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Chapter 9: Problem 70

A city with a population of 200,000 people operates a \(20.0 \times 10^{6}\) gal/day wastewater treatment plant. For every million gallons of wastewater treated, \(1875 \mathrm{lb}_{\mathrm{m}}\) of solids are generated, with \(75 \%\) of the solids being classified as "volatile" (meaning they are converted to gases during digestion). Solids generated in the treatment plant are fed to an anaerobic digester in which microorganisms break down biodegradable material in the absence of oxygen. The feed to the digester contains 45,000 mg solids/L at \(55^{\circ} \mathrm{F}\) and has a density approximately that of water. The digester operates at \(95^{\circ} \mathrm{F},\) converts \(50 \%\) of the volatile solids to a biogas containing 65 vol\% \(\mathrm{CH}_{4}\) and \(35 \%\) \(\mathrm{CO}_{2}\) at a rate of \(15 \mathrm{SCF}\) (standard cubic feet) gas per \(\mathrm{Ib}_{\mathrm{m}}\) of solids converted, and loses approximately \(250,000 \mathrm{Btu} / \mathrm{h}\) of heat to the surroundings. To supply the heat needed to raise the feed temperature from \(55^{\circ} \mathrm{F}\) to \(95^{\circ} \mathrm{F}\) and to make up for the heat loss, a stream of sludge is pumped from the digester through a heat exchanger in which it comes into thermal contact with a stream of hot water. The heated sludge is returned to the digester. The digester biogas is fed to a furnace in which a fraction of it is burned to heat the water for the heat exchanger from \(160^{\circ} \mathrm{F}\) to \(180^{\circ} \mathrm{F}\). A schematic of part of the process is shown below. (a) Calculate the rate (SCF/h) at which biogas is produced in the digester and the total heating value (Btu/h) of the gas (= fuel flow rate \(\times\) lower heating value). (b) Calculate the rate of heat transfer (Btu/h) between the hot water and sludge and the volumetric flow rate (ft \(^{3} / \mathrm{h}\) ) of the water passing through the heat exchanger. Assume the heat of reaction of the anaerobic digestion process is negligible. (c) If the biogas is burned in a boiler with \(80 \%\) efficiency (that is, \(80 \%\) of the heating value of the fuel goes to produce hot water for the heat exchanger), what fraction of the digester gas must be burned to heat the water from \(160^{\circ} \mathrm{F}\) to \(180^{\circ} \mathrm{F}\) ? What happens to the other \(20 \%\) of the heating value? (d) If there is excess digester gas available after meeting the process-water heating demand, what are its potential uses?

Short Answer

Expert verified
The detailed solution would provide the specific numerical values, but the methodology includes computing the rate of biogas production, determining the heating value of the produced biogas, calculating the required heat transfer rate, determining the volumetric flow rate of water in the heat exchanger, and specifying the required fraction of biogas to be burned for achieving desired temperature. Excess digester gas could be used for various purposes, such as further power generation or heating requirements.

Step by step solution

01

Calculate the amount of Solids Generated

Calculate the total amount of solids generated by using the information provided: \(20.0 \times 10^{6}\) gal/day of wastewater treated generates \(1875 \mathrm{lb}_{\mathrm{m}}\) of solids per million gallons.
02

Determine the Amount of Volatile Solids

Compute the amount of volatile solids by multiplying the total solids determined in Step 1 by \(75%\). It is also important to remember that the anaerobic digester converts \(50%\) of these volatile solids to biogas.
03

Compute the Rate of Biogas Production

Use the data that \(15 \mathrm{SCF}\) of gas is produced per \(\mathrm{Ib}_{\mathrm{m}}\) of solids converted to calculate the rate at which biogas is produced in the digester. The content of the biogas is \(65\% \mathrm{CH}_{4}\) and \(35 \% \mathrm{CO}_{2}\).
04

Calculate the Heating Value of the Biogas

Calculate the total heating value of the gas by multiplying the flow rate of the biogas by its lower heating value.
05

Calculate the Required Increase in Temperature

The temperature of feed in the digester has to be raised from \(55^{\circ} \mathrm{F}\) to \(95^{\circ} \mathrm{F}\), and the heat loss to surroundings has to be compensated. Use the specific heat capacity of solids to calculate the required heat transfer rate.
06

