A multiobjective steepest descent method with applications to optimal well control

Multiobjective optimization deals with mathematical optimization problems where two or more objective functions (cost functions) are to be optimized (maximized or minimized) simultaneously. In most cases of interest, the objective functions are in conflict, i.e., there does not exist a decision (design) vector (vector of optimization variables) at which every objective function takes on its optimal value. The solution of a multiobjective problem is commonly defined as a Pareto front, and any decision vector which maps to a point on the Pareto front is said to be Pareto optimal. We present an original derivation of an analytical expression for the steepest descent direction for multiobjective optimization for the case of two objectives. This leads to an algorithm which can be applied to obtain Pareto optimal points or, equivalently, points on the Pareto front when the problem is the minimization of two conflicting objectives. The method is in effect a generalization of the steepest descent algorithm for minimizing a single objective function. The steepest-descent multiobjective optimization algorithm is applied to obtain optimal well controls for two example problems where the two conflicting objectives are the maximization of the life-cycle (long-term) net-present-value (NPV) and the maximization of the short-term NPV. The results strongly suggest the multiobjective steepest-descent (MOSD) algorithm is more efficient than competing multiobjective optimization algorithms.     

Molybdenum Mass Fractions and Isotopic Compositions of International Geological Reference Materials

The double‐spike method with multi‐collector inductively coupled plasma‐mass spectrometry was used to measure the Mo mass fractions and isotopic compositions of a set of geological reference materials including the mineral molybdenite, seawater, coral, as well as igneous and sedimentary rocks. The long‐term reproducibility of the Mo isotopic measurements, based on two‐year analyses of NIST SRM 3134 reference solutions and seawater samples, was ≤ 0.07‰ (two standard deviations, 2s, n = 167) for δ^98/95Mo. Accuracy was evaluated by analyses of Atlantic seawater, which yielded a mean δ^98/95Mo of 2.03 ± 0.06‰ (2s, n = 30, relative to NIST SRM 3134 = 0‰) and mass fraction of 0.0104 ± 0.0006 μg g^?1 (2s, n = 30), which is indistinguishable from seawater samples taken world‐wide and measured in other laboratories. The comprehensive data set presented in this study serves as a reference for quality assurance and interlaboratory comparison of high‐precision Mo mass fractions and isotopic compositions.     

Characterization,dissolution and solubility of the hydroxypyromorphite–hydroxyapatite solid solution [(Pb<Subscript>x</Subscript>Ca<Subscript>1−x</Subscript>)<Subscript>5</Subscript>(PO<Subscript>4</Subscript>)<Subscript>3</Subscript>OH] at 25 °C and pH 2–9

Background

The interaction between Ca-HAP and Pb²⁺ solution can result in the formation of a hydroxyapatite–hydroxypyromorphite solid solution [(Pb_xCa_1?x)₅(PO₄)₃(OH)], which can greatly affect the transport and distribution of toxic Pb in water, rock and soil. Therefore, it’s necessary to know the physicochemical properties of (Pb_xCa_1?x)₅(PO₄)₃(OH), predominantly its thermodynamic solubility and stability in aqueous solution. Nevertheless, no experiment on the dissolution and related thermodynamic data has been reported.

Results

Dissolution of the hydroxypyromorphite–hydroxyapatite solid solution [(Pb_xCa_1?x)₅(PO₄)₃(OH)] in aqueous solution at 25 °C was experimentally studied. The aqueous concentrations were greatly affected by the Pb/(Pb + Ca) molar ratios (X_Pb) of the solids. For the solids with high X_Pb [(Pb_0.89Ca_0.11)₅(PO₄)₃OH], the aqueous Pb²⁺ concentrations increased rapidly with time and reached a peak value after 240–720 h dissolution, and then decreased gradually and reached a stable state after 5040 h dissolution. For the solids with low X_Pb (0.00–0.80), the aqueous Pb²⁺ concentrations increased quickly with time and reached a peak value after 1–12 h dissolution, and then decreased gradually and attained a stable state after 720–2160 h dissolution.

