Rate Equations and an Ion-pair Mechanism for Batch Dissolution of Gypsum: Repositioning the Shrinking Object Model at the Core of Hydrodynamic Modelling

Recent improvements to experiments and modelling of batch dissolution in a turbulent reactor, based upon the shrinking object model, are extended to middle loadings of gypsum, that is, in the region between low and high loadings, which lead, respectively, to high under-saturation or saturation with a great excess of solid left undissolved. Dissolved calcium sulphate concentration was monitored by change in electrical conductivity. This investigation uses an improved, ion-pair model for CaSO ₄ ⁰ to allow for the presence of calcium or sulphate added as common ions. The study demonstrates that the full dissolution curve for 5.82 mM loadings of 106-μm particles of gypsum (~1.00 g L^?1) in de-ionised water barely changed in the presence of either 4.64 or 8.09 mM calcium chloride, or 4.39 mM sodium sulphate. However, this masked a doubling of dissolution rate imposed by comparable increases in ionic strength from sodium chloride. The results are consistent with the ion pair, CaSO ₄ ⁰ , being the key species in the rate-determining step of the back-reaction, and perhaps all salt dissolutions, including calcium carbonate. In this case, the rate equation is as follows: \( {\frac{{{\text{d}}c}}{{{\text{d}}t}}} = \frac{S}{V} \cdot (k_{1} - k_{2}^{\prime } \cdot [{\text{CaSO}}_{ 4}^{0} ]) \), where k ₁ and k ₂′ are rate constants. The reported observations are interpreted as effects of ionic strength and common ion concentrations upon the formation equilibrium for the ion pair. This rate equation readily transforms mathematically to one involving the product of [Ca²⁺] and [SO₄ ^2?] in the back-reaction. The parallel of this with the well-known PWP equation used in calcium carbonate dissolution is discussed, with the CaHCO₃ ⁺ ion pair of the equation being replaced by that of CaCO ₃ ⁰ . Meanwhile, the earlier use of the product, [Ca²⁺]^½ × [CO₃ ^2?]^½, in the back-reaction term of another dissolution rate equation for calcite is shown to be incorrect. Finally, it is argued that the shrinking object model should be repositioned as a logical derivative of the hydrodynamical approach to dissolution.     

Sucrose Dissolution Studies Leading to a Generic Shrinking Object Model for Batch Dissolution of Regular-Shaped Particles

The dissolution of sieved sucrose crystals has been studied spectrophotometrically by observing the increase in dissolved sucrose concentration with time. Equations recently derived from the shrinking sphere model for the batch dissolution of a solid in under-saturated conditions tested successfully on both single crystal-size and mixtures of two sizes of sucrose crystals. Single-sized crystals provided a straight line for the plot of the fraction of un-dissolved solid to the power one-third, versus time ( vs. t). The dissolution of mixtures of two crystal sizes fitted the non-linear equation tested earlier on sodium chloride in water-propanone mixtures. Together, these two sets of tests on ionic and covalent substances verify that many simple dissolutions will be easily modelled using this physical model based on shrinkage, where the chemical composition of the solids is very much of secondary importance. Consequently, there is an increased chance that the equations will describe the dissolution of biogenic silica in seawater, the problem which originally inspired this study. More than this, though, the equations are discovered to be mathematically generic; very many geometries other than the sphere satisfy the same equations, and the “shrinking object dissolution model” is thereby defined. The approach should also apply even to non-aqueous dissolutions. A prototype plot of shrinking object rate constant (obtained from numerical fitting of the model to sucrose) versus particle size is presented, and it is shown how analogous treatments for other substances will be central to collection and use of much dissolution data in the future. The study is placed in context with much earlier solid phase decomposition studies, concluding that the key characteristic of the simplest of all dissolutions is that the interface between solid and liquid should advance at a uniform linear rate. It is shown how this approach leads to equations of the same mathematical forms already discussed above.     

