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Vacuum Pumpdown Time Calculation: A Step-by-Step Guide

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Section summary
1. Introduction
2. Main Concepts
3. Data Tables
4. Calculation Methods and Formulas
5. Complete worked example step by step
6. Applications
7. Operational Best Practices
7. Vacuum pump down time : Calculator

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1. Introduction

Why is understanding vacuum pumpdown time important?

Vacuum technology is key for many modern processes, from semiconductor fabrication to materials science. Getting a system to the required vacuum level efficiently is paramount. That's where understanding pumpdown time becomes critical. It's not just about slapping a pump on a chamber; it's about understanding the interplay of various factors that govern how quickly you can evacuate a system.

1.1. Overview of Vacuum Pumpdown Time Calculation

What factors influence vacuum pumpdown time?

Calculating pumpdown time isn't a simple plug-and-chug exercise. It's a fundamental engineering task that demands a solid grasp of the factors influencing gas removal from a closed volume. The pumpdown time isn't solely determined by the pump's stated pumping speed and the chamber volume. Instead, it's a complex interaction of several key parameters that must be carefully evaluated for an accurate estimate.

The main factors that affect pumpdown time are:

• Chamber Volume (V): Plain and simple, the bigger the volume, the more gas you've got to get rid of to hit your target pressure.
• Pumping Speed (S): This is the rate at which the pump can theoretically remove gas, usually measured in liters per second (L/s) or cubic meters per hour (m³/hr). Keep in mind this is the rated speed, is usually given at a particular pressure range, and pumps often have a speed vs pressure curve.
• Effective Pumping Speed (S_eff): This is the real pumping speed at the chamber, after you've accounted for the restrictions caused by piping, valves, and other components. It's almost always lower than the rated speed. S_eff ≤ S and conductance of the connecting hardware reduces it.
• Gas Load (Q): The total amount of gas entering the system from all sources. This includes leaks, outgassing from the materials inside the chamber, and any process gases you might be introducing.
• Ultimate Pressure (P_ultimate): The lowest pressure the pump can achieve in a perfectly sealed system with no gas load. It's a theoretical limit, but a useful benchmark.

The calculation process generally involves these steps:

1. Determine the Effective Pumping Speed (S_eff): This means calculating the conductance of all the components in your vacuum system and combining them to get an overall conductance. Then, you use that to figure out the effective pumping speed.
2. Calculate the Total Gas Load (Q_total): This involves estimating the contributions from leaks (Q_leak) and outgassing (Q_outgassing).
3. Calculate the Ultimate Pressure (P_ultimate): You can estimate the ultimate pressure using the equation: P_ultimate = Q_total / S_eff . This tells you what the limitations of your system are.
4. Apply the Fundamental Equation: The pumpdown time (t) is estimated using the complete pumpdown equation, which accounts for the system's gas load and ultimate pressure. A simplified version of the equation can be used when the target pressure is significantly higher than the ultimate pressure.

This article will break down each of these steps, giving you the formulas and practical considerations you need to accurately calculate pumpdown time. We'll cover the definitions of pumpdown time, vacuum pressure units, pumping speed, gas load, and ultimate pressure. We'll also provide data tables with typical outgassing rates for common materials and conductance values for piping components. Finally, we'll work through some examples to show you how to apply these concepts in real-world situations.

1.2. Importance of Accurate Pumpdown Time Estimation

Why is it important to accurately estimate pumpdown time?

Getting a good estimate of pumpdown time is crucial for a few key reasons.

First, it lets you schedule processes and allocate resources efficiently. If you know how long it'll take to reach the required vacuum level, you can plan the next steps, minimize downtime, and maximize throughput. This is especially important in high-volume manufacturing, where even small delays can have a big impact on production.

Second, it helps you maintain product quality. Many vacuum processes are sensitive to pressure, and if you're not at the right vacuum level, you can end up with defects or inconsistent results. For example, in thin film deposition, the pressure during deposition can affect the film's composition, uniformity, and adhesion. Accurate pumpdown time estimation lets you catch and correct any problems early on, preventing you from producing substandard materials.

Third, it protects your equipment. Running pumps outside their optimal pressure range can cause overheating, cavitation, or other damage. For example, running a diffusion pump at too high a pressure can cause oil backstreaming and contaminate the chamber. Similarly, running a turbomolecular pump at too high a pressure can cause it to overheat and damage the rotor. By estimating pumpdown time accurately, you can avoid these situations and extend the life of your equipment, saving on maintenance costs and downtime.

