Certainly! Let’s walk through the steps for an **energy balance** on your process, using the material balance and the assumptions you provided. --- ### 1. **Summary of Given Data** #### **Feed streams (Input)** - **Ethylene (C₂H₄):** 315.0 TPD - **Oxygen (O₂):** 180.0 TPD - **Water (H₂O):** 210.0 TPD - **Feed temperature:** 30°C #### **Output (Products)** - **EGs (MEG+DEG+TEG+HEG):** 693.356 TPD - **Product temperature:** 250°C - **CO₂ (Captured):** 0.635 TPD (very small; likely negligible for heat unless other CO₂ leaves in other streams) - **Wastewater:** Sent externally (not quantified in output, so assume balanced by H₂O input and product formation) #### **Reactions** 1. **Main Reaction (to Ethylene Oxide, EO):** \[ \ce{C2H4 + 1/2O2 -> C2H4O} \] - Selectivity: 90% to EO 2. **Side Reaction (Complete Combustion):** \[ \ce{C2H4 + 3O2 -> 2CO2 + 2H2O} \] - Selectivity: 10% to CO₂/H₂O #### **Assumptions** - Steady-state - Cp constant (values to be estimated or provided) - Negligible heat losses - All output at 250°C --- ### 2. **Calculate Moles of Each Component** Let’s use **mole fractions** and **mass flows** to get moles. #### **Molar Masses** - C₂H₄: 28.05 g/mol - O₂: 32.00 g/mol - H₂O: 18.02 g/mol - MEG (C₂H₆O₂): 62.07 g/mol #### **Inputs (convert TPD to kmol/day)** \[ \text{C}_2\text{H}_4: \frac{315,000\, \text{kg}}{28.05\, \text{kg/kmol}} = 11,236\, \text{kmol/day} \] \[ \text{O}_2: \frac{180,000}{32.00} = 5,625\, \text{kmol/day} \] \[ \text{H}_2\text{O}: \frac{210,000}{18.02} = 11,653\, \text{kmol/day} \] #### **Outputs** \[ \text{MEG}: \frac{684,664}{62.07} = 11,025\, \text{kmol/day} \] \[ \text{DEG}~(C_4H_{10}O_3,~m=106.12):~ \frac{5,813}{106.12} = 54.8\, \text{kmol/day} \] \[ \text{TEG}~(C_6H_{14}O_4,~m=150.17):~ \frac{1,471}{150.17} = 9.8\, \text{kmol/day} \] \[ \text{HEG}~(C_8H_{18}O_5,~m=194.22):~ \frac{1,408}{194.22} = 7.2\, \text{kmol/day} \] \[ \text{Total EGs}: 11,025 + 54.8 + 9.8 + 7.2 = 11,097\, \text{kmol/day} \] (Which matches the total mass output.) --- ### 3. **Reactions — How Much EO Produced?** **Selectivity:** 90% to EO **Total Ethylene in:** 11,236 kmol/day - **To EO:** 0.90 × 11,236 = 10,112 kmol/day - **To Side Reaction:** 0.10 × 11,236 = 1,124 kmol/day #### **Oxygen Consumed** - EO: 10,112 × 0.5 = 5,056 kmol O₂ - Side: 1,124 × 3 = 3,372 kmol O₂ - **Total O₂ consumed = 5,056 + 3,372 = 8,428 kmol O₂** But only **5,625 kmol O₂ is fed** — this suggests O₂ is limiting and not all ethylene is converted. (Alternatively, perhaps some O₂ is recycled or the numbers are rounded.) For this calculation, proceed as requested — using the stoichiometry and selectivity. --- ### 4. **Enthalpy Calculations** #### **A. Reference State** Let’s take **all reactants at 25°C (298 K), 1 atm** as the reference. We'll need: 1. **Enthalpy of feed at 30°C relative to 25°C** \((\Delta H_{\text{sens,feed}})\) 2. **Heats of reaction** (at 25°C) 3. **Enthalpy of products at 250°C relative to 25°C** \((\Delta H_{\text{sens,prod}})\) #### **B. Cp Values (approximate, J/mol·K)** - C₂H₄ (g): 43 - O₂ (g): 29 - H₂O (l): 75, (g): 34 - MEG (l): 160 (liquid, approx) - DEG (l): 227 (liquid, approx) - TEG (l): 300 (liquid, approx) - HEG: unknown, estimate ~370 - CO₂ (g): 37 #### **C. Heats of Formation (\(\Delta H_f^\circ\), kJ/mol)** - C₂H₄ (g): +52.3 - O₂ (g): 0 - H₂O (l): -285.8 - H₂O (g): -241.8 - MEG (l): -467.5 - DEG (l): -703.0 - TEG (l): -938.5 - HEG (l): -1173.3 (estimated) - CO₂ (g): -393.5 - C₂H₄O (g): -51.9 (Ethylene oxide) --- #### **Step 1: Sensible