Practical considerations in the application of simulated annealing to stochastic simulation

Realizations generated by conditional simulation techniques must honor as much data as possible to be reliable numerical models of the attribute under study. The application of optimization methods such as simulated annealing to stochastic simulation has the potential to honor more data than conventional geostatistical simulation techniques. The essential feature of this approach is the formulation of stochastic imaging as an optimization problem with some specified objective function. The data to be honored by the stochastic images are coded as components in a global objective function. This paper describes the basic algorithm and then addresses a number of practical questions: (1) what are the criteria for adding a component to the global objective function? (2) what perturbation mechanism should be employed in the annealing simulation? (3) when should the temperature be lowered in the annealing procedure? (4) how are edge/border nodes handled? (5) how are local conditioning data handled? and (6) how are multiple components weighted in the global objective function?     

Stochastic simulation of categorical variables using a classification algorithm and simulated annealing

An important step of reservoir characterization is the stochastic modeling of the geometry of lithofacies which control large-scale heterogeneities of petrophysical properties. Although multiple realizations are necessary to appreciate the uncertainty in the spatial distribution of facies, a common short cut consists of retaining the first realization drawn. This paper presents an alternative to this potentially hazardous selection: (1) a categorical map is generated by allocating a single facies to each grid node according to the local probabilities of occurrence of the facies, and (2) the map then is post-processed using a steepest descent-type algorithm so as to improve reproduction of spatial continuity and transition probabilities between facies. The procedure is illustrated using a synthetic dataset. A waterflood simulation shows that retaining a single realization would yield, in average, larger errors in production forecasts (water cuts and recovered oil) than the single postprocessed facies map.     

基于模拟退火遗传算法矿床勘探3DEM储量估算

矿床勘探3DEM储量估算是以三维可视化技术为核心,将我国传统的储量估算方法与计算机信息技术结合起来的储量估算工作流程。通过单工程矿体可视化圈定技术,能够保证矿体边界的合理性;通过剖面矿体连接技术,可以得到地质常用的剖面成果图件,同时为三维可视化提供断面数据;通过断面数据模拟退火遗传算法,能较好地解决复杂地质体的断面连接,组成三维地质体。以三雏矿体为限定条件,开展地质块段法或克里格地质统计学储量估算,并利用三维技术实现储量科学管理。     

Optimal pumping from Palmela water supply wells (Portugal) using simulated annealing

Aquifer systems are an important part of an integrated water resources management plan as foreseen in the European Union’s Water Framework Directive (2000). The sustainable development of these systems demands the use of all available techniques capable of handling the multidisciplinary features of the problems involved. The formulation and resolution of an optimization model is described for a planning and management problem based on the Palmela aquifer (Portugal), developed to supply a given number of demand centres. This problem is solved using one of the latest optimization techniques, the simulated annealing heuristic method, designed to find the optimal solutions while avoiding falling into local optimums. The solution obtained, providing the wells location and the corresponding pumped flows to supply each centre, are analysed taking into account the objective function components and the constraints. It was found that the operation cost is the biggest share of the final cost, and the choice of wells is greatly affected by this fact. Another conclusion is that the solution takes advantage of the economies of scale, that is, it points toward drilling a large capacity well even if this increases the investment cost, rather than drilling several wells, which together will increase the operation costs.     

Optimally locating additional drill holes in three dimensions using grade and simulated annealing

Average kriging variance is a standard tool used in optimization of the location of additional drill holes. However, this tool cannot distinguish between areas with different priorities. This limitation could be eliminated by using weighted average kriging variance. This paper extends the problem of optimal location to three dimensional cases, use grade as a weight and search optimum locations by simulated annealing. Weighted average kriging variance is used as objective function. The method is applied to a copper deposit. Results have shown that weighting of the estimation variance with ??grade?? is effective only when the difference among the grades estimated for different blocks is considerable.     

Characterizing heterogeneous permeable media with spatial statistics and tracer data using sequential simulated annealing

Characterizing heterogeneous permeable media using flow and transport data typically requires solution of an inverse problem. Such inverse problems are intensive computationally and may involve iterative procedures requiring many forward simulations of the flow and transport problem. Previous attempts have been limited mostly to flow data such as pressure transient (interference) tests using multiple observation wells. This paper discusses an approach to generating stochastic permeability fields conditioned to geologic data in the form of a vertical variogram derived from cores and logs as well as fluid flow and transport data, such as tracer concentration history, by sequential application of simulated annealing (SA). Thus, the method incorporates elements of geostatistics within the framework of inverse modeling. For tracer-transport calculations, we have used a semianalytic transit-time algorithm which is fast, accurate, and free of numerical dispersion. For steady velocity fields, we introduce a transit-time function which demonstrates the relative importance of data from different sources. The approach is illustrated by application to a set of spatial permeability measurements and tracer data from an experiment in the Antolini Sandstone, an eolian outcrop from northern Arizona. The results clearly reveal the importance of tracer data in reproducing the correlated features (channels) of the permeability field and the scale effects of heterogeneity.     