Fourth, understanding what affects pumpdown time can help you spot and fix potential problems in the vacuum system, like leaks or excessive outgassing. If the pumpdown time is longer than expected, it could be a sign of a developing leak or a change in the outgassing behavior of the materials inside the chamber. Being proactive can prevent costly repairs and downtime and keep your system running at peak performance.

Finally, accurate pumpdown time estimation is essential for optimizing energy consumption. By minimizing the time it takes to reach the desired vacuum level, you can reduce the overall energy usage of the vacuum system, saving money and reducing your environmental impact.

The following sections will go into the main concepts and calculation methods you need to accurately estimate pumpdown time. We'll cover definitions of key terms, relevant formulas, and practical examples. Understanding these principles will help you manage your vacuum systems effectively and achieve optimal performance.

2. Main Concepts

What are the key concepts for calculating vacuum pumpdown time?

This section defines the core concepts you need to understand and calculate vacuum pumpdown time. These concepts build on the overview in the introduction and will be used extensively in the following sections, which detail calculation methods and examples.

2.1. Definition of Pumpdown Time

What is pumpdown time in vacuum systems?

Pumpdown time is the time it takes to evacuate a closed volume, usually a vacuum chamber, from an initial pressure (typically atmospheric pressure) to a specified lower pressure. This target pressure is determined by the requirements of the process or experiment you're running inside the vacuum environment. Pumpdown time is a critical parameter in vacuum system design and operation, directly affecting process efficiency and overall system performance. It's usually measured in units of time, like seconds, minutes, or hours.

More formally, pumpdown time can be expressed as a function of several variables:

• V: The volume of the chamber being evacuated.
• P_initial: The initial pressure inside the chamber.
• P_final: The desired final pressure inside the chamber.
• S_eff: The effective pumping speed of the vacuum system at the chamber.
• Q_total: The total gas load inside the chamber, including leaks and outgassing.

The ideal pumpdown time, assuming no gas load and a constant pumping speed, can be estimated using a simplified equation. However, in real-world scenarios, the presence of gas loads and variations in pumping speed necessitate more complex calculations, which we'll discuss in detail later.

Understanding the definition of pumpdown time is the first step in accurately estimating it. The following sections will cover the various units used to measure vacuum pressure, the concept of pumping speed, the sources and types of gas loads, and the significance of ultimate pressure, all of which are crucial for a comprehensive understanding of pumpdown time calculations.

2.2. Vacuum Pressure Units and Conversions (Torr, Pa, mbar)

How do you convert between different vacuum pressure units?

Vacuum pressure is measured in a variety of units, each with its own scale and historical context. Knowing these units and how to convert between them is essential for accurate calculations and communication in the field of vacuum technology. The most common units include:

• Torr: A traditional unit of pressure, approximately equal to the pressure exerted by a millimeter of mercury (mmHg). 1 Torr is defined as 1/760 of standard atmospheric pressure. While you might still see it, using Torr is discouraged in favor of SI units.
• Pascal (Pa): The SI unit of pressure, defined as one Newton per square meter (N/m²). This is the preferred unit for scientific and engineering calculations.
• Millibar (mbar): A metric unit of pressure, equal to 100 Pascals. It's commonly used in vacuum applications because its scale is convenient for typical vacuum pressures and it's widely used in Europe.

Here are some useful conversion factors:

• 1 atm = 760 Torr = 101325 Pa = 1013.25 mbar
• 1 Torr ≈ 133.322 Pa ≈ 1.333 mbar
• 1 Pa = 0.0075 Torr ≈ 0.01 mbar
• 1 mbar ≈ 0.75 Torr ≈ 100 Pa

Pay close attention to units when you're doing pumpdown time calculations. Inconsistent units will lead to significant errors. The unit you choose often depends on the data you have or the specific application. For example, outgassing rates are often given in Torr·L/s, while pump speeds are typically given in L/s or m³/hr. So, you'll often need to convert all values to a consistent set of units before you start calculating. The examples in Section 5 will show you why unit consistency is so important. The next section will define pumping speed and its units.

2.3. Pumping Speed: Definition and Units (L/s, m3/hr)

What is pumping speed and how is it measured?

