Multi-objective Aggregate Production Planning Model Considering Overtime and Outsourcing Options Under Fuzzy Seasonal Demand

This paper investigates a novel fuzzy multi-objective multi-period Aggregate Production Planning (APP) problem under seasonal demand. As two of the main real-world assumptions, the options of workforce overtime and outsourcing are studied in the proposed Mixed-Integer Linear Programming (MILP) model. The main goals are to minimize the total cost including in-house production, outsourcing, workforce, holding, shortage and employment/ unemployment costs, and maximize the customers' satisfaction level. To deal with demand uncertainty, triangular fuzzy numbers are considered for demand parameters. Then the proposed model is validated by solving an illustrative example using a Weighted Goal Programming (WGP) method and CPLEX solver. Finally, it is demonstrated that uncertain conditions and considering real-world assumptions can yield different results in developing a practical aggregate production plan. Moreover, a sensitivity analysis is then performed to provide qualitative managerial insights and decision aids

Methane Diffusion and Adsorption in Shale Rocks: A Numerical Study Using the Dusty Gas Model in TOUGH2/EOS7C-ECBM

Gas production from shale gas reservoirs plays a significant role in satisfying increasing energy demands. Compared with conventional sandstone and carbonate reservoirs, shale gas reservoirs are characterized by extremely low porosity, ultra-low permeability and high clay content. Slip flow, diffusion, adsorption and desorption are the primary gas transport processes in shale matrix, while Darcy flow is restricted to fractures. Understanding methane diffusion and adsorption, and gas flow and equilibrium in the low-permeability matrix of shale is crucial for shale formation evaluation and for predicting gas production. Modeling of diffusion in low-permeability shale rocks requires use of the Dusty gas model (DGM) rather than Fick’s law. The DGM is incorporated in the TOUGH2 module EOS7C-ECBM, a modified version of EOS7C that simulates multicomponent gas mixture transport in porous media. Also included in EOS7C-ECBM is the extended Langmuir model for adsorption and desorption of gases. In this study, a column shale model was constructed to simulate methane diffusion and adsorption through shale rocks. The process of binary CH 4- N 2 diffusion and adsorption was analyzed. A sensitivity study was performed to investigate the effects of pressure, temperature and permeability on diffusion and adsorption in shale rocks. The results show that methane gas diffusion and adsorption in shale is a slow process of dynamic equilibrium, which can be illustrated by the slope of a curve in CH 4 mass variation. The amount of adsorption increases with the pressure increase at the low pressure, and the mass change by gas diffusion will decrease due to the decrease in the compressibility factor of the gas. With the elevated temperature, the gas molecules move faster and then the greater gas diffusion rates make the process duration shorter. The gas diffusion rate decreases with the permeability decrease, and there is a limit of gas diffusion if the permeability is less than 1.0×10-15m2. The results can provide insights for a better understanding of methane diffusion and adsorption in the shale rocks so as to optimize gas production performance of shale gas reservoirs

Changes in the chemistry of shallow groundwater related to the 2008 injection of CO2 at the ZERT field site, Bozeman, Montana

Approximately 300 kg/day of food-grade CO2 was injected through a perforated pipe placed horizontally 2–2.3 m deep during July 9–August 7, 2008 at the MSU-ZERT field test to evaluate atmospheric and near-surface monitoring and detection techniques applicable to the subsurface storage and potential leakage of CO2. As part of this multidisciplinary research project, 80 samples of water were collected from 10 shallow monitoring wells (1.5 or 3.0 m deep) installed 1–6 m from the injection pipe, at the southwestern end of the slotted section (zone VI), and from two distant monitoring wells. The samples were collected before, during, and following CO2 injection. The main objective of study was to investigate changes in the concentrations of major, minor, and trace inorganic and organic compounds during and following CO2 injection. The ultimate goals were (1) to better understand the potential of groundwater quality impacts related to CO2 leakage from deep storage operations, (2) to develop geochemical tools that could provide early detection of CO2 intrusion into underground sources of drinking water (USDW), and (3) to test the predictive capabilities of geochemical codes against field data. Field determinations showed rapid and systematic changes in pH (7.0–5.6), alkalinity (400–1,330 mg/l as HCO3), and electrical conductance (600–1,800 μS/cm) following CO2 injection in samples collected from the 1.5 m-deep wells. Laboratory results show major increases in the concentrations of Ca (90–240 mg/l), Mg (25–70 mg/l), Fe (5–1,200 ppb), and Mn (5–1,400 ppb) following CO2 injection. These chemical changes could provide early detection of CO2 leakage into shallow groundwater from deep storage operations. Dissolution of observed carbonate minerals and desorption-ion exchange resulting from lowered pH values following CO2 injection are the likely geochemical processes responsible for the observed increases in the concentrations of solutes; concentrations generally decreased temporarily following four significant precipitation events. The DOC values obtained are 5 ± 2 mg/l, and the variations do not correlate with CO2 injection. CO2 injection, however, is responsible for detection of BTEX (e.g. benzene, 0–0.8 ppb), mobilization of metals, the lowered pH values, and increases in the concentrations of other solutes in groundwater. The trace metal and BTEX concentrations are all significantly below the maximum contaminant levels (MCLs). Sequential leaching of core samples is being carried out to investigate the source of metals and other solutes