Conclusions

The dissolution process of the solids with high X_Pb (0.89–1.00) was different from that of the solids with low X_Pb (0.00–0.80). The average K _sp values were estimated to be 10^?80.77±0.20 (10^?80.57–10^?80.96) for hydroxypyromorphite [Pb₅(PO₄)₃OH] and 10^?58.38±0.07 (10^?58.31–10^?58.46) for calcium hydroxyapatite [Ca₅(PO₄)₃OH]. The Gibbs free energies of formation (ΔG _f ^o ) were determined to be ?3796.71 and ?6314.63 kJ/mol, respectively. The solubility decreased with the increasing Pb/(Pb + Ca) molar ratios (X_Pb) of (Pb_xCa_1?x)₅(PO₄)₃(OH). For the dissolution at 25 °C with an initial pH of 2.00, the experimental data plotted on the Lippmann diagram showed that the solid solution (Pb_xCa_1?x)₅(PO₄)₃(OH) dissolved stoichiometrically at the early stage of dissolution and moved gradually up to the Lippmann solutus curve and the saturation curve for Pb₅(PO₄)₃OH, and then the data points moved along the Lippmann solutus curve from right to left. The Pb-rich (Pb_xCa_1?x)₅(PO₄)₃(OH) was in equilibrium with the Ca-rich aqueous solution.

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Graphical abstractLippmann diagrams for dissolution of the hydroxypyromorphite–hydroxyapatite solid solution [(Pb_xCa_1?x)₅(PO₄)₃OH] at 25??C and an initial pH of 2.00.

     

经略21世纪海上丝路:重要航线、节点及港口特征

为了更好地认识21世纪海上丝绸之路(简称"海上丝路"),文章对"海上丝路"涉及的重要航线、节点及港口的地理位置、气候状况、水文特征、商业价值、人文背景等进行梳理。重要航线、节点及港口的使用与管理作为"海上丝路"建设的基础要素,是与造船能力并列的核心资源,三者之间环环相扣,构成"海上丝路"健康运营的完整体系。与沿"海上丝路"国家稳步推进航线、节点及港口的管理、开发与维护,打造坚实的战略支撑点、现代之"海上驿站",是成功实现我国资源多样化、产业走出去、贸易全球化的最佳路径之一,以此为契机,融入现有国际海洋法公约并在践行过程中制定利我的海上政策体制,助力"海之梦"、"中国梦"。     

南海某导管架海洋平台倒塌分析

针对在役老龄导管架平台进行倒塌计算分析,确定极限承载力进而评估老龄导管架的安全裕度。采用非线性有限元方法,考虑平台的波流载荷及桩-土的非线性相互作用,利用SACS软件建立导管架整体三维有限元计算分析模型,并用逐步加载的方式,对南海某导管架平台进行了全过程非线性倒塌分析。计算分析表明,该导管架平台极限强度很高,具有较大的安全裕度;导管架倒塌过程呈逐步破坏形式,先是撑杆屈服,造成局部结构破坏,然后是钢桩发生屈服,降低结构承载力,最后节点逐步失效,造成结构倒塌。揭示了导管架平台结构失效倒塌的机理,给出了倒塌分析的可行方法和步骤。     

格尔木河流域河水钾硼锂元素分布特征及富集规律

在柴达木格尔木河流域,随着内陆流域水系的产生与地表径流的消亡,从山区至盐湖区钾(K)硼(B)锂(Li)等有益元素的分布可以划分为淋溶-径流区、径流-蒸发区与溶滤-蒸发浓缩富集区3个具有显著特点的水文化学分带。河水中,K、B、Li含量随矿化度升高而升高,且呈正相关关系。在盐湖区,K、B、Li等资源性元素明显富集。研究发现,格尔木河东部主流(秀水河)是格尔木河水中B和Li的主要贡献者。     

Length of stay in urban areas of circular migrants from the mountainous areas in China

