Let's break down the problem step by step: --- ### **Step 1: Identify Hot and Cold Streams** **Hot Streams (need to be cooled):** - **B**: 160°C → 93°C - **D**: 250°C → 138°C **Cold Streams (need to be heated):** - **A**: 60°C → 160°C - **C**: 116°C → 220°C --- ### **Step 2: Utility Streams** - **Cooling water:** 25°C (for cooling, i.e., heat sink) - **Steam:** Saturated at 150 psig (about 180°C, for heating, i.e., heat source) --- ### **Step 3: Pinch Analysis (Qualitative Approach)** #### **Arrange Streams by Temperature:** | Stream | Inlet (°C) | Outlet (°C) | Duty | |--------|------------|-------------|------| | A | 60 | 160 | Heat up (cold) | | B | 160 | 93 | Cool down (hot)| | C | 116 | 220 | Heat up (cold) | | D | 250 | 138 | Cool down (hot)| #### **Match Streams for Maximum Energy Recovery** - **Goal:** Use hot streams to heat cold streams as much as possible before using utilities. --- ### **Step 4: Stream Matching** #### **Hot Stream D (250°C → 138°C):** - Can heat cold stream C (116°C → 220°C) and/or A (60°C → 160°C). #### **Hot Stream B (160°C → 93°C):** - Can heat cold stream A (60°C → 160°C) and/or C (116°C → 220°C) **only up to its own temperature (160°C).** #### **Strategy:** - Use D (very hot) to heat C (which needs to reach 220°C). - Use B to heat A (which needs to reach 160°C). --- ### **Step 5: Construct the Network** #### **(1) Match D and C:** - **C:** 116°C → 220°C (needs to be heated up to 220°C) - **D:** 250°C → 138°C (can supply heat from 250°C down to 138°C) **So:** - Heat C from 116°C to 138°C using D (from 250°C to 138°C). - **After 138°C, D is finished. C needs more heat (from 138°C to 220°C), which must come from utility (steam at 180°C is available).** #### **(2) Match B and A:** - **A:** 60°C → 160°C (needs to be heated up to 160°C) - **B:** 160°C → 93°C (can supply heat from 160°C down to 93°C) **So:** - Heat A from 60°C to 93°C using B (from 160°C to 93°C). - **After 93°C, B is finished. A needs more heat (from 93°C to 160°C), which must come from utility (again, steam at 180°C is available).** #### **(3) Cooling Needs:** - **D:** After giving heat to C (from 250°C to 138°C), may need to be cooled further (down to 138°C) with cooling water. - **B:** After giving heat to A (from 160°C to 93°C), may need to be cooled further (down to 93°C) with cooling water. --- ### **Step 6: Final Heat Exchange Network** #### **A. Cold Streams (Heated):** 1. **A (60°C to 160°C):** - 60°C → 93°C: Heated by B - 93°C → 160°C: Heated by steam 2. **C (116°C to 220°C):** - 116°C → 138°C: Heated by D - 138°C → 180°C: Heated by steam (since 180°C is the max from steam) - 180°C → 220°C: Heated by steam (if superheated steam is available, or else, another utility) #### **B. Hot Streams (Cooled):** 1. **B (160°C to 93°C):** - 160°C → 93°C: Cools A 2. **D (250°C to 138°C):** - 250°C → 138°C: Cools C **If further cooling is needed for B and D (down to their outlet temperatures), use cooling water.** --- ### **Step 7: Draw the Network (Schematic)** ``` D (250°C) ——> (Hex1) ——> D (138°C) ——> cooling water | v C (116°C) ——> (Hex1) ——> C (138°C) | v C (138°C) ——> (Hex2) ——> C (220°C) ^ steam B (160°C) ——> (Hex3) ——> B (93°C) ——> cooling water | v A (60°C) ——> (Hex3) ——> A (93°C) | v A (93°C) ——> (Hex4) ——> A (160°C) ^ steam ``` --- ### **Final Notes and Recommendations** - **Hex1:** Cross-exchanger between D and C - **Hex2:** Heater for C, using steam utility - **Hex3:** Cross-exchanger between B and A - **Hex4:** Heater for A, using steam utility - **Cooling water** is used for further cooling of B and D if needed. --- ## **Final Answer (Summary):** **The minimum-utility heat-exchange network:** - Use hot stream D to pre-heat cold stream C as much as possible. - Use hot stream B to pre-heat cold stream A as much as possible. - Use saturated steam utility to finish heating A and C to their desired outlet temperatures. - Use cooling water utility to cool B and D down to their outlet temperatures after maximum possible energy recovery. **This setup minimizes utility usage by maximizing energy recovery between process streams.** --- If you need calculations with specific heat capacities and mass flow rates, let me know! If you want a process flow diagram, I can sketch it for you as well.