Pumping speed (S) tells you how much gas a vacuum pump can remove from a system per unit of time. It's the theoretical maximum rate at which a pump can evacuate a chamber, assuming there are no restrictions in the connecting pipelines. Pumping speed is a crucial parameter in determining pumpdown time. Common units for pumping speed include:

• Liters per second (L/s): A commonly used unit, representing the volume of gas removed in liters per second.
• Cubic meters per hour (m³/hr): Another common unit, representing the volume of gas removed in cubic meters per hour.

Conversion: 1 m³/hr ≈ 0.2778 L/s

Remember that the effective pumping speed at the vacuum chamber can be much lower than the pump's rated pumping speed due to conductance limitations, as we'll discuss later.

2.4. Gas Load: Sources and Types

What are the sources and types of gas load in a vacuum system?

Gas load (Q) is the total amount of gas entering the vacuum system per unit of time. It's a critical parameter that affects both the pumpdown time and the ultimate pressure you can achieve in the system. The vacuum pump has to continuously remove this gas load to maintain the desired vacuum level. Gas load is usually expressed in units of pressure multiplied by volume per unit time, such as mbar·L/s, Torr·L/s, or Pa·m³/s. Understanding the sources and types of gas load is essential for accurate pumpdown time calculations and effective vacuum system management.

The main sources of gas load can be categorized as follows:

• Leaks (Q_leak): These are unwanted influxes of atmospheric gases into the vacuum system through imperfections in seals, joints, or the permeation of gases through the materials that make up the vacuum chamber and its components. Leaks can be either real or virtual.
  • Real leaks are physical breaches in the vacuum envelope, like cracks, pinholes, or poorly sealed connections. They provide a relatively direct path for gas to enter the system.
  • Virtual leaks are trapped volumes of gas within the system that slowly release over time. These can be caused by threaded connections with blind holes, improperly sealed components, or even absorbed gases within certain materials.
• Outgassing (Q_outgassing): This is the release of adsorbed or absorbed gases from the surfaces and bulk of materials inside the vacuum chamber. Outgassing is a major contributor to the gas load, especially at lower pressures, as the rate of gas release from materials becomes a dominant factor. The rate of outgassing depends on several factors, including:
  • Material type: Different materials have different outgassing rates. Polymers and elastomers generally have higher outgassing rates than metals like stainless steel or aluminum.
  • Surface area: The larger the surface area exposed to the vacuum, the greater the outgassing load.
  • Temperature: Outgassing rates increase with temperature. Heating the chamber (bakeout) can accelerate outgassing, allowing for a faster pumpdown to the desired ultimate pressure.
  • Surface treatment: Surface treatments like electropolishing or cleaning can reduce outgassing rates.
  • Prior exposure: Materials that have been exposed to the atmosphere for extended periods will have a higher initial outgassing load due to adsorbed water vapor and other gases.
• Permeation: Some gases can diffuse through solid materials, especially elastomers and polymers. The rate of permeation depends on the material, the gas, the temperature, and the partial pressure difference across the material.
• Process Gases: These are gases intentionally introduced into the chamber for specific processes, such as sputtering, chemical vapor deposition (CVD), or etching. The flow rate of process gases must be carefully controlled and accounted for in the overall gas load calculation.
• Vaporization: Liquids present in the vacuum chamber can vaporize, contributing to the gas load. This can include residual cleaning solvents, pump oil, or process liquids.

The composition of the gas load can vary depending on the specific application and the materials used in the vacuum system. Common components include:

• Water Vapor (H₂O): A major component of outgassing, especially from materials exposed to atmospheric humidity.
• Nitrogen (N₂): The primary constituent of air and a common component of leaks.
• Oxygen (O₂): Another major component of air and a common component of leaks.
• Argon (Ar): An inert gas present in air and used in some sputtering processes.
• Hydrogen (H₂): A common outgassing product from metals and a byproduct of some chemical reactions.
• Carbon Dioxide (CO₂): A common outgassing product from organic materials and a byproduct of some chemical reactions.
• Hydrocarbons: Released from pump oil, lubricants, and organic materials.

Accurately estimating the gas load is crucial for selecting the appropriate vacuum pump and predicting the pumpdown time. In the following sections, we'll discuss methods for quantifying the contributions of leaks and outgassing to the total gas load.

2.5. Ultimate Pressure: Definition and Significance

What is ultimate pressure and why is it important?

Ultimate pressure (P_ultimate) is the lowest pressure a vacuum pump can achieve in a closed, leak-tight system with a minimal gas load. It's the equilibrium point where the rate of gas removal by the pump equals the rate of gas influx from all remaining sources (primarily outgassing and minor permeation). The ultimate pressure is a key indicator of the vacuum system's overall performance and cleanliness. It's usually measured in units of pressure, like mbar, Torr, or Pa.