Calculate the Rate of Heat Transfer and the Volumetric Flow Rate of Water

Using the computed heat requirement, calculate the rate of heat transfer between the hot water and the sludge. Furthermore, the volumetric flow rate of the water passing through the heat exchanger can be calculated by equating it with the quantity of heat to be transferred.
07

Determine the Fraction of Biogas to Burn

With a boiler efficiency of \(80\%\), find the fraction of biogas that must be burned to raise the heat of the water from \(160^{\circ} \mathrm{F}\) to \(180^{\circ} \mathrm{F}\).
08

Discuss Potential Uses for Excess Digester Gas

Given any remaining digester gas after meeting the process-water heating demand, discuss its potential uses.'

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Anaerobic Digestion
Anaerobic digestion is a fascinating process that transforms organic matter into biogas by using microorganisms. These microscopic organisms break down waste without the need for oxygen. This is highly beneficial for environments where reducing waste is vital, such as wastewater treatment plants.
  • Energy-Efficient: Anaerobic digestion uses the energy within the organic matter, which saves on additional energy requirements.
  • Sustainability: Produces renewable energy in the form of biogas, primarily methane, which can be used as a clean-burning fuel.
  • Waste Reduction: Significantly reduces the volume of waste, making waste management more efficient.
By operating at a relatively constant temperature with a controlled environment, anaerobic digesters optimize the breakdown of volatile solids. This makes it a cornerstone of modern waste treatment solutions.
Wastewater Treatment
Wastewater treatment involves the process of removing contaminants from water released from homes, industries, and other sources. This ensures that the resulting water is safe and environmentally friendly.
  • Primary Treatment: Removes solid materials and large debris.
  • Secondary Treatment: Uses biological processes, often involving microbes, to further clean the water.
  • Tertiary Treatment: Enhances water quality to the highest standard, often targeting specific pollutants.
In the context of biogas production, wastewater treatment not only helps in cleaning water but also generates solids that are subsequently treated in anaerobic digesters. This is a dual-purpose system that effectively manages waste and produces valuable energy resources.
Heat Transfer Calculation
Heat transfer plays a crucial role in ensuring the efficiency of a wastewater treatment plant. Calculating the amount of heat required to bring the sludge to the necessary temperature is vital.First, determine the heat needed to raise the sludge from its initial temperature (in this case, from 55掳F to 95掳F). You can use the formula:\[ q = mc(T_{final} - T_{initial}) \]where:
  • \(q\) is the heat energy (Btu),
  • \(m\) is the mass of the sludge,
  • \(c\) is the specific heat capacity, and
  • \(T_{final}\) and \(T_{initial}\) are the final and initial temperatures, respectively.
Next, consider the heat loss to surroundings, which must be compensated by the energy provided from the biogas.These calculations also guide the design of heat exchange systems, necessary for maintaining the digester's operational temperature.
Volatile Solids
Volatile solids, a term used in waste management, refer to the portion of solids in the sludge that can be converted into gases, such as methane, during anaerobic digestion.
  • Composition: Includes organic compounds like carbohydrates, proteins, and fats.
  • Biodegradability: They are biodegradable, meaning they can be broken down by microorganisms.
  • Importance: Their conversion to biogas is crucial for the success of anaerobic digestion processes.
For maximum efficiency, digesters need to convert a high percentage of volatile solids. This is often measured as the volatile solids reduction percentage. The higher the reduction, the more biogas is produced, contributing significantly to the plant's energy output.

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Most popular questions from this chapter

A 2.00 mole \(\%\) sulfuric acid solution is neutralized with a 5.00 mole\% sodium hydroxide solution in a continuous reactor. All reactants enter at \(25^{\circ} \mathrm{C}\). The standard heat of solution of sodium sulfate is \(-1.17 \mathrm{kJ} / \mathrm{mol} \mathrm{Na}_{2} \mathrm{SO}_{4},\) and the heat capacities of all solutions may be taken to be that of pure liquid water [4.184 kJ/(kg.'C)]. (a) How much heat (kJ/kg acid solution fed) must be transferred to or from the reactor contents (state which it is) if the product solution emerges at \(40^{\circ} \mathrm{C} ?\) (b) Estimate the product solution temperature if the reactor is adiabatic, neglecting heat transferred between the reactor contents and the reactor wall.

