Conditional simulation of random fields by successive residuals

This paper presents a new approach to the LU decomposition method for the simulation of stationary and ergodic random fields. The approach overcomes the size limitations of LU and is suitable for any size simulation. The proposed approach can facilitate fast updating of generated realizations with new data, when appropriate, without repeating the full simulation process. Based on a novel column partitioning of the L matrix, expressed in terms of successive conditional covariance matrices, the approach presented here demonstrates that LU simulation is equivalent to the successive solution of kriging residual estimates plus random terms. Consequently, it can be used for the LU decomposition of matrices of any size. The simulation approach is termed conditional simulation by successive residuals as at each step, a small set (group) of random variables is simulated with a LU decomposition of a matrix of updated conditional covariance of residuals. The simulated group is then used to estimate residuals without the need to solve large systems of equations.

Simulation of the load-unload response ratio and critical sensitivity in the lattice solid model

The Load-Unload Response Ratio (LURR) method is an intermediate-term earthquake prediction approach that has shown considerable promise. It involves calculating the ratio of a specified energy release measure during loading and unloading where loading and unloading periods are determined from the earth tide induced perturbations in the Coulomb Failure Stress on optimally oriented faults. In the lead-up to large earthquakes, high LURR values are frequently observed a few months or years prior to the event. These signals may have a similar origin to the observed accelerating seismic moment release (AMR) prior to many large earthquakes or may be due to critical sensitivity of the crust when a large earthquake is imminent. As a first step towards studying the underlying physical mechanism for the LURR observations, numerical studies are conducted using the particle based lattice solid model (LSM) to determine whether LURR observations can be reproduced. The model is initialized as a heterogeneous 2-D block made up of random-sized particles bonded by elastic-brittle links. The system is subjected to uniaxial compression from rigid driving plates on the upper and lower edges of the model. Experiments are conducted using both strain and stress control to load the plates. A sinusoidal stress perturbation is added to the gradual compressional loading to simulate loading and unloading cycles and LURR is calculated. The results reproduce signals similar to those observed in earthquake prediction practice with a high LURR value followed by a sudden drop prior to macroscopic failure of the sample. The results suggest that LURR provides a good predictor for catastrophic failure in elastic-brittle systems and motivate further research to study the underlying physical mechanisms and statistical properties of high LURR values. The results provide encouragement for earthquake prediction research and the use of advanced simulation models to probe the physics of earthquakes.

Simulation of the micro-physics of rocks using LSMearth

The particle-based Lattice Solid Model (LSM) was developed to provide a basis to study the physics of rocks and the nonlinear dynamics of earthquakes (MORA and PLACE, 1994; PLACE and MORA, 1999). A new modular and flexible LSM approach has been developed that allows different microphysics to be easily included in or removed from the model. The approach provides a virtual laboratory where numerical experiments can easily be set up and all measurable quantities visualised. The proposed approach provides a means to simulate complex phenomena such as fracturing or localisation processes, and enables the effect of different micro-physics on macroscopic behaviour to be studied. The initial 2-D model is extended to allow three-dimensional simulations to be performed and particles of different sizes to be specified. Numerical bi-axial compression experiments under different confining pressure are used to calibrate the model. By tuning the different microscopic parameters (such as coefficient of friction, microscopic strength and distribution of grain sizes), the macroscopic strength of the material and can be adjusted to be in agreement with laboratory experiments, and the orientation of fractures is consistent with the theoretical value predicted based on Mohr-Coulomb diagram. Simulations indicate that 3-D numerical models have different macroscopic properties than in 2-D and, hence, the model must be recalibrated for 3-D simulations. These numerical experiments illustrate that the new approach is capable of simulating typical rock fracture behaviour. The new model provides a basis to investigate nucleation, rupture and slip pulse propagation in complex fault zones without the previous model limitations of a regular low-level surface geometry and being restricted to two-dimensions.

Simulation of the influence of rate- and state-dependent friction on the macroscopic behavior of complex fault zones with the lattice solid model

In order to understand the earthquake nucleation process, we need to understand the effective frictional behavior of faults with complex geometry and fault gouge zones. One important aspect of this is the interaction between the friction law governing the behavior of the fault on the microscopic level and the resulting macroscopic behavior of the fault zone. Numerical simulations offer a possibility to investigate the behavior of faults on many different scales and thus provide a means to gain insight into fault zone dynamics on scales which are not accessible to laboratory experiments. Numerical experiments have been performed to investigate the influence of the geometric configuration of faults with a rate- and state-dependent friction at the particle contacts on the effective frictional behavior of these faults. The numerical experiments are designed to be similar to laboratory experiments by DIETERICH and KILGORE (1994) in which a slide-hold-slide cycle was performed between two blocks of material and the resulting peak friction was plotted vs. holding time. Simulations with a flat fault without a fault gouge have been performed to verify the implementation. These have shown close agreement with comparable laboratory experiments. The simulations performed with a fault containing fault gouge have demonstrated a strong dependence of the critical slip distance D-c on the roughness of the fault surfaces and are in qualitative agreement with laboratory experiments.