The ultimate pressure is related to the total gas load (Q_total) and the effective pumping speed (S_eff) by the following equation (at steady state) :

P_ultimate = Q_total / S_eff

A lower ultimate pressure means a cleaner system with a lower gas load or a more effective pumping system (higher S_eff). Achieving a low ultimate pressure is crucial for applications that require high vacuum, such as surface analysis, electron microscopy, and certain thin film deposition processes.

Several factors influence the ultimate pressure:

• Pump Performance: The type and condition of the vacuum pump significantly affect the achievable ultimate pressure. Different pump technologies have inherent limitations. For example, a rotary vane pump will typically have a higher ultimate pressure than a turbomolecular pump.
• Gas Load: As the equation above shows, the total gas load directly impacts the ultimate pressure. Reducing leaks and minimizing outgassing are essential for achieving a low ultimate pressure.
• System Cleanliness: Contaminants inside the vacuum system, like residual solvents or pump oil, can contribute to outgassing and increase the gas load, raising the ultimate pressure.
• Temperature: The temperature of the vacuum chamber and its components affects the outgassing rate of materials. Higher temperatures generally lead to higher outgassing rates and a higher ultimate pressure.
• Conductance: While not directly in the equation, conductance plays a role. A low conductance in the pumping line will reduce the effective pumping speed (S_eff), which in turn increases the ultimate pressure.

Keep in mind that the ultimate pressure is a theoretical limit and may not be achievable in practice due to factors like limitations in measurement accuracy or the presence of persistent leaks. Also, the ultimate pressure isn't a fixed value for a given system; it can change depending on the operating conditions and the history of the system.

Understanding the ultimate pressure is crucial for several reasons:

• System Design: It helps you choose the right vacuum pump and system components to meet the specific vacuum requirements of your application.
• Performance Monitoring: It serves as a benchmark for evaluating the performance of the vacuum system over time. A significant increase in the ultimate pressure can indicate a developing problem, like a leak or increased outgassing.
• Troubleshooting: It helps you identify the source of vacuum problems. For example, if the ultimate pressure is higher than expected, you may need to investigate potential leaks, outgassing sources, or pump malfunctions.

The next section will delve into the data tables, providing typical outgassing rates for common materials and conductance values for piping components, which are essential for calculating the gas load and effective pumping speed, and ultimately, the pumpdown time.

3. Data Tables

What data is needed to calculate pumpdown time?

3.1. Typical Outgassing Rates for Common Materials

What are the typical outgassing rates for common vacuum materials?

Outgassing is a major contributor to the gas load in a vacuum system. The rate at which materials release adsorbed or absorbed gases depends on several things, including the material's composition, surface area, temperature, surface finish, and how long it's been exposed to the atmosphere. Choosing materials with low outgassing rates is crucial for achieving and maintaining high vacuum levels and minimizing pumpdown times.

The following table shows typical outgassing rates for a few materials commonly used in vacuum systems. This table is just an example; a more complete guide would include common elastomers (Viton, Buna-N) and plastics (Teflon, PEEK). These values are just guidelines and can vary a lot depending on the specific conditions and how the material has been pre-treated. It's important to consult more detailed data sheets and take specific measurements when you need precise outgassing information for critical applications.

The outgassing rates are usually expressed in units of pressure multiplied by volume per unit time, normalized by the surface area of the material. Common units include Torr·L/s/cm² and mbar·L/s/cm². The values in the table are generally measured after a certain period of pumping (e.g., 24 hours) at room temperature (around 25°C) to allow for the initial rapid desorption of surface contaminants.

Material	Outgassing Rate (Torr·L/s/cm²)	Outgassing Rate (mbar·L/s/cm²)	Notes
Stainless Steel (304)(bake)	1 x 10^-12	1.33 x 10^-12	After bakeout at 200°C. Can be reduced further with electropolishing.
Aluminum	5 x 10^-11	6.67 x 10^-11	Typical value for untreated aluminum. Rate is highly variable due to porous oxide layer.

3.2. Conductance Values for Common Piping Components

What are the conductance values for common vacuum piping components?

The effective pumping speed at the vacuum chamber is often lower than the pump's rated speed because of the flow restrictions caused by piping, valves, fittings, and other components. These restrictions are quantified by a property called conductance (C), which represents how easily gas flows through a particular component. Conductance depends on the geometry of the component, the type of gas, temperature, and the pressure regime (viscous, transitional, or molecular flow).

