Who can provide the calculation method for steam ejectors
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The calculations for steam ejectors are not covered in detail in many professional books; could someone please explain the specific methods? Thank you very much!
7.4 Calculation Formulas 7.4.1 The critical mass flow rate of air is given by equation (1): qm1 = 114.22 cd² p₁ / √T ………………………………(1) 7.4.2 The subcritical mass flow rate of air is given by equation (2): qm2 = 236.91 cd² Yp₁ √(1 / T – p/p) ……………………(2) 7.4.3 The critical mass flow rate of steam is given by equation (3): q′m1 = 1.8867 cd² √(p₁ / v₁) ………………………………(3) 7.4.4 The subcritical mass flow rate of steam is given by equation (4): q′m2 = 3.9989 cd² Y √(1 / (v/p) – 1) ………………………………(4) 7.4.5 The flow rate through a burette is given by equation (5): Q = t Vp ………………………………………(5) Where: qm1 – Critical mass flow rate of air, in kg/h； qm2——subcritical mass flow rate of air, kg/h ； q′m1 —— critical mass flow rate of steam, kg/h ； q′m2 —— subcritical mass flow rate of steam, kg/h ； JB/T 8540－1997 13 p1——Fluid pressure upstream of the flow nozzle, MPa ； p2 —— Fluid pressure downstream of the flow nozzle, MPa ； T1 — Fluid temperature upstream of the flow nozzle, K ； v1 — specific volume of steam upstream of the flow nozzle, m3/kg ； d——throat diameter of the flow nozzle, mm ； c —— flow coefficient, generally taken as 0.970; see Appendix A (standard appendix) for details ； Y — Expansion coefficient; see Appendix B (standard appendix) for details ； Q —— Dropper air flow rate, Pa·m3/s ； V —— Volume of the burette between liquid level 1 and liquid level 2, in m3 (L) ； t —— the time required for the liquid level to rise from position 1 to position 2, in seconds ； p —— Pressure of gas inflow to the dropper, Pa.
I’m sorry; for some reason, some of the text uploaded came out as garbled characters
I have prepared it using your formula; thank you!
The post you sent is great; I really need it
I. General Properties of Methanol
The molecular formula of methanol is CH3OH, with a molecular weight of 32.04. At normal temperature and pressure, pure methanol is a colorless, transparent, fluid, volatile, and flammable liquid. It has an odor similar to that of ethanol. Its general properties are shown in the table below:
General Properties of Methanol
Property | Value
Density | 0.81 g/cm³ (0°C)
Viscosity | 5.945×10⁻⁴ Pa•s (0.5945 cP) (20°C)
Relative Density | 0.7913 (d420)
Thermal Conductivity | 2.09×10⁻³ J/(cm•s•K)
Boiling Point | 64.5–64.7°C
Surface Tension | 22.55×10⁻⁵ N/cm (22.55 dyn/cm) (20°C)
Melting Point | –97.8°C
Refractive Index | 1.3287 (20°C)
Flash Point | 16°C (open container), 12°C (closed container)
Vaporization Heat | 35.295 KJ/mol (64.7°C)
Spontaneous Combustion Temperature | 473°C (in air), 461°C (in oxygen)
Enthalpy of Fusion | 3.169 KJ/mol
Critical Temperature | 240°C
Heat of Combustion | 727.038 KJ/mol (liquid at 25°C), 742.738 KJ/mol (gas at 25°C)
Critical Pressure | 79.54×10⁵ Pa
Enthalpy of Formation | 238.798 KJ/mol (liquid at 25°C), 201.385 KJ/mol (gas at 25°C)
Critical Volume | 117.8 ml/mol
Coefficient of Expansion | 0.00119 (20°C)
Critical Compression Factor | 0.224
Corrosivity | Non-corrosive at normal temperatures, except for lead and aluminum
Vapor Pressure | 1.2879×10⁴ Pa (96.6 mmHg) (20°C)
Heat Capacity | 2.51–2.53 J/(g•°C) (liquid at 20–25°C), 45 J/(mol•°C) (gas at 25°C)
Explosibility | 6.0–36.5% (by volume) (explosion range in air)
Table showing how the density, viscosity, and surface tension of methanol change with temperature
Temperature (°C): 0, 10, 20, 30, 40, 50, 60
Density (g/cm³): 0.81, 0.8008, 0.7915, 0.7825, 0.774, 0.765, 0.7555
Viscosity (cP): 0.817, 0.69, 0.597, 0.51, 0.45, 0.396, 0.35
Surface Tension (dyn/cm): 24.5, 23.5, 22.6, 21.8, 20.9, 20.1, 19.3
Note: 1 cP = 10⁻⁴ Pa•s; 1 dyn = 10⁻⁵ N.
