MATH 1050QC Mathematical Modeling in the Environment Lecture 20. Characterization of Toxicity Hazards. Chemical Principles. Dmitriy Leykekhman Spring 2009 D. Leykekhman - MATH 1050QC Mathematical Modeling in the Environment Course info 1
Characterization of Toxicity Hazards Acute Toxic Hazards Chronic Toxic Hazards. Leykekhman - MATH 1050QC Mathematical Modeling in the Environment Course info 2
Characterization of Toxicity Hazards Acute Toxic Hazards Chronic Toxic Hazards TLV - Threshold Limit Value - Level of acceptable exposure (Based on recommendations by the American Conference of Government Industrial Hygienists, ACGIH) Subdivided into: Under normal working conditions Daily time-weighted averages Short term exposures (generally 15 minutes) IDLH Values - Immediately dangerous to life or health (Published by NIOSH, National Institute for Occupational Safety and Health) Generally expressed in PPMs, parts per million; sometimes in mass per unit volume. Leykekhman - MATH 1050QC Mathematical Modeling in the Environment Course info 2
Chemical Principles 1. Under fixed conditions of pressure and temperature, a given volume of gas will contain the same number of molecules of any gaseous substance whether the molecules are small, light molecules or larger, heavy molecules. D. Leykekhman - MATH 1050QC Mathematical Modeling in the Environment Course info 3
Chemical Principles 1. Under fixed conditions of pressure and temperature, a given volume of gas will contain the same number of molecules of any gaseous substance whether the molecules are small, light molecules or larger, heavy molecules. 2. Avogadros Number: 6.022 10 23. This is the number of molecules contained in M grams of a substance with molecular weight M. D. Leykekhman - MATH 1050QC Mathematical Modeling in the Environment Course info 3
Chemical Principles 1. Under fixed conditions of pressure and temperature, a given volume of gas will contain the same number of molecules of any gaseous substance whether the molecules are small, light molecules or larger, heavy molecules. 2. Avogadros Number: 6.022 10 23. This is the number of molecules contained in M grams of a substance with molecular weight M. 3. One mole of a gas under standard temperature and pressure conditions occupies a volume of 22.4 liters. D. Leykekhman - MATH 1050QC Mathematical Modeling in the Environment Course info 3
Chemical Principles 1. Under fixed conditions of pressure and temperature, a given volume of gas will contain the same number of molecules of any gaseous substance whether the molecules are small, light molecules or larger, heavy molecules. 2. Avogadros Number: 6.022 10 23. This is the number of molecules contained in M grams of a substance with molecular weight M. 3. One mole of a gas under standard temperature and pressure conditions occupies a volume of 22.4 liters. 4. The number of moles of a gas is the quotient of its mass (in grams) divided by its molecular weight. D. Leykekhman - MATH 1050QC Mathematical Modeling in the Environment Course info 3
Chemical Principles 1. Under fixed conditions of pressure and temperature, a given volume of gas will contain the same number of molecules of any gaseous substance whether the molecules are small, light molecules or larger, heavy molecules. 2. Avogadros Number: 6.022 10 23. This is the number of molecules contained in M grams of a substance with molecular weight M. 3. One mole of a gas under standard temperature and pressure conditions occupies a volume of 22.4 liters. 4. The number of moles of a gas is the quotient of its mass (in grams) divided by its molecular weight. 5. The number of molecules of of a gas is the product of the number of moles and the Avogadros Number. D. Leykekhman - MATH 1050QC Mathematical Modeling in the Environment Course info 3
Conversion of units These principles enable one to translate between mass per unit volume and parts per million. Problem Assume it is given that an emergency level for ethylene glycol is 110mg/m 3. What does it correspond to ppm units? Solution Step 1. Get the chemical formula for ethylene glycol. Step 2. From the chemical formula compute the molecular weight. Step 3. Convert m 3 of air into millions of atoms of air. Step 4. Convert 110 mg of glycol into millions of atoms of glycol. Step 5. Take the ratio. D. Leykekhman - MATH 1050QC Mathematical Modeling in the Environment Course info 4