A gaseous fuel containing methane and ethane is burned with excess air. The fuel enters the furnace at \(25^{\circ} \mathrm{C}\) and 1 atm, and the air enters at \(200^{\circ} \mathrm{C}\) and 1 atm. The stack gas leaves the furnace at \(800^{\circ} \mathrm{C}\) and 1 atm and contains 5.32 mole\% \(\mathrm{CO}_{2}, 1.60 \%\) CO, \(7.32 \%\) O \(_{2}, 12.24 \% \mathrm{H}_{2} \mathrm{O}\), and the balance \(\mathrm{N}_{2}\). (a) Calculate the molar percentages of methane and ethane in the fuel gas and the percentage excess air fed to the reactor. (b) Calculate the heat (kJ) transferred from the reactor per cubic meter of fuel gas fed. (c) A proposal has been made to lower the feed rate of air to the furnace. State advantages and a drawback of doing so.

In the production of many microelectronic devices, continuous chemical vapor deposition (CVD) processes are used to deposit thin and exceptionally uniform silicon dioxide films on silicon wafers. One CVD process involves the reaction between silane and oxygen at a very low pressure. $$\mathrm{SiH}_{4}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{SiO}_{2}(\mathrm{s})+2 \mathrm{H}_{2}(\mathrm{g})$$ The feed gas, which contains oxygen and silane in a ratio \(8.00 \mathrm{mol} \mathrm{O}_{2} / \mathrm{mol} \mathrm{SiH}_{4},\) enters the reactor at 298 \(\mathrm{K}\) and 3.00 torr absolute. The reaction products emerge at \(1375 \mathrm{K}\) and 3.00 torr absolute. Essentially all of the silane in the feed is consumed. (a) Taking a basis of \(1 \mathrm{m}^{3}\) of feed gas, calculate the moles of each component of the feed and product mixtures and the extent of reaction, \(\xi\) (b) Calculate the standard heat of the silane oxidation reaction (kJ). Then, taking the feed and product species at \(298 \mathrm{K}\left(25^{\circ} \mathrm{C}\right)\) as references, prepare an inlet-outlet enthalpy table and calculate and fill in the component amounts (mol) and specific enthalpies (kJ/mol). (See Example 9.5-1.) Data $$\left(\Delta \hat{H}_{\mathrm{f}}\right)_{\mathrm{SiH}_{4}(\mathrm{g})}=-61.9 \mathrm{kJ} / \mathrm{mol}, \quad\left(\Delta \hat{H}_{\mathrm{f}}^{\mathrm{o}}\right)_{\mathrm{SiO}_{2}(\mathrm{s})}=-851 \mathrm{kJ} / \mathrm{mol}$$ $$\left(C_{p}\right)_{\mathrm{SiH}_{4}(g)}[\mathrm{k} \mathrm{J} /(\mathrm{mol} \cdot \mathrm{K})]=0.01118+12.2 \times 10^{-5} T-5.548 \times 10^{-8} T^{2}+6.84 \times 10^{-12} T^{3}$$ $$\left(C_{p}\right)_{\mathrm{SiO}_{2}(\mathrm{s})}[\mathrm{kJ} /(\mathrm{mol} \cdot \mathrm{K})]=0.04548+3.646 \times 10^{-5} T-1.009 \times 10^{3} / T^{2}$$ The temperatures in the formulas for \(C_{p}\) are in kelvins. (c) Calculate the heat ( \(k\) J) that must be transferred to or from the reactor (state which it is). Then determine the required heat transfer rate ( \(\mathrm{kW}\) ) required for a reactor feed of \(27.5 \mathrm{m}^{3} / \mathrm{h}\).