Parallel simulation system for earthquake generation: Fault analysis modules and parallel coupling analysis

Solid earth simulations have recently been developed to address issues such as natural disasters, global environmental destruction and the conservation of natural resources. The simulation of solid earth phenomena involves the analysis of complex structures including strata, faults, and heterogeneous material properties. Simulation of the generation and cycle of earthquakes is particularly important, but such simulations require the analysis of complex fault dynamics. GeoFEM is a parallel finite-element analysis system intended for solid earth field phenomena problems. This paper describes recent development in the GeoFEM project for the simulation of earthquake generation and cycles.

An overview of APSIM, a model designed for farming systems simulation

The Agricultural Production Systems Simulator (APSIM) is a modular modelling framework that has been developed by the Agricultural Production Systems Research Unit in Australia. APSIM was developed to simulate biophysical process in farming systems, in particular where there is interest in the economic and ecological outcomes of management practice in the face of climatic risk. The paper outlines APSIM's structure and provides details of the concepts behind the different plant, soil and management modules. These modules include a diverse range of crops, pastures and trees, soil processes including water balance, N and P transformations, soil pH, erosion and a full range of management controls. Reports of APSIM testing in a diverse range of systems and environments are summarised. An example of model performance in a long-term cropping systems trial is provided. APSIM has been used in a broad range of applications, including support for on-farm decision making, farming systems design for production or resource management objectives, assessment of the value of seasonal climate forecasting, analysis of supply chain issues in agribusiness activities, development of waste management guidelines, risk assessment for government policy making and as a guide to research and education activity. An extensive citation list for these model testing and application studies is provided. Crown Copyright (C) 2002 Published by Elsevier Science B.V. All rights reserved.

Sequencing batch reactor technology: the key to a BP refinery (Bulwer Island) upgraded environmental protection system - a low cost lagoon based retro-fit

BP Refinery (Bulwer Island) Ltd (BP) located on the eastern Australian coast is currently undergoing a major expansion as a part of the Queensland Clean Fuels Project. The associated wastewater treatment plant upgrade will provide a better quality of treated effluent than is currently possible with the existing infrastructure, and which will be of a sufficiently high standard to meet not only the requirements of imposed environmental legislation but also BP's environmental objectives. A number of challenges were faced when considering the upgrade, particularly; cost constraints and limited plot space, highly variable wastewater, toxicity issues, and limited available hydraulic head. Sequencing Batch Reactor (SBR) Technology was chosen for the lagoon upgrade based on the following; SBR technology allowed a retro-fit of the existing earthen lagoon without the need for any additional substantial concrete structures, a dual lagoon system allowed partial treatment of wastewaters during construction, SBRs give substantial process flexibility, SBRs have the ability to easily modify process parameters without any physical modifications, and significant cost benefits. This paper presents the background to this application, an outline of laboratory studies carried out on the wastewater and details the full scale design issues and methods for providing a cost effective, efficient treatment system using the existing lagoon system.

Simultaneous nitrification, denitrification, and phosphorus removal in a lab-scale sequencing batch reactor

Simultaneous nitrification and denitrification (SND) via the nitrite pathway and anaerobic-anoxic-enhanced biological phosphorus removal (EBPR) are two processes that can significantly reduce the energy and COD demand for nitrogen and phosphorus removal. The combination of these two processes has the potential of achieving simultaneous nitrogen and phosphorus removal with a minimal requirement for COD. A lab-scale sequencing batch reactor (SBR) was operated in alternating anaerobic-aerobic mode with a low dissolved oxygen (DO) concentration (0.5 mg/L) during the aerobic period, and was demonstrated to accomplish nitrification, denitrification, and phosphorus removal. Under anaerobic conditions, COD was taken up and converted to poly-hydroxyalkanoates (PHAs), accompanied by phosphorus release. In the subsequent aerobic stage, PHA was oxidized and phosphorus was taken up to