A New Differentiation Operator for Seismic Wave Equation

1. Introduction The pseudospcetral (PS) method was employed in the calculations for fluid dynamics (Orszag, 1972). The method has also been employed widely in the simulations of acoustic wave and elastic wave equations because of its high accuracy and efficiency in use of the computer memory compared with the other discrete numerical method (Kosloff and Kosloff, 1982; Fornberg, 1987; Reshef et al., 1988). The time differentiation in the PS method is generally performed by using a second or…     

一种新的储层孔隙成因类型--石英溶解型次生孔隙

石英作为碎屑岩储层中的一种难溶组分,普遍认为它和次生孔隙的形成关系不十分密切。研究认为泌阳凹陷核桃园组储层中的碎屑石英颗粒存在明显的溶解现象,并形成以石英直接溶解型孔隙为主的储集空间特征。石英颗粒被溶解的部分在薄片中所占的范围为 2 %～ 7%者常见,高者达 8%以上,在总孔隙中所占的相对含量也多数在10 %～ 35 %之间,早成岩B期是其最主要形成期。石英溶解型次生孔隙的大量存在为碎屑岩储层中SiO₂ 胶结物及次生孔隙成因等问题的解释以及储层预测和评价提供了新的可能性。     

A New Equation for the Shear Strength of Cable Bolts Incorporating the Energy Balance Theory

The application of cable bolts as a secondary support system is an increasing trend in underground coal mines worldwide. The performances of cable bolts have been evaluated under both axial and shear loading conditions. Two methods of testing cables for shear, single and double shear, have been recognised. This paper examines the shear behaviour of a variety of cable bolts under different pre-tension loads by double shear testing. Plain, spiral and the combination of both cable types were used in this study. The initial axial load and the type of cable bolts are the main factors affecting their shear strength. By increasing the axial pre-tension load, the peak shear load occurs at lower shear displacement. The failure angle due to cable bending across the joint at different pre-tension loads varied between 41° and 49°. This demonstrates that the ratio of axial and perpendicular displacements is almost constant and on average the failure occurs at about 45°. A novel analytical model is proposed to evaluate the shear behaviour of pre-tensioned fully grouted cable bolts subjected to double shearing. Energy and Fourier Series methods were incorporated in the model to simulate the shear behaviour of cable bolts. The comparison of the experimental results with the proposed model shows a good agreement.     

一种基于Kozeny-Carmen方程改进的渗透率预测新方法

在计算复杂孔隙结构储层渗透率时,常规采用的孔渗指数方法或流动单元分类方法几乎很难准确评价渗透率。针对这一问题,本文提出一种引入修正迂曲度因子的改进的Kozeny-Carmen方程渗透率计算新方法。首先引入迂曲度因子修正Kozeny-Carmen方程,迂曲度因子可以表达为孔隙度与岩电参数的函数;然后对改进的Kozeny-Carmen方程进行推演变换,得到新的流动单元指数,能够更好地将储层进行分类;最后利用自适应神经模糊推理系统建立取心段岩心渗透率与测井曲线的模型,并将此模型应用到非取心段的渗透率评价中。岩心渗透率与预测渗透率的对比验证了该方法的正确性与有效性,且渗透率计算精度较常规孔渗指数方法和流动单元分类方法有较大提高。该方法在南海西部海域莺歌海盆地东方气田储层评价中应用效果良好。     

离子色谱法测定地表水中六种无机阴离子

研究了利用直接电导检测-离子色谱法分离测定地表水中常见的六种无机阴离子(F-,Cl-,NO2-,NO3-,SO42-,PO43-)的方法.实验采用lonpac AS11-HC阴离子交换色谱柱,选用NaOH为淋洗液,考察了淋洗液浓度、流速及柱压对上述常见无机阴离子的影响.确定最佳色谱条件为:以20 mmol/L NaOH为淋洗液,流速1.0 mL/min,柱温18～25℃.在此条件下可同时基线分离6种阴离子,且色谱峰形对称.所测阴离子的检出限为0.055～0.61 mg/L;离子浓度的相对标准偏差(RSD,n=3)在1.56%～2.50%之间.准确度实验表明,各种阴离子的检测结果均在标准样品所标注的浓度误差许可范围之内.方法简便实用,用于实际样品分析,所得结果令人满意.     