Currently, there is limited literature dealing with the length of stay of circular migrants in urban areas (LSCMU), although many studies have discussed the phenomenon of migration and the determinants of migration. This study attempts to fill that gap using survey data from the mountainous areas of Chongqing, Southwest China. From a comparative perspective, this study divided workers into two groups (a young group aged between 16 and 35 years and an old group aged between 36 and 65 years). The average LSCMU values for the young and old groups were 225 days and 174 days, respectively. Two multi-regression models were used to estimate the determinants of LSCMU in the two groups. The results showed that LSCMU was closely related to individual factors in both groups, including gender, age and job training. Family and community factors, including household size, arable land per capita and the distance from market, had much weaker effects on the dependent variable, especially in the older group. It was noticeable that job training had significant positive effects on LSCMU in both groups; these findings have special implications for the urbanization process in China.     

内蒙古东乌旗沙麦钨矿床的成矿时代

内蒙古东乌旗沙麦钨矿位于贺根山断裂带以北的兴蒙造山系二连-东乌旗弧盆带内,为岩浆期后高温热液黑钨矿石英脉型矿床。采用黑钨矿Sm-Nd同位素分析获得黑钨矿的形成年龄为137.9±1.7Ma,采用TIMS锆石U-Pb同位素定年获得赋矿黑云母花岗岩的形成年龄为139.1±0.93Ma,据此提出,沙麦钨矿床的形成时代为燕山晚期,这与区域上大兴安岭西坡主要金属矿床的形成年龄数据相吻合。黑钨矿的初始ε_(Nd)值为正值,与中亚造山带内大量花岗岩的εNd值均为正值的特点相一致,表明其来源于亏损地幔源。     

蒙古戈壁阿尔泰巴音陶勒盖地区二长花岗岩LA-ICP-MS锆石U-Pb年龄及其地质意义

蒙古戈壁阿尔泰省巴音陶勒盖地区地处南戈壁-阿尔泰构造带南缘,区内构造活动活跃,中酸性侵入岩比较发育。采用LA-ICP-MS锆石U-Pb测年技术,对区内二长花岗岩中的锆石进行同位素年龄研究。阴极发光图像显示,锆石颗粒多为自形-半自形,且有明显的初始岩浆振荡环带,少见蚀变微区,结合较高的Th/U值(0.65~1.79),断定其为典型的岩浆成因锆石;30颗锆石的~(206)Pb/~(238)U年龄加权平均值为300.2±0.9Ma,显示二长花岗岩成岩时代为晚石炭世,代表了华力西中期的一次构造-岩浆事件,为约束南戈壁-阿尔泰构造带晚石炭世深成岩浆活动时限提供了新证据。     

对湖北大洪山地区一套紫红色砂-砾岩系沉积年代的再认识——碎屑锆石U-Pb年龄及其地质意义

湖北大洪山地区花山群六房咀组之上不整合覆盖了一套紫红色砂-砾岩。这套岩石的沉积时代存在争议,一种观点认为是南华纪早期;另一种观点认为是晚侏罗世。利用LA-ICP-MS分析技术,对这套碎屑沉积岩进行了碎屑锆石U-Pb测年,获得有效年龄数据125组,年龄值变化范围较大(3223~771Ma),主要集中于新太古代末—古元古代早期(约2500Ma)、古元古代(约2000Ma)和新元古代(约800Ma)3个时间段。对比鄂东南地区和三峡地区莲沱组岩石学特征和碎屑锆石年龄分布特征,认为其具有相似的物源,这套岩系沉积时代应该为南华纪早期而非晚侏罗世。综合分析扬子地块的前寒武纪年龄,认为扬子地块可能存在大量未岀露的新太古代末—古元古代早期(约2500Ma)基底,约2500Ma的岩石应该是扬子地块深部基底的重要组成部分。扬子地块存在广泛的古元古代(约2000Ma)岩浆活动,这期岩浆活动可能是Columbia超大陆聚合在扬子地块的响应。新元古代(约800Ma)扬子地块北缘存在Rodinia超大陆裂解同期裂谷,裂谷内基性岩可能为大洪山地区南华纪地层中基性岩砾石的物源。