ENE 570/CBE 570/MAE 570 Advanced Optimization Methods for Energy Systems Engineering Homework Assignment #3 (Due 3/1/2022) 1. Introduction 1.1. Characterization of Crude Oils Paraffinic/asphaltic/mixed. This classification refers to the nature of the heavier components of the crude. Paraffinic crude, such as Pennsylvania crude, is not suitable for making asphalt and tends to leave a waxy deposit in pipelines. Yet it yields a relatively large gasoline fraction. Asphaltic crude, such as California crude, contains relatively more aromatics and heavy naphthalene. Mixed-based crude is typical of the Middle East and may or may not be suitable for asphalt manufacture. Sulfur content. Low-sulfur (“sweet”) crudes, such as those of the U.S. Gulf coast, are valuable because they are less corrosive and meet environmental standards. High-sulfur (“sour”) crudes, such as Alaska crude, require special processing to remove the sulfur. API gravity. This is a measure of density indexed to a standard temperature. Degrees API = [141.5/(specific gravity at 600F) – 131. Denser oils (i.e., smaller API gravity) have more energy content per barrel and, other things equal, bring a higher price. 1.2. Distillation of Crude The lighter components of crude oil boil at a temperature lower than heavier components. This phenomenon provides a means of separating groups of components in a fractionating tower. Hot oil enters at the bottom, where it vaporizes. Vapors of the lighter fractions rise to the cooler top of the tower, while heavier fractions condense before reaching the top. The heavier components that never vaporize are drained into a vacuum distillation unit, where the reduced pressure causes them to vaporize and separate. The principal fractions are listed in Table 1. Table 1: Principal Fractions of Crude Oil. fraction composition boiling point (OC) uses (at 1 atm) Flue gases C1-C7 below 90 Fuel, solvents, div cleaning fluid, refrigerants Light straight- C5-C16 40-220 Motor fuel and feedstock for reforming run gasoline, to raise octane number naphtha Kerosene C12-C16 200-315 Jet fuel, heating fuel, etc. Gas oil C15-C18 315-375 Fuel oil, diesel fuel. feedstock for cracking Vacuum gas oil C16-C20 over 375 Lubrication, feedstock for cracking Greases > C18 Semisolid Lubrication. etc. Wax > C20 melts at 51-55 Candles, etc. Pitch. tar Residue roofing, paving, etc. Coke Residue fuel, etc. 1.3. Other Refinery Processes Mere distillation of crude does not yield enough light products, especially gasoline, to satisfy U.S. demand. Also, distilled gasoline often has an octane number that is too low for modern engines. Several processes have been developed to increase the output of high-octane light products and otherwise to improve the characteristics of products. Addition of tetraethyllead (TEL). Many gasoline blends burn too explosively for smooth operation of an internal combustion engine, resulting in knocking or ping and waste of fuel (plus possible damage to cylinders). The tendency of a gasoline to knock is measured by comparing its knocking with that of isooctane in a standard test engine. Isooctane is itself given an octane number of 100. The two most prevalent tests result in the “research” octane number (RON) and the “motor” octane number, which are averaged to compute the posted octane numbers at the pump ((R + M)/2 method). The posted octane number runs about 4 below the RON. Diesel fuel is assigned an analogous “cetane number.” The octane number of gasoline can be raised (improved) by adding tetraethyllead, which unfortunately emits poisonous lead oxides when burned. In the U.S. and some other countries, legally mandated catalytic converters (which are contaminated by lead compounds) on automobiles have been the major cause for the phaseout of leaded gasolines. The expanded use of the catalytic hydrocracking process has partially offset the low octane rating of unleaded gasolines. Catalytic reforming. The octane number of heavy straight run gasolines and naphthas can be increased, without adding lead, by a “reforming” process. Paraffins and naphthalene are dehydrogenized and restructured, in the presence of a catalyst, to form aromatics, which cause the gasoline to burn more evenly. Catalytic reforming requires a good deal of heat. Catalytic cracking. The heavier oils can be converted to more valuable gasoline and other light products by a series of reactions that “crack” the complex hydrocarbons of heavy oils. The resulting lower molecular weight causes the boiling point to fall, and the output can be reformed to improve the octane number. Catalytic hydrocracking. Oils too heavy to respond to catalytic cracking can undergo a catalyzed reaction in the presence of hydrogen gas and high temperatures to produce the same result. Hydrotreating. Hydrogen and high temperatures can be used to remove impurities from oil, such as: sulfur (desulfurization), which is corrosive to equipment and emits corrosive SO2 when burned; nitrogen (denitrogenation), which emits poisonous oxides of nitrogen when burned: chlorine (dehalogenation). 