Silica Gel as a Surrogate for Biogenic Silica in Batch Dissolution Experiments at pH 9.2: Further Testing of the Shrinking Object Model and a Novel Approach to the Dissolution of a Population of Particles

Recently, the increase in dissolved concentration in the batch dissolution of various salts or sucrose has been successfully modelled with three equations, one a cubic in time. However, from three separate earlier investigations with ocean sediments and phytoplankton frustules, there is residual suspicion that biogenic silica does not follow this behaviour. This paper shows that the Shrinking Object Model applies to the dissolution of sieved silica gel particles, as well as to a sample of unsieved, freeze-dried frustules of Odentella sp. Silica gel, being readily available in quantities that can be sieved, is a useful surrogate for biogenic silica in allowing problems of experimental design to be overcome. The dissolutions covered three possible analytic integrations that arise from the model: an exponential for approach to saturation with excess solid silica; the approach to near saturation with either a slight excess or deficiency of silica; dissolution at high under-saturation. Good agreement was found between experimental results and mathematical modelling. The paper provides template calculations by which future raw results can be parameterized. Nevertheless, the reasons for non-linear kinetics reported in earlier work have not been identified, and so controversy over non-linear dissolution kinetics is enhanced. Stirring regime was found to be important with silica gel dissolution, and so biogenic silica dissolution is therefore likely to be ‘transport limited’ at low stirring rate. Accordingly, all archived and future data should be scrutinized for stirring effects before being applied to the oceanic environment. A rigorous test for determining whether a substance’s dissolution deviates from the model is recommended as a preliminary to any future dissolutions, whether in batch or with the chemo-stat. A fixed amount of frustule sample is added to a series of buffered mixtures containing increasing background silicic acid concentrations. Absence of any problem is marked by a linear plot between the increase in silicic concentration accruing over a fixed reaction period and that of the background silicic acid. A novel mathematical proof is provided to justify the test’s use. The reasons for the earlier deviations from expected behaviour of, for example, oceanic sediments, are discussed. Lastly, the paper provides a novel approach to the dissolution of a population of particles of mixed sizes which will probably find ready future application in oceanography.     

一种新的凝析气藏无因次产能评价方程

凝析气藏在衰竭开发过程中存在复杂的相态变化,凝析油的析出使得地层呈现出油气两相混合渗流状态.针对目前凝析气藏无因次产能评价方程的研究较少的现状,在凝析气藏拟稳态流入动态方程的基础上,利用泰勒级数展开、多项式回归等一系列解析方法建立了一种新的凝析气藏无因次产能评价方程.首先对拟稳态流入动态方程中的拟压力函数定积分进行泰勒级数展开,然后利用稳态定理和多项式回归方法求解出泰勒展开式的各项系数,最后通过解析方法得到了凝析气藏的无因次产能评价方程.应用实例表明,该无因次产能方程与实际系统试井数据基本吻合,能够较好地描述凝析气藏的油气两相流入动态;无因次产能评价法所得到无阻流量比常规干气法低,且考虑高速效应的无因次产能评价法所得到的无阻流量要大于忽略高速流动的无因次产能评价法所得到的结果.      

察尔汗盐湖固体钾盐溶解对溶剂注入速率响应机制研究

察尔汗盐湖浅部储卤层赋存有储量可观的固体钾盐资源, 目前正处于溶解液化开采阶段。储卤层中固体钾盐矿物溶解及储卤层结构变化特征受到溶剂注入速率控制, 但其控制机制尚不明确。本文以察尔汗盐湖浅部储卤层典型钻孔岩芯为研究对象, 通过开展室内岩芯柱渗流模拟实验, 研究岩芯在三种流速条件下储卤层渗透系数和固体钾盐矿物溶出的变化规律。结果表明: (1)随着注入溶剂速率的增大, 岩芯渗透系数呈现逐渐增大的趋势, 渗出液中钾离子浓度呈现持续减小的趋势, 但在流速改变的时间节点处, 岩芯渗透系数和其对应溶出液中钾离子浓度均出现异常增加现象。矿物的溶解引起储层孔隙度增加, 而溶剂流速的改变会导致松散盐类矿物颗粒重组。(2)储卤层岩芯固体钾盐矿物溶解受到溶剂注入速率的影响明显。注入速率增加引起矿物颗粒重组以及滞留孔隙高浓度水体释放是造成渗出液中K+浓度短暂性升高的主要原因。本次实验研究对于研究区低品位固体钾盐的水溶开采具有一定理论指导意义。     