A computer method based on simulated annealing to identify aquifer parameters using pumping‐test data

Conventional graphical or computer methods for identifying aquifer parameters have their own inevitable limitations. This paper proposes a computer method based on a drawdown model and a heuristic approach of simulated annealing (SA) to determine the best‐fit aquifer parameters of the confined and unconfined aquifer systems. The drawdown model for the confined aquifer is the Theis solution and the unconfined aquifer is the Neuman solution. The estimated results of proposed method have better accuracy than those of the graphical methods and agree well with those of the computer methods based on the extended Kalman filter and Newton's method. Finally, the sensitivity analyses for the control parameters of SA indicate that the proposed method is very robust and stable in parameter identification procedures. Copyright © 2007 John Wiley & Sons, Ltd.     

Framework silica structures generated using simulated annealing with a potential energy function based on an H6Si2O7 molecule

A simulated annealing technique was used to search for global and local minimum energy structures of a potential energy model for silica. The model is based on ab initio SCF MO calculations on the disilicic acid molecule, H₆Si₂O₇. Starting with 4 SiO₂ units, with the atoms randomly distributed in the unit cell, 23 distinct silica tetrahedral framework structures were found, with a variety of space group symmetries and cell dimensions. Despite the assumption of P 1 space group symmetry for the starting structure, only 7 of the local minimum energy structures were found to possess triclinic symmetry with the remainder exhibiting symmetries ranging from P c to to within 0.001 Å. Although the interaction potential for the disilicic acid molecule has a single minimum energy SiO bond length and SiOSi angle, the local minimum energy structures exhibit angles that range between 105° and 180° and bond lengths that range between 1.55 and 1.68 Å. The correlation observed for coesite and the other silica polymorphs between SiO bond length and f_s(O) is reproduced. The generated structures show a wide variety of coordination sequences, ring sizes and framework densities, the later ranging from 19.8 to 35.5 Si/1000 ų. The energies of these structures correlate with their framework densities, particularly for higher energy structures.     

Determining the equivalent permeability tensor for fractured rock masses using a stochastic REV approach: Method and application to the field data from Sellafield,UK

A numerical procedure to determine the equivalent permeability tensor of a fractured rock is presented, using a stochastic REV (Representative Elementary Volume) concept that uses multiple realizations of stochastic DFN (Discrete Fracture Network) models. Ten square DFN models are generated using the Monte Carlo simulations of the fracture system based on the data obtained from a site characterization program at Sellafield, Cumbria, UK. Smaller models with varying sizes of from 0.25 m×0.25 m to 10 m×10 m are extracted from the generated DFN models and are used as two-dimensional geometrical models for calculation of equivalent permeability tensor. The DFN models are also rotated in 30º intervals to evaluate the tensor characteristics of calculated directional permeability. Results show that the variance of the calculated permeability values decreases significantly as the side lengths of the DFN models increase, which justifies the existence of a REV. The REV side length found in this analysis is about 5 m and 8 m with 20% and 10% acceptable variations, respectively. The calculated directional permeability values at the REV size have tensor characteristic that is confirmed by a close approximation of an ellipse in a polar plot of the reciprocal of square roots of the directional permeability.

Whey as a substrate for generation of bioelectricity in microbial fuel cell using E.coli

While oil prices raise and the supply remains unsteady, it may be beneficial to use the high content of energy available in food processing wastes, such as cheese whey waste, by converting it to bioenergy. As well, there have been many new waste biotreatment technologies developed recently, which may well be used directly to food processing wastes. Microbial fuel cell represents a new technology for simultaneous use of waste materials and bioelectricity generation. In this study, bioelectricity generation with whey degradation was investigated in a two-chamber microbial fuel cell with mediators. E.coli was able to use the carbohydrate found in whey to generate bioelectricity. The open-circuit voltage in absence of mediator was 751.5mV at room temperature. The voltage was stable for more than 24 h. Riboflavin and humic acid were used as conceivable mediators. The results showed that humic acid was a few times more effective than Riboflavin. Additionally, four chemicals employed as catholyte. Based on polarization curve, FeCl₃ (III) was the best. Maximum power generation and current were 324.8 μW and 1194.6μA, respectively.     