Methanol can mix infinitely with water and many organic liquids such as ethanol and ether, but it cannot mix with aliphatic hydrocarbons. It readily absorbs water vapor, carbon dioxide, etc. Methanol is toxic; ingesting 10 ml of it can pose a risk of blindness, while 30 ml can be fatal. The maximum allowable concentration of methanol vapor in the air is 0.05 mg/L. The density of aqueous methanol solutions increases as the temperature decreases. At the same temperature, it decreases almost proportionally with increasing methanol concentration. See the table below:
Density of aqueous methanol solutions in relation to methanol concentration and temperature
| CH3OH % | Density (g/cm³) at -30°C | Density (g/cm³) at 0°C | Density (g/cm³) at 20°C | Density (g/cm³) at 30°C | Density (g/cm³) at 40°C | Density (g/cm³) at 60°C |
|---------|--------------------------|------------------------|------------------------|------------------------|------------------------|------------------------|
| 10 | – | 0.9842 | 0.9815 | 0.9794 | 0.9750 | 0.9635 |
| 20 | – | 0.9725 | 0.9666 | 0.9625 | 0.9567 | 0.9450 |
| 30 | – | 0.9604 | 0.9515 | 0.9442 | 0.9383 | 0.9260 |
| 40 | 0.9595 | 0.9459 | 0.9345 | 0.9250 | 0.9200 | 0.9061 |
| 50 | 0.9434 | 0.9287 | 0.9156 | 0.9050 | 0.9000 | 0.8844 |
| 60 | 0.9250 | 0.9090 | 0.8946 | 0.8835 | 0.8783 | 0.8609 |
| 70 | 0.9073 | 0.8869 | 0.8715 | 0.8610 | 0.8540 | 0.8355 |
| 80 | 0.8870 | 0.8634 | 0.8469 | 0.8361 | 0.8280 | 0.8083 |
| 90 | 0.8640 | 0.8374 | 0.8202 | 0.8090 | 0.8000 | 0.7800 |
The density ρ (g/cm³) of aqueous methanol solutions can be calculated using the following formula:
ρ = 1.034 – 0.0008t – 0.0022C
where T is the temperature in °C, and C is the methanol concentration in %.
Table of hydrogen solubility in methanol (cm³/g CH₃OH):
| Pressure (kgf/cm²) | Temperature (°C) | Pressure (kgf/cm²) | Temperature (°C) |
|--------------------|------------------|--------------------|------------------|
| 25 | 1.6 | 25 | 18.0 |
| 50 | 2.7 | 50 | 20.2 |
| 75 | 3.5 | 75 | 22.4 |
| 100 | 4.0 | 100 | 24.1 |
| 125 | 4.3 | 125 | 30.2 |
| | | 150 | 37.5 |
| 50 | 5.5 | 200 | 45.0 |
| 75 | 6.4 | 250 | 54.0 |
| 100 | 7.3 | 300 | 63.0 |
| 125 | 8.3 | | |
| | | 350 | 72.0 |
Table of carbon dioxide solubility in methanol (cm³/g CH₃OH):
| Pressure (kgf/cm²) | Temperature (°C) | Pressure (kgf/cm²) | Temperature (°C) |
|--------------------|------------------|--------------------|------------------|
| 0 | 25 | 0 | 25 |
| | 49.8 | | 49.8 |
| | 75 | | 75 |
| 6.8 | 59.5 | 6.8 | 197 |
| 12.8 | 29.9 | 12.8 | 112 |
| | 19.5 | | 71.5 |
| | 10.7 | | 10.7 |
| 94.9 | 49.3 | 94.9 | 161 |
| 32.1 | 22.3 | 32.1 | 103 |
| 39.7 | – | 39.7 | 16.5 |
| | | 287 | 174 |
| | | 51.8 | 82.5 |
| | | 35.5 | 51.8 |
| | | 49.4 | 35.5 |
| | | – | 228 |
| | | | 104 |
| | | | 22.3 |
| | | | 270 |
| | | | 118 |
| | | | 71.9 |
| | | | 48.6 |
| | | | 55.2 |
Table of carbon monoxide solubility in methanol (cm³/g CH₃OH):
| Pressure (kgf/cm²) | Temperature (°C) | Pressure (kgf/cm²) | Temperature (°C) |
|--------------------|------------------|--------------------|------------------|
| 25 | 90 | 25 | 90 |
| | 140 | | 140 |
| 55 | 10.5 | 55 | 46.4 |
| | 15.9 | | 48.2 |
| | – | | 57.0 |
| 200 | 23.0 | 200 | 60.0 |
| 75 | 17.4 | 75 | 55.8 |
| | – | | 64.7 |
| 250 | 23.2 | 250 | 60.0 |
| | 28.5 | | 55.8 |
| | 32.9 | | 64.7 |
| 300 | – | 300 | 62.1 |
| | 71.2 | | 71.2 |
| 150 | 34.1 | 150 | 62.1 |
| | 38.9 | | 71.2 |
| | 47.2 | | – |
II. Reaction equations for methanol
CO + 2H₂ → CH₃OH ΔH = −90.56 kJ/mol
CO₂ + 3H₂ → CH₃OH + H₂O ΔH = −49.43 kJ/mol
Chapter 2: Production of raw gas for methanol synthesis
Section 1: Requirements for raw gas used in methanol synthesis
1. Appropriate H₂/CO ratio