Conversion of units Solution Step 1. Chemical formula for ethylene glycol is C 2 H 6 O 2. Step 2. From the periodic table the molecular weight is 2 12.011 + 6 1.001 + 2 15.9994 = 62.03 D. Leykekhman - MATH 1050QC Mathematical Modeling in the Environment Course info 5
Conversion of units Step 3. Using that we have 1 m 3 of air = (100 cm) 3 1000 cm 3 of air = 1 liter of air 22.4 liters of air = 1 mole of air 1 mole of air = 6.022 10 23 molecules of air 1 m 3 of air = (100 cm) 3 1000 liters of air = 1000 22.4 moles of air = 1000 22.4 6.022 1023 molecules of air. D. Leykekhman - MATH 1050QC Mathematical Modeling in the Environment Course info 6
Conversion of units Step 4. In addition using that we have 62.03 g glycol = 1 mole of glycol 1 g = 1000 mg, 110 mg of glycol = 110 1 g of glycol 1000 = 110 1000 1 moles of glycol 62.03 = 110 1000 1 62.03 6.022 1023 molecules of glycol. D. Leykekhman - MATH 1050QC Mathematical Modeling in the Environment Course info 7
Conversion of units Step 5. Taking the ration w have 110 1000 1 62.03 6.022 1023 molecules of glycol 1000 22.4 6.022 39.7ppm. 1023 molecules of air D. Leykekhman - MATH 1050QC Mathematical Modeling in the Environment Course info 8
Conversion of units Step 5. Taking the ration w have 110 1000 1 62.03 6.022 1023 molecules of glycol 1000 22.4 6.022 39.7ppm. 1023 molecules of air Problem Convert the concentration of 50 ppm of glycol back to mg/m 3 units? D. Leykekhman - MATH 1050QC Mathematical Modeling in the Environment Course info 8
Typical Quantitative Issues Chapter 4.4 describes three situations: First situation (Derailment, possible chemical leak). Questions: Vapor concentrationsin various directions and at various distances Flammable and toxicity limits Potential for flammable or toxic vapor cloud to extend a distance from the accident Other hazards? D. Leykekhman - MATH 1050QC Mathematical Modeling in the Environment Course info 9
Typical Quantitative Issues Second situation (Nearby manufacturing plant has chemical storage tanks) Interesting range of participants: fire department, police, hazmat team, EPA, FEMA, environmental agencies, transportation departments, civil defense, public works, hospital emergency room, local companies, private contractors, university consultants, school department Modeling can play a significant role in local planning and training when analyzing hazards of a hypothetical incident D. Leykekhman - MATH 1050QC Mathematical Modeling in the Environment Course info 10
Typical Quantitative Issues Third situation (Develop priorities for hazardous chemicals shipped in bulk) Different approaches are possible There are several distinct levels at which models can be useful, including site-specific response, long-range planning, training and prioritization D. Leykekhman - MATH 1050QC Mathematical Modeling in the Environment Course info 11
Input: Chemical involved Leak conditions e.g source, size of opening affects rate of leakage Duration of leak Liquid pool area limitations size may be constrained Weather conditions temperature, wind D. Leykekhman - MATH 1050QC Mathematical Modeling in the Environment Course info 12
Chemical Data: Dominant hazards Hazardous concentration levels Physical and chemical properties Hazardous reaction or combustion products D. Leykekhman - MATH 1050QC Mathematical Modeling in the Environment Course info 13
Geographic Data: Map of area Sensitive facilities Storm sewers and water bodies D. Leykekhman - MATH 1050QC Mathematical Modeling in the Environment Course info 14
Models: Tank or pipeline discharge rate Pool size Evaporation rate Vapor dispersion Thermal radiation Flame jet distance Explosion overpressures Tank pressurization (from heat) BLEVE impacts D. Leykekhman - MATH 1050QC Mathematical Modeling in the Environment Course info 15
Output: Hazard distances and directions Concentrations as functions of time and location Concentration map Hazard zone map D. Leykekhman - MATH 1050QC Mathematical Modeling in the Environment Course info 16
Considerations: Units Chemical data Feasible scenarios make sure your input is reasonable Care with illogical input requirements Adapting the model it may, more likely will, not fit the situation exactly D. Leykekhman - MATH 1050QC Mathematical Modeling in the Environment Course info 17