Phenocryst complexity in andesites and dacites from the Tequila volcanic field,Mexico: resolving the effects of degassing vs. magma mixing

The petrology of five phenocryst-poor (2–5%) andesites and dacites, all of which were erupted from different short-lived, monogenetic vents, is compared to that of phenocryst-rich (10–25%) andesites erupted from the adjacent stratovolcano, Volcán Tequila, in the Mexican arc. Despite differences in phenocryst abundances, these magmas have comparable phase assemblages (plagioclase + orthopyroxene + titanomagnetite + ilmenite + apatite ± augite ± hornblende), and similarly wide variations in phenocryst compositions, coupled to complex zoning patterns. For the phenocryst-poor lavas, equilibrium pairs of two Fe–Ti oxides lead to a narrow range of calculated temperatures for each sample that range from 934 (±24) to 1,073 (±6)°C and oxygen fugacities that range from +0.1 to +0.7 log units relative to the Ni–NiO buffer. Application of the plagioclase-liquid hygrometer to each sample at these calculated temperatures leads to maximum melt water concentrations of 4.6–3.1 wt% during plagioclase crystallization, indicating that the magmas were fluid saturated at depths ≥6.4–4.5 km. There is a wide, continuous range in the composition of plagioclase (≤44 mol% An) and orthopyroxene (≤16% Mg#) phenocrysts in each sample, which is consistent with a loss of dissolved water (≤2.8 wt%) from the melt phase during degassing as the magmas ascended rapidly to the surface. Evidence is presented that shows the effect of dissolved water is to reduce the activity of MgO relative to FeO in the melt phase, which indicates that degassing will also affect the Mg# of pyroxene phenocrysts, with higher melt water concentrations favoring Fe-rich pyroxene. Both plagioclase and orthopyroxene commonly display diffusion-limited growth textures (e.g., skeletal and hopper crystals, large interior melt hollows, and swallow tails), which are consistent with large undercoolings produced by degassing-induced crystallization. Therefore, degassing is proposed as a possible cause for the phenocryst compositional diversity documented in the phenocryst-poor andesite and dacite lavas erupted from peripheral vents, including the coexistence of normally zoned plagioclase and reversely zoned orthopyroxene. Degassing-induced crystallization may also explain some of the phenocryst complexity in crystal-rich andesites erupted from large stratovolcanoes, including Volcán Tequila.     

川东北地区海相深层多源生烃动态转化机制——以普光气田为例

海相碳酸盐岩层系深层-超深层油气形成机制是石油地质学研究的热点和难点。以川东北普光气田为例,通过烃源(岩)评价及其与原油、储层沥青和天然气之间的地球化学对比、油气藏形成演化与保存过程分析,结合不同类型天然气组分、流体包裹体以及多种烃源生烃模拟等实验数据,对油气来源和成烃成藏过程进行了系统分析。结果表明,在多期沉积构造活动背景下,海相深层烃源岩系和主力产层均经历过高温高压环境与高热演化,形成了不同类型的干酪根、以分散和富集状态赋存的可溶有机质,以及以有机酸盐形式存在的不溶有机质等多种形式烃源,并普遍存在不同类型烃源、不同成因油气的连续或叠置动态相态转化,及其对油气成藏贡献的接替过程,呈现出"来源的多样性、转化的接替性、过程的多期性和成因的复合性"之油气形成演化特点,提出"多源生烃动态转化"是深层油气形成演化的主要机制,将烃源生气过程延续到更高的演化阶段,有利于深层-超深层条件下油气藏的再充注和聚集保存。     

Early maturation processes in coal. Part 2: Reactive dynamics simulations using the ReaxFF reactive force field on Morwell Brown coal structures

This paper reports reactive dynamics (RD) simulations of a macro-model of Morwell Brown coal using the ReaxFF reactive force field. We find that these reactive MD simulations successfully reproduce thermal decomposition processes of defunctionalization, depolymerization and rearrangement of the residual structure observed in various experimental studies. For example, our simulations indicate that the decarboxylation and dehydroxylation of the lignin side chain of the Morwell model involves the formation of double bonds conjugated with the aromatic rings. The process of defunctionalization of the methoxy functions involving the formation of phenolic structures in the residue has been confirmed. We also observe that gaseous hydrocarbons are generated by cleavage of C–C bonds of the lignin side chain.The success in using ReaxFF RD to describe the molecular processes underlying the kinetics in pyrolysis of this model of coal plus the success of a similar previous study on the algaenan of Botryococcus braunii race L biopolymer model of kerogens suggests that such computation can be useful in providing molecular based kinetic models for other pyrolysis processes underlying the organic transformations in sedimentary materials.     

Thermal decomposition process in algaenan of Botryococcus braunii race L. Part 2: Molecular dynamics simulations using the ReaxFF reactive force field

This paper reports ReaxFF MD simulation results on pyrolysis of a molecular model of the algaenan Botryococcus braunii race L biopolymer, specifically, ReaxFF predictions on the pyrolysis of prototypical chemical structures involving aliphatic chain esters and aldehydes. These preliminary computational experiments are then used to analyze the thermal cracking process within algaenan race L biopolymers. The simulations indicate that the thermal decomposition of the algaenan biopolymer is initiated by the cleavage of a C–O bond in the ester group, followed by the release of carbon dioxide. We also observe a significant, strongly temperature dependent, release of ethylene. This degradation mechanism leads to products similar to those observed in pyrolysis experiments, validating this computational approach.