Generally, the raw gas used for methanol synthesis contains H₂, CO, and CO₂. Therefore, it must satisfy the condition (H₂−CO₂)/(CO+CO₂) = 2; this is the optimal stoichiometric ratio for methanol production. The chemical equivalent ratio of hydrogen to carbon monoxide for methanol synthesis is 2, while it is 3 for synthesis with carbon dioxide. When both CO and CO2 are present, there are two ways to express the hydrogen-to-carbon ratio (f or M value) in the feed gas: f = (H2 – CO2) / (CO + CO2) = 2.10–2.15, or H2 / (CO + 1.5CO2) = 2.0–2.05. The composition of the feed gas obtained using different raw materials and processes often deviates from these f values or M values; the hydrogen-to-carbon ratio of the crude feed gas produced from coal is too low, so a shift process is required to convert the excess CO into H2, followed by the removal of the excess CO2. When natural gas (whose main component is CH4) is used as the feed gas, the crude feed gas obtained through steam reforming contains an excessive amount of hydrogen, so CO2 needs to be added before or after the reforming process to adjust this. In production, the appropriate hydrogen-to-carbon ratio should be slightly higher than the chemical equivalent ratio; based on the chemical equivalent ratio, the f-value or M-value is around 2. In practice, this ratio is kept slightly above 2, meaning that a slightly higher hydrogen content is maintained. Excess hydrogen helps to reduce the formation of iron carbonyl and higher alcohols, as well as to extend the lifespan of the catalyst. The C/H ratio in the methanol molecule is 0.5. As can be seen from the overall reaction equation 12/7m (CH0.5)m + 11/7 H2O + 3/7 O2 → CH3OH + 5/7 CO2, when the C/H ratio in the reactants is less than 0.5, there is an excess of H2, and CO2 needs to be added ； When C/H in the reactants is greater than 0.5, CO2 must be removed from the system; therefore, shift and decarburization units must be installed in methanol plants that use coal as a raw material. II. An appropriate ratio of CO to CO2: A certain amount of CO2 should be present in the raw gas used for methanol synthesis; the presence of CO2 helps to increase the reaction rate of methanol synthesis on zinc-chromium catalysts as well as copper-based catalysts. An appropriate level of CO2 enables the catalysts to maintain high activity. Additionally, in the presence of CO2, the heat effect associated with methanol synthesis is lower compared to when methanol is synthesized solely from CO and H2, which makes it easier to control the temperature of the catalytic bed. This is beneficial for preventing the catalyst from overheating during production and for extending its lifespan. However, too high a concentration of CO2 can lead to an increased water content in the crude methanol, reducing the compressor’s capacity and increasing the energy consumption required for gasification, compression, and distillation of the crude methanol. The optimal content of CO2 in the feed gas should be adjusted accordingly based on the catalyst used in methanol synthesis and the operating temperature of the methanol synthesis process. When a copper-based catalyst is used, the CO2 content in the feed gas can be increased appropriately, which reduces the total heat release within the tower and helps to prevent the copper-based catalyst from overheating, thereby extending its service life. In high-pressure synthesis units using zinc-chromium catalysts, when the raw gas contains 4–5% CO2, the catalyst life and production capacity remain unaffected; the synthesis equipment operates stably and can generate its own heat. However, since the water content in crude methanol is 14–16%, it is advisable to keep the CO2 concentration in the raw gas below 5% for the methanol synthesis reaction on the zinc-chromium catalyst.
