An ore containing 90 wt % MgSO4 ·H2 O and the balance insoluble minerals is fed to a dissolution

Name: Problem 90, Chapter 6: Elementary Principles of Chemical Processes
Uploaded: 2021-02-11T09:59:30-08:00
Duration: 4 min 37 s
Channel: Lottie Adams

step 1 So our solution of magnesium sulfate, heptohydrate, and insoluble solids, is heated to dissolve

Question

An ore containing $90 \mathrm{wt} \% \mathrm{MgSO}_{4} \cdot \mathrm{H}_{2} \mathrm{O}$ and the balance insoluble minerals is fed to a dissolution tank at a rate of $60,000 \mathrm{lb}_{\mathrm{m}} / \mathrm{h}$ along with fresh water and a recycle stream. The tank contents are heated to $120^{\circ} \mathrm{F}$, causing all of the magnesium sulfate monohydrate in the ore to dissolve, forming a solution 10^0 F above saturation. The resulting slurry of the insoluble minerals in MgSO_solution is pumped to a heated filter, where a wet filter cake is separated from a solids-free filtrate. The filter cake retains $5 \mathrm{lb}_{\mathrm{m}}$ of solution per $100 \mathrm{lb}_{\mathrm{m}}$ of solids. The filtrate is sent to a crystallizer in which the temperature is reduced to $50^{\circ} \mathrm{F},$ producing a slurry of $\mathrm{MgSO}_{4} \cdot 7 \mathrm{H}_{2} \mathrm{O}$ crystals in a saturated solution that is sent to another filler. The product filter cake contains all of the prea entrained solution in a ratio of $5 \mathrm{Ib}_{\mathrm{m}}$ solution per $100 \mathrm{lb}_{\mathrm{m}}$ crystals. The filtrate from this filter is returned to the dissolution tank as the recycle stream.Solubility data: Saturated magnesium sulfate solutions at $110^{\circ} \mathrm{F}$ and $50^{\circ} \mathrm{F}$ contain $32 \mathrm{wt} \%$ $\mathrm{MgSO}_{4}$ and $23 \mathrm{wt} \% \mathrm{MgSO}_{4},$ respectively.(a) Explain why the solution is first heated (in the dissolution tank) and filtered and then cooled (in the crystallizer) and filtered. (b) Calculate the production rate of crystals and the required feed rate of fresh water to the dissolution tank. (Note: Don't forget to include water of hydration when you write a mass balance on water.)(c) Calculate the ratio $\mathrm{lb}_{\mathrm{m}}$ recycle/lb $_{\mathrm{m}}$ makeup water.

   An ore containing $90 \mathrm{wt} \% \mathrm{MgSO}_{4} \cdot \mathrm{H}_{2} \mathrm{O}$ and the balance insoluble minerals is fed to a dissolution tank at a rate of $60,000 \mathrm{lb}_{\mathrm{m}} / \mathrm{h}$ along with fresh water and a recycle stream. The tank contents are heated to $120^{\circ} \mathrm{F}$, causing all of the magnesium sulfate monohydrate in the ore to dissolve, forming a solution 10^0 F above saturation. The resulting slurry of the insoluble minerals in MgSO_solution is pumped to a heated filter, where a wet filter cake is separated from a solids-free filtrate. The filter cake retains $5 \mathrm{lb}_{\mathrm{m}}$ of solution per $100 \mathrm{lb}_{\mathrm{m}}$ of solids. The filtrate is sent to a crystallizer in which the temperature is reduced to $50^{\circ} \mathrm{F},$ producing a slurry of $\mathrm{MgSO}_{4} \cdot 7 \mathrm{H}_{2} \mathrm{O}$ crystals in a saturated solution that is sent to another filler. The product filter cake contains all of the prea entrained solution in a ratio of $5 \mathrm{Ib}_{\mathrm{m}}$ solution per $100 \mathrm{lb}_{\mathrm{m}}$ crystals. The filtrate from this filter is returned to the dissolution tank as the recycle stream.Solubility data: Saturated magnesium sulfate solutions at $110^{\circ} \mathrm{F}$ and $50^{\circ} \mathrm{F}$ contain $32 \mathrm{wt} \%$ $\mathrm{MgSO}_{4}$ and $23 \mathrm{wt} \% \mathrm{MgSO}_{4},$ respectively.(a) Explain why the solution is first heated (in the dissolution tank) and filtered and then cooled (in the crystallizer) and filtered.
(b) Calculate the production rate of crystals and the required feed rate of fresh water to the dissolution tank. (Note: Don't forget to include water of hydration when you write a mass balance on water.)(c) Calculate the ratio $\mathrm{lb}_{\mathrm{m}}$ recycle/lb $_{\mathrm{m}}$ makeup water.