2. A Refinery Modeling Problem The refinery to be modeled is depicted in Fig. 1. The primary objective is to decide how to operate the refinery for one day so as to maximize the contribution margin (revenues minus variable costs). Other objectives are to analyze the factors that influence the profitable operation of the refinery, to evaluate some expansion options, and to respond to several other questions posed by your clients. To do this a simplified linear programming model of the refinery will be constructed. The refinery may use one or more of four domestic crudes, whose assays are indicated in Table 2. Table 2: Crude Assay. Crude API gravity Sulfur Assay (% yield by volume)* Price Location (O API) (lb S/bbl) LSRG Naphtha Keros LGO HGO VGO Res ($/bbl) CA 23.8 4.77 3.6 14.3 0.0 21.0 8.5 9.9 41.9 16.52 LA 36.0 0.67 3.3 14.4 24.4 14.2 14.1 8.0 20.8 20.54 CO 34.8 1.88 6.9 19.8 10.3 15.3 12.7 7.6 26.5 20.20 TX 32.5 7.12 11.3 20.5 4.3 19.5 9.5 6.7 27.0 19.61 *
Yields of naphtha, kerosene and gas oil are obtained in atmospheric
distillation. There is also a 2 lb/bbl yield of flue gases (methane, propane, butane). Vacuum gas oil is obtained by distilling the atmospheric bottoms at 40mm Hg. The model considers no new investment. It maximizes contribution margin, which is the difference between sales revenues and variable costs, where sales revenues = income (Table 3) from the sale of: blended gasoline to wholesale distributors commercial jet fuel; no. 2 fuel oil (for heating and diesel fuel); no 4 fuel oil (for heating, locomotive fuel, etc.; residual fuel oil (for process heat, bunker fuel, lubrication, etc.) residuum (vacuum bottoms) to refineries for conversion to coke; and lubricating oils; variable costs = total variable costs per day (24 hours), including cost of crude oil, electricity, catalysts and royalty payments. Note that the objective function of the LP does not measure profit, because it ignores fixed costs. Fuel for process heat is provided by burning fuel gases or no. 2 fuel oil, depending on the process. The fuel gases are collected from the top of the atmospheric still and as a byproduct of reformer. No. 2 oil used by the refinery is provided by the refinery itself. Table 3 contains the refiners’ wholesale price of each product. Table 3: Product Prices Product Selling price ($/gal) Unleaded premium gasoline 0.807 Unleaded mid-grade gasoline 0.741 Unleaded regular gasoline 0.681 Kerosene-type jet fuel 0.658 No. 2 fuel oil 0.616 No. 4 fuel oil 0.495 Residual fuel 0.349 Vacuum bottoms* 0.349 * Since no price was available, it was estimated to be the same as that of residual fuel.
3. Process Specifications Each process in Fig. 1 is discussed separately. In these descriptions, % yield is % of feed, unless stated otherwise. That is, an operation that yields 20% gasoline is one that produces one bbl of gasoline for every 5 bbl of input. A barrel (bbl) is 42 U.S. gallons. 3.1 Stills (Atmospheric and Vacuum) Feed (bbl/d domestic crude): max 250,000; two or more crudes may be blended. Yield: flue gases, LSRG, naphtha, kerosene, light gas oil, heavy gas oil, vacuum gas oil. residuum. Quantities depend on crude type; see Table 2. If crudes are blended, assume total output is the same as when equal amounts of the crudes are run through separately. Requirements (for each bbl feed): 0.7 kwh electricity, plus 94,000 Btu process heat. The refinery was built in 1998. Investment includes $67 million for the atmospheric still, $43.5 million for the vacuum still, and $4.6 million for the flue gas processing unit (all amounts are in 2020 dollars). 3.2 Hydrotreaters (for sulfur removal) RCD Unibon process Since different oils contain different amounts of sulfur, some of the operational characteristics of the hydrotreaters depend on the feed volume and others on the actual amount of sulfur in the oil. Assume that all the sulfur in the crude passes into the hydrotreater. Feed: LSRG, naphtha, kerosene, light gas oil, heavy gas oil, and vacuum gas oil; no capacity limit. Yield: Same as feed by volume, plus hydrogen sulfide gas (feedstock for hydrogen manufacture). Requirements: 0.21 kwh electricity per bbl feed. 0.016 lb desulfurizing catalyst per pound sulfur in feedstock (regardless of the volume of feed). 56,700 btu process heat per bbl feed 0.24 x 103 ft3 H2 per pound sulfur in feedstock. Total investment: $201 million. Fig. 1: Simplified block flow diagram of refinery. 