Heat of Inputs (\(\Delta H_{\text{sens,feed}}\))** \[ \Delta T = 30 - 25 = 5\, \text{K} \] \[ \Delta H_{\text{sens,feed}} = \sum n_i C_{p,i} \Delta T \] - C₂H₄: \(11,236\, \text{kmol} \times 43\, \text{J/mol·K} \times 5\, \text{K} = 2,416,540\, \text{kJ}\) - O₂: \(5,625\, \text{kmol} \times 29\, \text{J/mol·K} \times 5\, \text{K} = 816,125\, \text{kJ}\) - H₂O: \(11,653\, \text{kmol} \times 75\, \text{J/mol·K} \times 5\, \text{K} = 4,369,875\, \text{kJ}\) **Total:** \(2,416,540 + 816,125 + 4,369,875 = 7,602,540\, \text{kJ/day}\) --- #### **Step 2: Heats of Reaction (\(\Delta H_{\text{rxn}}\))** **A. Main Reaction (per kmol):** \[ \ce{C2H4 + 1/2O2 -> C2H4O} \] \[ \Delta H_{rxn,1} = \Delta H_f^\circ[\ce{C2H4O}] - [\Delta H_f^\circ[\ce{C2H4}] + 0.5 \Delta H_f^\circ[\ce{O2}]] \] \[ = -51.9 - [52.3 + 0] = -104.2\, \text{kJ/mol} \] \[ \text{Total:}\ 10,112\, \text{kmol} \times -104.2 = -1,053,678\, \text{kJ/day} \] **B. Side Reaction (per kmol):** \[ \ce{C2H4 + 3O2 -> 2CO2 + 2H2O} \] \[ \Delta H_{rxn,2} = 2 \Delta H_f^\circ[\ce{CO2}] + 2 \Delta H_f^\circ[\ce{H2O}] - [\Delta H_f^\circ[\ce{C2H4}] + 3\Delta H_f^\circ[\ce{O2}]] \] \[ = 2(-393.5) + 2(-285.8) - [52.3 + 0] = -787 - 571.6 - 52.3 = -1,410.9\, \text{kJ/mol} \] \[ \text{Total:}\ 1,124\, \text{kmol} \times -1,410.9 = -1,587,452\, \text{kJ/day} \] **Total Heats of Reaction:** \[ -1,053,678 + (-1,587,452) = -2,641,130\, \text{kJ/day} \] --- #### **Step 3: Sensible Heat of Products (\(\Delta H_{\text{sens,prod}}\))** \[ \Delta T = 250 - 25 = 225\, \text{K} \] - MEG: \(11,025\, \text{kmol} \times 160 \times 225 = 396,900,000\, \text{J} = 396,900\, \text{kJ}\) - DEG: \(54.8\, \text{kmol} \times 227 \times 225 = 2,799,915\, \text{J} = 2,800\, \text{kJ}\) - TEG: \(9.8\, \text{kmol} \times 300 \times 225 = 661,500\, \text{J} = 662\, \text{kJ}\) - HEG: \(7.2\, \text{kmol} \times 370 \times 225 = 599,400\, \text{J} = 599\, \text{kJ}\) **Total:** \(396,900 + 2,800 + 662 + 599 = 400,961\, \text{kJ/day}\) - CO₂: \(0.635\, \text{TPD} = 635\, \text{kg} / 44.01 = 14.4\, \text{kmol}\) \[ 14.4 \times 37 \times 225 = 119,880\, \text{J} = 120\, \text{kJ} \] - Wastewater: Not specified, skip for this summary. **Grand Total Sensible Product Heat:** \(401,081\, \text{kJ/day}\) --- ### 5. **Energy Balance Equation** \[ Q = [\Delta H_{\text{prod,sens}}] - [\Delta H_{\text{feed,sens}}] - [\Delta H_{\text{rxn}}] \] \[ Q = (401,081) - (7,602) - (-2,641,130) \] \[ Q = 401,081 - 7,603 + 2,641,130 = 3,034,608\, \text{kJ/day} \] --- ### 6. **Interpretation** - **Q positive:** Heat **MUST BE REMOVED** from the reactor (exothermic process). - **Magnitude:** ~3,035,000 kJ/day or **35.1 kW** (divide by 86,400 s). --- ## **Summary Table (Sample)** | Term | Value (kJ/day) | |-------------------------------|------------------| | Sensible Heat, Feed | 7,600 | | Heat of Reaction (exothermic) | -2,641,130 | | Sensible Heat, Products | 401,100 | | **Net Q (must be removed)** | 3,034,600 | --- ## **Conclusions & Recommendations** - **This energy (Q) must be removed, likely via cooling in the reactor, to maintain 250°C.** - **Check actual O₂ consumption and balances for accuracy.** - **If more precise Cp values or product phase data is available, update calculations accordingly.** - **If you want per hour or per second values, divide by 24 hours or 86,400 seconds.** --- **If you want a full detailed spreadsheet or more refined numbers, or if you want to include the heat of vaporization for water, or more precise Cp values, let me know!**