Production scheduling under uncertainty of an open-pit mine using Lagrangian relaxation and branch-and-cut algorithm

ABSTRACT

The life-of-mine optimization of open pit mine production scheduling under geological uncertainty is a computationally intensive process. Production scheduling determines the optimal extraction sequence by maximizing net present value (NPV). In this paper, an algorithm is proposed to schedule an open pit mine under geological uncertainty, where instead of solving the whole problem at once, the production schedule is generated by sequentially solving sub-problems. The sub-gradient method is used to generate the upper bound solution of a Lagrangian relaxed sub-problem. If the upper bound relaxed solution is infeasible, a mixed integer programming is applied to the latter solution. The algorithm is validated by solving six problems and is compared to the linear relaxation of the original production scheduling problem. The results show that the proposed algorithm generates a solution that is very close to optimal, with less than a 3% optimality gap. An application at a copper mine, where geological uncertainty is quantified with geostatistical simulations of the related orebody, shows that all constraints are satisfied and an 11% higher NPV is generated when compared to the corresponding deterministic equivalent of the proposed approach, while a 26% higher NPV is generated compared to a common conventional industry approach.     

Microstructure-Based Estimation of Strength and Ductility Distributions for $$\alpha +\beta $$ Titanium Alloys

Titanium alloys are processed to develop a wide range of microstructure configurations and therefore material properties. While these properties are typically measured experimentally, a framework for property prediction could greatly enhance alloy design and manufacturing. Here a microstructure-sensitive framework is presented for the prediction of strength and ductility as well as estimates of the bounds in variability for these properties. The framework explicitly considers distributions of microstructure via new approaches for instantiation of structure in synthetic samples. The parametric evaluation strategy, including the finite element simulation package FEpX, is used to create and test virtual polycrystalline samples to evaluate the variability bounds of mechanical properties in Ti-6Al-4V. Critical parameters for the property evaluation framework are provided by measurements of single crystal properties and advanced characterization of microstructure and slip system strengths in 2D and 3D. Property distributions for yield strength and ductility are presented, along with the validation and verification steps undertaken. Comparisons between strain localization and slip activity in virtual samples and in experimental grain-scale strain measurements are also discussed.

     

Adsorption‐concentration polarization model for ultrafiltration in mixed matrix membrane

Adsorption has been found to be significant in ultrafiltration by mixed matrix membrane. Removal of very low molecular weight solutes compared to the molecular weight cut off of the membrane is facilitated by adsorption. The modeling of the adsorption coupled with concentration polarization is presented based on the mathematical approach developed by Gekas et al. (Gekas et al. Chem Eng Sci. 1993;48:2753–2765), from the first principles. However, extensive modifications were included in theoretical development including those suggested by Ruiz‐Bevia et al. (Ruiz‐Bevia et al. Chem Eng Sci. 1997;52:2343–2352). The developed model captured the rejection dynamics with the help of retention factor. The model equations were solved under the framework of boundary layer analysis, using the integral approach. Effects of the adsorption isotherm and the different parameters affecting the system performance were also investigated. Further, experimental validation of the model results with two different mixed matrix ultrafiltration studies was also elucidated. © 2014 American Institute of Chemical Engineers AIChE J, 60: 2354–2364, 2014     

Capillary forces between sediment particles and an air-water interface

In the vadose zone, air-water interfaces play an important role in particle fate and transport, as particles can attach to the air-water interfaces by action of capillary forces. This attachment can either retard or enhance the movement of particles, depending on whether the air-water interfaces are stationary or mobile. Here we use three standard PTFE particles (sphere, circular cylinder, and tent) and seven natural mineral particles (basalt, granite, hematite, magnetite, mica, milky quartz, and clear quartz) to quantify the capillary forces between an air-water interface and the different particles. Capillary forces were determined experimentally using tensiometry, and theoretically assuming volume-equivalent spherical, ellipsoidal, and circular cylinder shapes. We experimentally distinguished between the maximum capillary force and the snap-off force when the air-water interface detaches from the particle. Theoretical and experimental values of capillary forces were of similar order of magnitude. The sphere gave the smallest theoretical capillary force, and the circular cylinder had the largest force due to pinning of the air-water interface. Pinning was less pronounced for natural particles when compared to the circular cylinder. Ellipsoids gave the best agreement with measured forces, suggesting that this shape can provide a reasonable estimation of capillary forces for many natural particles.     

Effect of steam environment on severe core damage behaviour for VVER-1000 with the ASTEC V1 code

Severe accident studies for very low frequency events for VVER-1000 (V320) are carried out to estimate in-vessel damage progression under steam-rich and starved conditions. The analyses with code ASTEC, jointly developed by IRSN (France) and GRS, Germany), have shown the influence of steam environment on core heat-up followed by material relocation, hydrogen production, vessel failure and aerosol generation along with release to containment. Hydro-accumulator injection for studied transients also gives rise to a steam-rich environment enhancing the material oxidation depending on the injection time and period. The generated information along with PSA-Level 2 is helpful to decide Plant Damage State (PDS) and fruitfully develop accident management strategies for the plant.     

Thermoelectric cold-chain chests for storing/transporting vaccines in remote regions

The cold chain is one of the key elements of the preventive health-care delivery system. Vaccines have to be carried long distances, stored in remote places and during this period the temperature has to be maintained within certain specified values. Realizing the needs of such requirements, the Department of Science & Technology, New Delhi (Govt. of India) assigned a project to the R&D Division of MECON, Ranchi for development of Thermoelectric Cold-Chain Chest operated by 12 V DC vehicular battery. The resulting portable thermoelectric (i.e. Peltier effect) Cold-Chain Chest (TCC) operated successfully even in an ambient environment of 45 °C, mainly for preserving and transporting life-saving medicines for urban as well as rural areas.     

Synthesis of Flexible Graphene/Polymer Composites for Supercapacitor Applications

In this paper, the graphene was synthesized using biocompatible cellulosic component from onions. Onion epidermal cells were chosen as raw material. During heating at high temperature, the bonding among atoms in material was rearranged and forms two-dimensional hexagonal carbon layer (graphene). The characterization of synthesized graphene was done by x-ray diffractometer, Raman spectrometer and field emission scanning electron microscopy, respectively. An attempt has been taken to form the capacitors with two different current collector electrodes, anticipating the performance of the supercapacitors. The observed capacitance values as-obtained for Al and Au current collector were 1.3 μF and 6.08 μF, respectively. However, when thermally exfoliated graphene was used as an electrode on Al and Au current collector, the capacitance value was drastically increased and found to be 1.6 and 41.25 μF, respectively.     

Analytic solution for planar indeterminate impact problems using an energy constraint

This work proposes an analytic method for resolving planar multi-point indeterminate impact problems for rigid-body systems. An event-based approach is used to detect impact events, and constraints consistent with the rigid-body assumption are used to resolve the indeterminacy associated with multi-point impact analysis. The work-energy relation is utilized to determine post-impact velocities based on an energetic coefficient of restitution to model energy dissipation, thereby yielding an energetically consistent set of post-impact velocities based on Stronge’s energetic coefficient of restitution for the treatment of rigid impacts. The effect of stick–slip transition is analyzed based on Coulomb friction. This paper also discusses the transition from impact to contact. This analysis is essential for considering the rocking block problem that is used as an example herein. The predictions of the model for the rocking block problem are compared to experimental results published in the literature. An example of a planar ball undergoing two-point impact is also presented.     

Intermetallic Precipitation in Low-Density Steel

Metallurgical and Materials Transactions A - Low-density steels (LDS) represent a relatively new class of material that contains a large concentration of aluminum. In the present work, we studied...