用改进的时间差分有限分析法模拟地下水非稳定井流方程

提出了一种改进的时间差分有限分析算法,它能够避免在求解水头剧烈变化时用一般有限分析法计算精度较差的缺陷.算法的稳定性好.     

典型岩溶断陷盆地溶蚀速率对海拔高度和土地利用方式的响应

采用标准溶蚀试片法,研究典型岩溶断陷盆地内不同海拔高度区域(中山区、平坝区和河谷区)6种土地利用方式下(弃耕地、草地、灌木地、松树林地、柏树林地及其他林地)的试片溶蚀速率,并分析其影响因素.结果显示:土下0–60 cm的试片平均溶蚀速率按大小排列顺序为:松树林地((3.98±0.41)mg·cm–2·a–1)>草地((...     

频域波动方程的多重网格法

针对差分法求解过程中细网格计算所需时间和空间要求高以及在粗网格上计算又达不到所要求的精度等问题，利用粗网格上的残差校正特性消除迭代误差的低频分量，同时利用细网格上的松弛光滑特性消除迭代误差的高频分量，采用不同疏密的网格距消除不同频率范围内的误差分量，将多重网格方法成功应用于频域波动方程的求解，并给出了实际算例。算例中，分别用Gauss-Seidel迭代法和多重网格法求其数值解，并绘出效果图；比较得出多重网格方法具有精度高、收敛速度快和易于实现的特性，更适合于高维波动问题的求解。     

A Potential New Chalcopyrite Reference Material for Secondary Ion Mass Spectrometry Sulfur Isotope Ratio Analysis

Chalcopyrite is an important sulfide mineral in many types of ore deposits, but matrix‐matched chalcopyrite reference materials for microanalysis are lacking. A new natural chalcopyrite‐bearing specimen (HTS4‐6) was analysed in this study to investigate its potential as a reference material for microbeam sulfur isotope ratio measurement. Detailed textural examination and major element determination showed that the HTS4‐6 chalcopyrite grains have no growth rim or zoning. A total of 607 sulfur isotope ratio spot measurements with secondary ion mass spectrometry (SIMS) conducted on the cruciform sections, and over 120 randomly selected grains yielded highly consistent sulfur isotope ratio. The intermediate measurement precision for four measurement sessions of the ³⁴S/³²S measurement results was better than 0.39‰ (2s). Randomly selected chalcopyrite grains of HTS4‐6 were further analysed by LA‐MC‐ICP‐MS, which gave a mean δ³⁴S value of +0.58 ± 0.38‰ (2s, n = 95). The maximum variance (expressed as intermediate precision from SIMS and LA‐MC‐ICP‐MS measurements) is not worse than 0.39‰ (the SIMS value), indicating that HTS4‐6 chalcopyrite is a potential reference material for in situ microbeam sulfur isotope measurements. The mean δ³⁴S value determined by gas source isotope ratio mass spectrometry (GS‐IRMS) is +0.63 ± 0.16‰ (2s, n = 23), consistent with that derived by LA‐MC‐ICP‐MS, and can represent the recommended value for this potential reference material.     