Ethylbenzene is converted to styrene in the catalytic dehydrogenation reaction $$\mathrm{C}_{8} \mathrm{H}_{10}(\mathrm{g}) \rightarrow \mathrm{C}_{8} \mathrm{H}_{8}(\mathrm{g})+\mathrm{H}_{2}: \quad \Delta H_{\mathrm{r}}^{\circ}\left(600^{\circ} \mathrm{C}\right)=+124.5 \mathrm{kJ}$$ A flowchart of a simplified version of the commercial process is shown here. Fresh and recycled liquid ethylbenzene combine and are heated from \(25^{\circ} \mathrm{C}\) to \(500^{\circ} \mathrm{C} \mathrm{C}\) ? and the heated ethylbenzene is mixed adiabatically with steam at \(700^{\circ} \mathrm{C}\) ? to produce the feed to the reactor at \(600^{\circ} \mathrm{C}\) (The steam suppresses undesired side reactions and removes carbon deposited on the catalyst surface.) A once-through conversion of \(35 \%\) is achieved in the reactor ? and the products emerge at \(560^{\circ} \mathrm{C}\).The product stream is cooled to \(25^{\circ} \mathrm{C}\) ? condensing essentially all of the water, ethylbenzene, and styrene and allowing hydrogen to pass out as a recoverable by-product of the process. The water and hydrocarbon liquids are immiscible and are separated in a settling tank decanter ? The water is vaporized and heated ? to produce the steam that mixes with the cthylbenzene feed to the reactor. The hydrocarbon stream leaving the decanter is fed to a distillation tower ? (actually, a seriesof towers), which separates the mixture into essentially pure styrene and ethylbenzene, each at \(25^{\circ} \mathrm{C}\) after cooling and condensation steps have been carried out. The ethylbenzene is recycled to the reactor preheater, and the styrene is taken off as a product. (a) On a basis of \(100 \mathrm{kg} / \mathrm{h}\) styrene produced, calculate the required fresh ethylbenzene feed rate, the flow rate of recycled ethylbenzene, and the circulation rate of water, all in mol/h. (Assume \(P=1\) atm.) (b) Calculate the required rates of heat input or withdrawal in \(\mathrm{kJ} / \mathrm{h}\) for the ethylbenzene preheater ? steam generator ? ind reactor ? (c) Suggest possible ways to improve the energy economy of this process.

In a surface-coating operation, a polymer (plastic) dissolved in liquid acetone is sprayed on a solid surface and a stream of hot air is then blown over the surface, vaporizing the acetone and leaving a residual polymer film of uniform thickness. Because environmental standards do not allow discharging acetone into the atmosphere, a proposal to incinerate the stream is to be evaluated. The proposed process uses two parallel columns containing beds of solid particles. The air-acetone stream, which contains acetone and oxygen in stoichiometric proportion, enters one of the beds at \(1500 \mathrm{mm} \mathrm{Hg}\) absolute at a rate of 1410 standard cubic meters per minute. The particles in the bed have been preheated and transfer heat to the gas. The mixture ignites when its temperature reaches \(562^{\circ} \mathrm{C}\), and combustion takes place rapidly and adiabatically. The combustion products then pass through and heat the particles in the second bed, cooling down to \(350^{\circ} \mathrm{C}\) in the process. Periodically the flow is switched so that the heated outlet bed becomes the feed gas preheater/combustion reactor and vice versa. Use the following average values for \(C_{p}\left[\mathrm{kJ} /\left(\mathrm{mol} \cdot^{\circ} \mathrm{C}\right)\right]\) in solving the problems to be given: 0.126 for \(\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}, 0.033\) for \(\mathrm{O}_{2}, 0.032\) for \(\mathrm{N}_{2}, 0.052\) for \(\mathrm{CO}_{2},\) and 0.040 for \(\mathrm{H}_{2} \mathrm{O}(\mathrm{v})\) (a) If the relative saturation of acetone in the feed stream is \(12.2 \%,\) what is the stream temperature? (b) Determine the composition of the gas after combustion, assuming that all of the acetone is converted to \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O},\) and estimate the temperature of this stream. (c) Estimate the rates ( \(\mathrm{kW}\) ) at which heat is transferred from the inlet bed particles to the feed gas prior to combustion and from the combustion gases to the outlet bed particles. Suggest an alternative to the two-bed feed switching arrangement that would achieve the same purpose.
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