The molecular formula of methanol is CH3OH, with a molecular weight of 32.04. At normal temperature and pressure, pure methanol is a colorless, transparent, fluid, volatile, and flammable liquid. It has an odor similar to that of ethanol. Its general properties are shown in the table below:
General Properties of Methanol
Property | Value
Density | 0.81 g/cm³ (0°C)
Viscosity | 5.945×10⁻⁴ Pa•s (0.5945 cP) (20°C)
Relative Density | 0.7913 (d420)
Thermal Conductivity | 2.09×10⁻³ J/(cm•s•K)
Boiling Point | 64.5–64.7°C
Surface Tension | 22.55×10⁻⁵ N/cm (22.55 dyn/cm) (20°C)
Melting Point | –97.8°C
Refractive Index | 1.3287 (20°C)
Flash Point | 16°C (open container), 12°C (closed container)
Vaporization Heat | 35.295 KJ/mol (64.7°C)
Spontaneous Combustion Temperature | 473°C (in air), 461°C (in oxygen)
Enthalpy of Fusion | 3.169 KJ/mol
Critical Temperature | 240°C
Heat of Combustion | 727.038 KJ/mol (liquid at 25°C), 742.738 KJ/mol (gas at 25°C)
Critical Pressure | 79.54×10⁵ Pa
Enthalpy of Formation | 238.798 KJ/mol (liquid at 25°C), 201.385 KJ/mol (gas at 25°C)
Critical Volume | 117.8 ml/mol
Coefficient of Expansion | 0.00119 (20°C)
Critical Compression Factor | 0.224
Corrosivity | Non-corrosive at normal temperatures, except for lead and aluminum
Vapor Pressure | 1.2879×10⁴ Pa (96.6 mmHg) (20°C)
Heat Capacity | 2.51–2.53 J/(g•°C) (liquid at 20–25°C), 45 J/(mol•°C) (gas at 25°C)
Explosibility | 6.0–36.5% (by volume) (explosion range in air)
Table showing how the density, viscosity, and surface tension of methanol change with temperature
Temperature (°C): 0, 10, 20, 30, 40, 50, 60
Density (g/cm³): 0.81, 0.8008, 0.7915, 0.7825, 0.774, 0.765, 0.7555
Viscosity (cP): 0.817, 0.69, 0.597, 0.51, 0.45, 0.396, 0.35
Surface Tension (dyn/cm): 24.5, 23.5, 22.6, 21.8, 20.9, 20.1, 19.3
Note: 1 cP = 10⁻⁴ Pa•s; 1 dyn = 10⁻⁵ N.