An approach to verifying and debugging simulation models governed by ordinary differential equations: Part 1. Methodology for residual generation

For dynamic simulations to be credible, verification of the computer code must be an integral part of the modelling process. This two-part paper describes a novel approach to verification through program testing and debugging. In Part 1, a methodology is presented for detecting and isolating coding errors using back-to-back testing. Residuals are generated by comparing the output of two independent implementations, in response to identical inputs. The key feature of the methodology is that a specially modified observer is created using one of the implementations, so as to impose an error-dependent structure on these residuals. Each error can be associated with a fixed and known subspace, permitting errors to be isolated to specific equations in the code. It is shown that the geometric properties extend to multiple errors in either one of the two implementations. Copyright (C) 2003 John Wiley Sons, Ltd.

An approach to verifying and debugging simulation models governed by ordinary differential equations: Part 2. Residuals analysis and a case study

In Part 1 of this paper a methodology for back-to-back testing of simulation software was described. Residuals with error-dependent geometric properties were generated. A set of potential coding errors was enumerated, along with a corresponding set of feature matrices, which describe the geometric properties imposed on the residuals by each of the errors. In this part of the paper, an algorithm is developed to isolate the coding errors present by analysing the residuals. A set of errors is isolated when the subspace spanned by their combined feature matrices corresponds to that of the residuals. Individual feature matrices are compared to the residuals and classified as 'definite', 'possible' or 'impossible'. The status of 'possible' errors is resolved using a dynamic subset testing algorithm. To demonstrate and validate the testing methodology presented in Part 1 and the isolation algorithm presented in Part 2, a case study is presented using a model for biological wastewater treatment. Both single and simultaneous errors that are deliberately introduced into the simulation code are correctly detected and isolated. Copyright (C) 2003 John Wiley Sons, Ltd.

Nitrifying microbial community analysis of nitrite accumulating biofilm reactor by fluorescence in situ hybridization

Biological nitrogen removal via nitrite pathway in wastewater treatment is very important especially in the cost of aeration and as an electron donor for denitrification. Wastewater nitrification and nitrite accumulations were carried out in a biofilm reactor. The biofilm reactor showed almost complete nitrification and most of the oxidized ammonium was present as nitrite at the ammonium load of 1.2 kg N/m3/d. Nitrite accumulation was achieved by the selective inhibition of nitrite oxidizers by free ammonia and oxygen limitation. Nitrite oxidation activity was recovered as soon as the inhibition factor was removed. Fluorescence in situ hybridization studies of the nitrite accumulating biofilm system have shown that genus Nitrosomonas which is specifically hybridized with probe NSM 156 was the dominant nitrifying bacteria while Nitrospira was less abundant than those of normal nitrification systems. Further FISH analysis showed that the combinations of Nitrosomonas and Nitrospira cells were identified as important populations of nitrifying bacteria in an autotrophic nitrifying biofilm system.

Nitrification of high strength ammonia wastewtaer treatment - process selection is the major factor.

Biological nitrogen removal via the nitrite pathway in wastewater treatment is very important in Saving the cost of aeration and as an electron donor for denitrification. Wastewater nitrification and nitrite accumulation were carried out in a biofilm airlift reactor with autotrophic nitrifying biofilm. The biofilm reactor showed almost complete nitrification and most of the oxidized ammonium was present as nitrite at the ammonium load of 1.5 to 3.5 kg N/m3.d. Nitrite accumulation was stably achieved by the selective inhibition of nitrite oxidizers with free ammonia and dissolved oxygen limitation. Stable 100% conversion to nitrite could also be achieved even under the absence of free ammonia inhibition on nitrite oxidizers. Batch ammonium oxidation and nitrite oxidation with nitrite accumulating nitrifying biofilm showed that nitrite Oxidation was completely inhibited when free ammonia is higher than 0.2 mg N/L. However, nitrite oxidation activity was recovered as soon as the free ammonia concentration was below the threshold level when dissolved oxygen concentration was not the limiting factor. Fluorescence in situ hybridization analysis of cryosectioned nitrite accumulating nitrifying biofilm showed that the β-subclass of Proteobacteria, where ammonia oxidizers belong, was distributed outside the biofilm whereas the α-subclass of Proteobacteria, where nitrite oxidizers belong, was found mainly in the inner part of the biofilm. It is likely that dissolved oxygen deficiency or limitation in the inner part of the nitrifying biofilm, where nitrite oxidizers exist, is responsible for the complete shut down of the nitrite oxidizers activity under the absence of free ammonia inhibition.