovery), while simultaneously satisfying operational constraints (such as ensuring a positive bias rate to prevent gangue entrainment and therefore concentrate grade deterioration). Several other operational constraints on wash-water, gas rate, gas hold-up and bias rate were considered, their use being justified from a processing point of view. Since this study deals with the hydrodynamic characteristics of flotation columns, a pilot flotation column working with a two-phase system is sufficient to demonstrate the advantages of using predictive control for this process optimization.     

黏弹性节理岩体的位移不连续模型研究

选用三参数标准线性固体作为岩石本构,提出了一种考虑岩体黏弹性的位移不连续模型;根据一维黏弹性波的特征线法,推导了节理处质点速度、应力和应变递推公式。首先,基于分离式霍普金森压杆（SHPB）对砂层进行试验,得到其应力-应变关系,并换算出砂层节理的法向刚度;接着,通过一维强间断黏弹性波的波速公式、高频波衰减系数以及任一频率下的衰减系数,确定出数值算法中的三参数。最后,基于自制的摆锤装置,探讨了一维应力波在节理岩体中的传播规律,试验中以两根长1 000 mm、直径为68.50 m的岩杆作为入射和透射杆,以3 mm砂层模拟节理。试验和数值结果吻合度良好,进一步验证了该方法的可靠性。     

A spatial estimation model for continuous rock mass characterization from the specific energy of a TBM

Summary  Basic principles of the theory of rock cutting with rolling disc cutters are used to appropriately reduce tunnel boring machine (TBM) logged data and compute the specific energy (SE) of rock cutting as a function of geometry of the cutterhead and operational parameters. A computational code written in Fortran 77 is used to perform Kriging predictions in a regular or irregular grid in 1D, 2D or 3D space based on sampled data referring to rock mass classification indices or TBM related parameters. This code is used here for three purposes, namely: (1) to filter raw data in order to establish a good correlation between SE and rock mass rating (RMR) (or tunnelling quality index Q) along the chainage of the tunnel, (2) to make prediction of RMR, Q or SE along the chainage of the tunnel from boreholes at the exploration phase and design stage of the tunnel, and (3) to make predictions of SE and RMR or Q ahead of the tunnel’s face during excavation of the tunnel based on SE estimations during excavation. The above tools are the basic constituents of an algorithm to continuously update the geotechnical model of the rock mass based on logged TBM data. Several cases were considered to illustrate the proposed methodology, namely: (a) data from a system of twin tunnels in Hong Kong, (b) data from three tunnels excavated in Northern Italy, and (c) data from the section Singuerlin-Esglesias of the Metro L9 tunnel in Barcelona. Correspondence: G. Exadaktylos, Department of Mineral Resources Engineering, Technical University of Crete, Chania, Greece     

The motion of a star with variable mass inside a layered inhomogeneous elliptical galaxy

We consider the motion of a variable-mass star inside a layered, inhomogeneous, rotating elliptical variable-mass galaxy. Under certain conditions, the differential equations of motion of a star inside the galaxy admit autonomization. The autonomized differential equations in this problem are similar to those for the motion of a constant-mass star. We have found analogs for the Jacobi integral and the Eddington-Jeans law for the variation of the density of the galaxy in its center and layers.     

A unified model for the formation and distribution of both conventional and unconventional hydrocarbon reservoirs

The discovery and large-scale exploration of unconventional oil/gas resources since 1980s have been considered as the most important advancement in the history of petroleum geology;that has not only changed the balance of supply and demand in the global energy market,but also improved our understanding of the formation mechanisms and distribution characteristics of oil/gas reservoirs.However,what is the difference of conventional and unconventional resources and why they always related to each other in petroliferous basins is not clear.As the differences and correlations between unconventional and conventional resources are complex challenging issues and very critical for resources assessment and hydrocarbon exploration,this paper focused on studying the relationship of formations and distributions among different oil/gas reservoirs.Drilling results of 12,237 exploratory wells in 6 representative petroliferous basins of China and distribution characteristics for 52,926 oil/gas accumulations over the world were applied to clarify the formation conditions and genetic relations of different oil/gas reservoirs in a petroliferous basin,and then to establish a unified model to address the differences and correlations of conventional and unconventional reservoirs.In this model,conventional reservoirs formed in free hydrocarbon dynamic field with high porosity and permeability located above the boundary of hydrocarbon buoyancy-driven accumulation depth limit.Unconventional tight reservoirs formed in confined hydrocarbon dynamic field with low porosity and permeability located between hydrocarbon buoyancy-driven accumulation depth limit and hydrocarbon accumulation depth limit.Shale oil/gas reservoirs formed in the bound hydrocarbon dynamic field with low porosity and ultra-low permeability within the source rock layers.More than 75%of proved reserves around the world are discovered in the free hydrocarbon dynamic field,which is estimated to contain only 10%of originally generated hydrocarbons.Most of undiscovered resources distributed in the confined hydrocarbon dynamic field and the bound hydrocarbon dynamic field,which contains 90%of original generated hydrocarbons,implying a reasonable and promising area for future hydrocarbon explorations.The buried depths of hydrocarbon dynamic fields become shallow with the increase of heat flow,and the remaining oil/gas resources mainly exist in the deep area of“cold basin”with low geothermal gradient.Lithology changing in the hydrocarbon dynamic field causes local anomalies in the oil/gas dynamic mechanism,leading to the local formation of unconventional hydrocarbon reservoirs in the free hydrocarbon dynamic field or the occurrence of oil/gas enrichment sweet points with high porosity and permeability in the confined hydrocarbon dynamic field.The tectonic movements destroy the medium conditions and oil/gas components,which leads to the transformation of conventional oil/gas reservoirs formed in free hydrocarbon dynamic field to unconventional ones or unconventional ones formed in confined and bound hydrocarbon dynamic fields to conventional ones.     

Calculation of mass transfer coefficients for dolomitization models

Reversible mass transfer associated with alteration of carbonate rocks can be modeled in terms of a pore fluid migrating across a temperature field slowly enough that chemical equilibrium is maintained. These types of models yield both the spatial distribution of the alteration and the absolute amounts of minerals dissolved and precipitated. In order to compute the total mass transfer involved, it is necessary to obtain mass transfer coefficients for each mineral. This paper presents detailed examples of mass transfer in closed systems for the system calcite-dolomite-solution over the temperature range 0–200°C. It is shown that the mass transfer coefficients for the reversible process can be obtained from thermodynamic data and elementary solubility calculations. The connection between these reversible coefficients and the more familiar irreversible mass transfer coefficients is shown to be a simple derivative relation. Calculations are presented for two cases: calcite-ordered dolomite solution and calcite-disordered dolomite solution in both pure water and brines with Ca/Mg ratios similar to seawater. The large mass transfer coefficients obtained for the brines relative tot he pure water is attributed to the fact that the presence of both calcite and dolomite in a system fixes the Ca/Mg cation ratio in the solution as a function of temperature. Dolomitization occurring in nature likely involves both reversible and irreversible processes and accurate interpretation of field data requires the ability to distinguish between these two cases.