Methanol can mix infinitely with water and many organic liquids such as ethanol and ether, but it cannot mix with aliphatic hydrocarbons. It readily absorbs water vapor, carbon dioxide, etc. Methanol is toxic; ingesting 10 ml of it can pose a risk of blindness, while 30 ml can be fatal. The maximum allowable concentration of methanol vapor in the air is 0.05 mg/L. The density of aqueous methanol solutions increases as the temperature decreases. At the same temperature, it decreases almost proportionally with increasing methanol concentration. See the table below:
Density of aqueous methanol solutions in relation to methanol concentration and temperature
| CH3OH % | Density (g/cm³) at -30°C | Density (g/cm³) at 0°C | Density (g/cm³) at 20°C | Density (g/cm³) at 30°C | Density (g/cm³) at 40°C | Density (g/cm³) at 60°C |
|---------|--------------------------|------------------------|------------------------|------------------------|------------------------|------------------------|
| 10 | – | 0.9842 | 0.9815 | 0.9794 | 0.9750 | 0.9635 |
| 20 | – | 0.9725 | 0.9666 | 0.9625 | 0.9567 | 0.9450 |
| 30 | – | 0.9604 | 0.9515 | 0.9442 | 0.9383 | 0.9260 |
| 40 | 0.9595 | 0.9459 | 0.9345 | 0.9250 | 0.9200 | 0.9061 |
| 50 | 0.9434 | 0.9287 | 0.9156 | 0.9050 | 0.9000 | 0.8844 |
| 60 | 0.9250 | 0.9090 | 0.8946 | 0.8835 | 0.8783 | 0.8609 |
| 70 | 0.9073 | 0.8869 | 0.8715 | 0.8610 | 0.8540 | 0.8355 |
| 80 | 0.8870 | 0.8634 | 0.8469 | 0.8361 | 0.8280 | 0.8083 |
| 90 | 0.8640 | 0.8374 | 0.8202 | 0.8090 | 0.8000 | 0.7800 |
The density ρ (g/cm³) of aqueous methanol solutions can be calculated using the following formula:
ρ = 1.034 – 0.0008t – 0.0022C
where T is the temperature in °C, and C is the methanol concentration in %.
Table of hydrogen solubility in methanol (cm³/g CH₃OH):
| Pressure (kgf/cm²) | Temperature (°C) | Pressure (kgf/cm²) | Temperature (°C) |
|--------------------|------------------|--------------------|------------------|
| 25 | 1.6 | 25 | 18.0 |
| 50 | 2.7 | 50 | 20.2 |
| 75 | 3.5 | 75 | 22.4 |
| 100 | 4.0 | 100 | 24.1 |
| 125 | 4.3 | 125 | 30.2 |
| | | 150 | 37.5 |
| 50 | 5.5 | 200 | 45.0 |
| 75 | 6.4 | 250 | 54.0 |
| 100 | 7.3 | 300 | 63.0 |
| 125 | 8.3 | | |
| | | 350 | 72.0 |
Table of carbon dioxide solubility in methanol (cm³/g CH₃OH):
| Pressure (kgf/cm²) | Temperature (°C) | Pressure (kgf/cm²) | Temperature (°C) |
|--------------------|------------------|--------------------|------------------|
| 0 | 25 | 0 | 25 |
| | 49.8 | | 49.8 |
| | 75 | | 75 |
| 6.8 | 59.5 | 6.8 | 197 |
| 12.8 | 29.9 | 12.8 | 112 |
| | 19.5 | | 71.5 |
| | 10.7 | | 10.7 |
| 94.9 | 49.3 | 94.9 | 161 |
| 32.1 | 22.3 | 32.1 | 103 |
| 39.7 | – | 39.7 | 16.5 |
| | | 287 | 174 |
| | | 51.8 | 82.5 |
| | | 35.5 | 51.8 |
| | | 49.4 | 35.5 |
| | | – | 228 |
| | | | 104 |
| | | | 22.3 |
| | | | 270 |
| | | | 118 |
| | | | 71.9 |
| | | | 48.6 |
| | | | 55.2 |
Table of carbon monoxide solubility in methanol (cm³/g CH₃OH):
| Pressure (kgf/cm²) | Temperature (°C) | Pressure (kgf/cm²) | Temperature (°C) |
|--------------------|------------------|--------------------|------------------|
| 25 | 90 | 25 | 90 |
| | 140 | | 140 |
| 55 | 10.5 | 55 | 46.4 |
| | 15.9 | | 48.2 |
| | – | | 57.0 |
| 200 | 23.0 | 200 | 60.0 |
| 75 | 17.4 | 75 | 55.8 |
| | – | | 64.7 |
| 250 | 23.2 | 250 | 60.0 |
| | 28.5 | | 55.8 |
| | 32.9 | | 64.7 |
| 300 | – | 300 | 62.1 |
| | 71.2 | | 71.2 |
| 150 | 34.1 | 150 | 62.1 |
| | 38.9 | | 71.2 |
| | 47.2 | | – |
II. Reaction equations for methanol
CO + 2H₂ → CH₃OH ΔH = −90.56 kJ/mol
CO₂ + 3H₂ → CH₃OH + H₂O ΔH = −49.43 kJ/mol
Chapter 2: Production of raw gas for methanol synthesis
Section 1: Requirements for raw gas used in methanol synthesis
1. Appropriate H₂/CO ratio