不同土地利用土下溶蚀速率季节差异及其影响因素——以重庆金佛山为例

不同土地利用土壤往往具有不同的水分和CO2特征,进而影响到土下岩溶作用的强度和方向。以重庆金佛山为例,选择两个不同高程的岩溶泉流域,研究了流域内典型土地利用土壤水和土壤CO2的变化,土壤水分特征及土下溶蚀速率,并分析了土下岩溶作用的主要驱动因子。结果表明土下溶蚀作用主要发生在夏季:碧潭泉和水房泉流域不同土地利用土下雨季平均溶蚀量分别占年溶蚀量的65.5%和71.9%。进一步证实土壤CO2和土壤水的滞留时间是驱动岩溶作用的两个关键因子,土壤水传导能力可能是控制旱季土下溶蚀速率的决定性因素。     

二溴羟基苯基萤光酮胶束增溶光度法测定痕量锗的研究及应用

系统地研究了二溴羟基苯基萤光酮在不同表面活性剂存在下与Ｇｅ的显色反应。在０．２－２．０ｍｏｌ／Ｌ的Ｈ２ＳＯ４介质中,显色反应灵敏度高（ε５１８＝１．４１×１０＾５）、显色速度快且至少稳定２４ｈ,干扰少,Ｇｅ量在０－５００ｎｇ／ｍｌ范围内符合比耳定律,经应用于矿石中痕量Ｇｅ的直接测定,证明方法可行。     

Shrinking Sphere Kinetics for Batch Dissolution of Mixed Particles of a Single Substance at High Under-Saturation: Validation with Sodium Chloride, but with Biogenic Silica in Mind

The cubic equation recently derived for the increase in concentration of a solute with time, as the solid dissolves in batch according to the shrinking sphere model at high under-saturation, is extended to dissolutions of mixtures of differently sized particles. This problem needs to be solved if batch dissolutions are to play their part in the proposed amelioration of global warming and associated climate change by accelerated ‘re-burial’ of excess CO₂ in ocean sediment. The upgraded model was tested using sodium chloride dissolved in 50% aqueous propanone, whence the model fitted two separate runs with 500 and 212 μm, and 212 and 38 μm, diameter crystals, respectively. The key to simulating dissolution in this way lies in the dissolutions being independent of each other. It is further shown that although this condition was implicit in the recent derivation of the cubic equation, it was not recognised at the time. The work should be applicable to any batch dissolution of mixed particles at high under-saturation, and hence, may find use in many industrial and laboratory dissolutions. Simulations show how agglomerated mixtures can yield a straight line on the plot of ln(1 − C/C _T) versus time, as was reported to occur recently with sodium chloride taken ‘straight from the bottle’. It is shown that this probably explains why exponential dissolutions may have seemed appropriate to the dissolution of biogenic silica in earlier literature. This study suggests that a new round of biogenic silica dissolutions, but with sieved samples, would be worthwhile, with the likelihood that shrinking sphere behaviour might well be found to characterise the kinetics. The opportunity is taken to investigate a number of aspects of the shrinking sphere model not generally discussed before, e.g. the graph for the change in surface area with time. The limitations of using cubic salt crystals with the shrinking sphere model are discussed.     

深部碎屑岩储层溶蚀作用实验模拟研究

结合渤海湾深层天然气勘探实际,选用渤海湾盆地深埋储层的长石砂岩和灰质长石砂岩,配制与地层有机酸组分相近的反应液,模拟开放-半开放条件下,晚成岩期有机酸溶解作用。通过样品定位对比分析,结果证明:①乙酸对碎屑岩颗粒,特别是钾长石、钠长石、方解石、白云石溶蚀过程中,Ca、Mg、Na、K离子优先释放,Al、Si离子释放较慢。②扫描电镜定位对比分析表明,在实验模拟的高温、开放成岩环境下,乙酸优先溶解方解石,方解石溶出速度大于白云石;钠长石比钾长石更易溶解。③溶解试验反应161h后,孔隙度平均提高2%~3%,证实了乙酸可提高深部储层的次生孔隙空间。溶解量的大小与矿物中可溶物质含量有关(特别是方解石、长石、白云石的含量有关)。④X衍射、能谱分析和扫描电镜资料证实,溶解沉淀物为硅质、铝硅酸盐沉积物,呈块状、粒状产出。由于沉淀时间短,其晶形较差,而且随着反应时间增加,沉淀物数量增加。