3.3 Catalytic Reformer (Fixed Bed Process) The reformer raises the octane number of naphtha. Feed (bbl/d desulfurized naphtha): max 20,000. Desulfurized LSRC is piped directly to the blender. Naphtha that is not reformed is blended with kerosene to be sold as commercial jet fuel. To keep the Reid vapor pressure within safety specs, the jet fuel sold must contain no more than 40% naphtha. Yield: Reformate for blender feed (blending RON = 100): 76.0% by volume H2: 0.981×103 ft3 per bbl feed (H2 may be used in the hydrotreaters and cracker) methane, propane, butane: 26.5 lb per bbl feed Requirements (for each bbl feed): 0.55 kwh electricity 0.018 lb R-50 catalyst 10,600 btu process heat. Total investment: $81 million 3.4 Catalytic Cracker: Fluidized Bed Catalytic Cracking (FCC), UOP HC Unibon process. The cracker converts heavier oils into feedstock for gasoline blending. Feed (vacuum gas oil): max 20,000 bbl/d. The operating characteristics depend on the “severity” of the cracking. Higher severity yields more gasoline or higher octanes but costs more. Severity can occur on a continuous scale. but it is adequate to consider three grades of severity. For modeling purposes, the cracker can be regarded as three crackers, each operating at a different severity level. The relative volumes of their output streams indicates the actual severity level. For instance, if half the volume is in the first stream half in the second and none in the third, the severity is halfway between the first two levels, and the resulting octane level is roughly halfway between the octane levels of the first two streams. The operating characteristics of each severity level are summarized in Table 4. Table 4: Cracker operating characteristics for three severity levels. Operating mode: distillate gasoline high severity FCC yield (% of feed) 32 59 55 RON of FCC 91 92 93.5 Cycle oil yield (% of feed) 46 15 10 Si-Al catalyst (lb per bbl feed) 0.015 0.025 0.035 H2 requirement (l03 ft3 per bbl) 1 2 3 Process heat (106 btu per bbl) 0.1 0.2 0.3 Electricity (kwh per bbl) 8 13 15 The cracker also produces cycle oil as a byproduct, which is blended with LGO. Total investment: $80.6 million. 3.5 Hydrogen Manufacture Feed: Hydrogen sulfide gas, recycled from desulfurizers. Assume that the supply is adequate. Sulfur is recovered and sold, but the costs of the recovery operation roughly balance the revenue. Yield: maximum 80 x 106 ft3/day H2 Requirements (for each 103 ft3/d of hydrogen gas produced): 0.72 kwh electricity; 0.225 106 Btu process heat (fuel gases); negligible catalysts. Total investment: $42 million. 3.6 Gasoline Blending Gasolines are blended to produce fuels with the desired viscosity, vapor pressure and octane number as cheaply as possible. All three depend on the viscosities, vapor pressures and octane numbers of the components in a highly nonlinear fashion. Special tricks are necessary to approximate these nonlinear relationships with linear constraints. To keep things manageable, you are concerned only with the research octane number of the blended gasolines. Light straight-run gasoline (LSRG) from the still is blended with reformate from the reformer and FCC gasoline from the cracker. The research octane numbers (RON) of the blended products must be at least the following: premium unleaded gasoline — 95 mid-grade unleaded gasoline — 93 regular unleaded gasoline — 91 The RON at the blend is estimated by taking a weighted average of the blending (rather than the actual) octane numbers of the feedstocks, where the weights are the volumes of the feedstocks. These are 66 RON for LSRG, 100 RON for reformate, and 91, 92 or 93.5 RON for FCC gasoline (depending on the cracking severity). Since the RON of LSRG is quite low, it may be disadvantageous to use all the available LSRG in gasoline blending. Unwanted LSRG is “dumped” (i.e., disposed of at zero net cost). 4. Costs 1) When computing costs, you assume the refinery runs 24 hr/d. Electricity: $0.06/kwh. Desulfurizing catalyst: $2.20/lb. R-50 catalyst: $12/lb. Silica-aluminum catalyst: $12/lb. Proprietary processes: i. Reformer royalty: $0.099/bbl feed. ii. Hydrotreater royalty: $0.033/bbl feed. iii. Cracker royalty: $0.100/bbl feed. 2) Process heat: Fuel for Process heat is not purchased but is obtained from either of two sources within the refinery: a) methane, propane and butane from the still or reformer (heating value 20,000 btu/lb); b) no. 2 fuel oil from still and/or cracker (heating value 5.8 x 106 Btu/bbl). Excess fuel gases axe burned off, and excess no. 2 is sold. 5. Exercises 1) The optimal contribution margin (objective function value), rounded to the nearest dollar, is $277,351. What fraction of total revenue is this 2) What fraction of total variable costs can be attributed to the internal operating cost of the refinery (i.e., all variable costs except crude cost) Based on this, what do you conclude 3) What is the optimal product slate That is, how much of each of the eight refined products should be made each day 4) How much price movement (in cents per gallon) would call for a change in the optimal gasoline slate That is, how much must the price of each grade rise or fall before it becomes optimal to produce more or less Summarize your results in a form similar to Table 5. 5) Based on this analysis, would you say that gasoline output is generally sensitive to gasoline prices Table 5: Template for sensitivity analysis for gasoline prices. Product all premium premium mid-grade Regular Price change (c/gal) none + – + + 6) There is a chance the refinery can get a good deal on Colorado crude. How much would the price have to drop before it would be advisable to buy it Note: a drop in crude price implies an increase in the objective function coefficient of input (cocrude) because the objective function measures income rather than cost.