Generally, the raw gas used for methanol synthesis contains H₂, CO, and CO₂. Therefore, it must satisfy the condition (H₂−CO₂)/(CO+CO₂) = 2; this is the optimal stoichiometric ratio for methanol production. The chemical equivalent ratio of hydrogen to carbon monoxide for methanol synthesis is 2, while it is 3 for synthesis with carbon dioxide. When both CO and CO2 are present, there are two ways to express the hydrogen-to-carbon ratio (f or M value) in the feed gas: f = (H2 – CO2) / (CO + CO2) = 2.10–2.15, or H2 / (CO + 1.5CO2) = 2.0–2.05. The composition of the feed gas obtained using different raw materials and processes often deviates from these f values or M values; the hydrogen-to-carbon ratio of the crude feed gas produced from coal is too low, so a shift process is required to convert the excess CO into H2, followed by the removal of the excess CO2. When natural gas (whose main component is CH4) is used as the feed gas, the crude feed gas obtained through steam reforming contains an excessive amount of hydrogen, so CO2 needs to be added before or after the reforming process to adjust this. In production, the appropriate hydrogen-to-carbon ratio should be slightly higher than the chemical equivalent ratio; based on the chemical equivalent ratio, the f-value or M-value is around 2. In practice, this ratio is kept slightly above 2, meaning that a slightly higher hydrogen content is maintained. Excess hydrogen helps to reduce the formation of iron carbonyl and higher alcohols, as well as to extend the lifespan of the catalyst. The C/H ratio in the methanol molecule is 0.5. As can be seen from the overall reaction equation 12/7m (CH0.5)m + 11/7 H2O + 3/7 O2 → CH3OH + 5/7 CO2, when the C/H ratio in the reactants is less than 0.5, there is an excess of H2, and CO2 needs to be added ； When C/H in the reactants is greater than 0.5, CO2 must be removed from the system; therefore, shift and decarburization units must be installed in methanol plants that use coal as a raw material. II. An appropriate ratio of CO to CO2: A certain amount of CO2 should be present in the raw gas used for methanol synthesis; the presence of CO2 helps to increase the reaction rate of methanol synthesis on zinc-chromium catalysts as well as copper-based catalysts. An appropriate level of CO2 enables the catalysts to maintain high activity. Additionally, in the presence of CO2, the heat effect associated with methanol synthesis is lower compared to when methanol is synthesized solely from CO and H2, which makes it easier to control the temperature of the catalytic bed. This is beneficial for preventing the catalyst from overheating during production and for extending its lifespan. However, too high a concentration of CO2 can lead to an increased water content in the crude methanol, reducing the compressor’s capacity and increasing the energy consumption required for gasification, compression, and distillation of the crude methanol. The optimal content of CO2 in the feed gas should be adjusted accordingly based on the catalyst used in methanol synthesis and the operating temperature of the methanol synthesis process. When a copper-based catalyst is used, the CO2 content in the feed gas can be increased appropriately, which reduces the total heat release within the tower and helps to prevent the copper-based catalyst from overheating, thereby extending its service life. In high-pressure synthesis units using zinc-chromium catalysts, when the raw gas contains 4–5% CO2, the catalyst life and production capacity remain unaffected; the synthesis equipment operates stably and can generate its own heat. However, since the water content in crude methanol is 14–16%, it is advisable to keep the CO2 concentration in the raw gas below 5% for the methanol synthesis reaction on the zinc-chromium catalyst.
Currently working on the design of an ejector; high-pressure fluid: cold water, liquid； Low-pressure fluids: water vapor, gases. After mixing, it becomes hot water. I seek advice and recommendations for reference books! Where did your formula come from? ? ?
Great stuff; exactly what’s needed