Elementary Principles of Chemical Processes

Richard M. Felder,… 4th Edition

Chapter 6, Problem 90

Instant Answer

Solved by Expert Lottie Adams

02/11/2021

Step 1

This is done to dissolve all of the $\mathrm{MgSO}_{4} \cdot \mathrm{H}_{2} \mathrm{O}$ in water. The solution is then filtered to remove the insoluble minerals. Show more…

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An ore containing $90 \mathrm{wt} \% \mathrm{MgSO}_{4} \cdot \mathrm{H}_{2} \mathrm{O}$ and the balance insoluble minerals is fed to a dissolution tank at a rate of $60,000 \mathrm{lb}_{\mathrm{m}} / \mathrm{h}$ along with fresh water and a recycle stream. The tank contents are heated to $120^{\circ} \mathrm{F}$, causing all of the magnesium sulfate monohydrate in the ore to dissolve, forming a solution 10^0 F above saturation. The resulting slurry of the insoluble minerals in MgSO_solution is pumped to a heated filter, where a wet filter cake is separated from a solids-free filtrate. The filter cake retains $5 \mathrm{lb}_{\mathrm{m}}$ of solution per $100 \mathrm{lb}_{\mathrm{m}}$ of solids. The filtrate is sent to a crystallizer in which the temperature is reduced to $50^{\circ} \mathrm{F},$ producing a slurry of $\mathrm{MgSO}_{4} \cdot 7 \mathrm{H}_{2} \mathrm{O}$ crystals in a saturated solution that is sent to another filler. The product filter cake contains all of the prea entrained solution in a ratio of $5 \mathrm{Ib}_{\mathrm{m}}$ solution per $100 \mathrm{lb}_{\mathrm{m}}$ crystals. The filtrate from this filter is returned to the dissolution tank as the recycle stream.Solubility data: Saturated magnesium sulfate solutions at $110^{\circ} \mathrm{F}$ and $50^{\circ} \mathrm{F}$ contain $32 \mathrm{wt} \%$ $\mathrm{MgSO}_{4}$ and $23 \mathrm{wt} \% \mathrm{MgSO}_{4},$ respectively.(a) Explain why the solution is first heated (in the dissolution tank) and filtered and then cooled (in the crystallizer) and filtered. (b) Calculate the production rate of crystals and the required feed rate of fresh water to the dissolution tank. (Note: Don't forget to include water of hydration when you write a mass balance on water.)(c) Calculate the ratio $\mathrm{lb}_{\mathrm{m}}$ recycle/lb $_{\mathrm{m}}$ makeup water.

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Key Concepts

Recycle Streams

Recycle streams are used in process engineering to improve efficiency and resource utilization. By returning part of the process output (in this case, the filtrate from crystallization) to the dissolution tank, the process minimizes waste and conserves water. Managing recycle flows is essential for maintaining steady state operation and balancing material flows within the entire process.

Filtration and Solid/Liquid Separation

Filtration is the process of separating solids from liquids using a porous medium. In this scenario, filtration is employed twice: after dissolution to remove insoluble minerals from the solution, and after crystallization to separate the product crystals from the residual mother liquor. The technique relies on defined retention properties within the filter cake, ensuring that a specific amount of liquid is retained in the solids, which must be considered for an accurate overall material balance.

Crystallization Process

Crystallization is achieved by cooling a previously saturated, heated solution. As the temperature drops, the solubility of the dissolved substance decreases, leading to the formation of crystals. This temperature swing method allows controlled precipitation of the product while leaving behind a saturated solution, which is then recycled. This step is crucial for efficient product recovery and purity.

Solubility and Temperature Dependence

Solubility is the maximum amount of a solute that can dissolve in a solvent at a given temperature, and it typically varies with temperature. In this context, heating the solution increases solubility, ensuring complete dissolution, while cooling reduces solubility, leading to crystallization. This temperature-dependent behavior is fundamental in controlling the dissolution and subsequent precipitation stages of the process.

Mass Balance

Mass balance involves accounting for every component entering and leaving a process, including reactants, products, and by?products. In processes like this one, careful balancing is critical not only for the chemical substances but also for bound water (water of hydration), which must be included when tracking the overall water content to ensure accurate design and analysis of processing streams.

Dissolution Process

In the dissolution stage, the ore is heated along with water and recycle stream which facilitates the complete dissolution of the soluble mineral component. Heating ensures that even minerals that are slightly supersaturated become fully dissolved, preparing the solution for downstream separation processes and maintaining process consistency by creating a uniform feed for filtration.

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