Important Note: Giving single conductance values is a big simplification. The values below are for air at 20°C in the molecular flow regime and should only be used as examples. In a real system, you need to first determine the flow regime (using the Knudsen number) before choosing the right calculation method, as detailed in Section 4.2.1. Using these values at higher pressures (viscous or transitional flow) will lead to significant errors. Always check the manufacturer's specifications for more accurate data.

Component	Conductance (L/s)	Notes
Straight Pipe (1m long, 10cm diameter)	120	For air at 20°C in molecular flow.
90-degree Elbow (10cm diameter)	150	For air at 20°C in molecular flow.
Gate Valve (10cm diameter)	200	For air at 20°C in molecular flow.
Baffle (10cm diameter)	50	For air at 20°C in molecular flow.

4. Calculation Methods and Formulas

What are the formulas for calculating vacuum pumpdown time?

This section presents the fundamental equations and methods used to calculate vacuum pumpdown time. It builds on the concepts defined in Section 2 and uses the data provided in Section 3. The examples in Section 5 will further illustrate how to apply these principles.

4.1. The Fundamental Pumpdown Equations

What are the fundamental equations for calculating pumpdown time?

The basis for estimating pumpdown time is the relationship between the volume being evacuated, the effective pumping speed, the gas load, and the initial and final pressures.

The complete and correct equation for pumpdown time, which accounts for the gas load ( Q_total ) via the ultimate pressure ( P_ultimate ), is:

t = (V / S_eff) * ln( (P_initial - P_ultimate) / (P_final - P_ultimate) )

Where:

• t = Pumpdown time (typically in seconds, minutes, or hours)
• V = Volume of the chamber being evacuated (typically in Liters or m³)
• S_eff = Effective pumping speed at the chamber (typically in L/s or m³/hr)
• P_initial = Initial pressure in the chamber (typically in Torr, Pa, or mbar)
• P_final = Target pressure in the chamber (typically in Torr, Pa, or mbar)
• P_ultimate = The ultimate pressure of the system, calculated as Q_total / S_eff
• ln = Natural logarithm (logarithm to the base e )

This equation correctly shows that as the final pressure ( P_final ) approaches the system's ultimate pressure ( P_ultimate ), the time required ( t ) approaches infinity. This is the equation that should be used for accurate engineering calculations.

Simplified Equation (Approximation for Low Gas Load):

If the gas load is negligible and the target pressure ( P_final ) is much higher (e.g., >100 times) than the ultimate pressure ( P_ultimate ), you can use this simplified equation as an approximation:

t ≈ (V / S_eff) * ln(P_initial / P_final)

Important Considerations and Limitations:

• Using the Wrong Equation: Using the simplified equation when P_final is close to P_ultimate is a critical error that will lead to a significant underestimation of the pumpdown time.
• Constant Effective Pumping Speed: Both equations assume that S_eff remains constant. In reality, S_eff can vary, especially when transitioning between flow regimes.
• Ideal Gas Behavior: The equations are based on the ideal gas law, which is a reasonable approximation for most vacuum applications.

The following sections will detail the methods for calculating the effective pumping speed ( S_eff ) and the gas load ( Q_total ), which are necessary inputs for these equations.

4.2. Effective Pumping Speed (S_eff)

How do you calculate effective pumping speed?

The effective pumping speed (S_eff) is the actual pumping speed at the vacuum chamber, taking into account the restrictions caused by the conductance of connecting pipes, valves, and other components. It's always less than or equal to the pump's rated pumping speed (S). Understanding and calculating S_eff is crucial for accurately predicting pumpdown time.

4.2.1. Calculating Conductance of Piping

How do you calculate the conductance of vacuum piping?

The conductance (C) of a pipe or component is a measure of its ability to allow gas to flow through it. It's like electrical conductance, where a higher conductance means a lower resistance to flow. Conductance is a crucial parameter in vacuum system design, as it directly affects the effective pumping speed at the chamber. The calculation of conductance depends on several factors, including the geometry of the component, the type of gas, the temperature, and the pressure regime.

The pressure regime dictates the dominant mode of gas transport, and therefore the appropriate equations to use. The three primary flow regimes are viscous flow, transitional flow, and molecular flow.

• Viscous Flow: At relatively high pressures, gas molecules collide frequently with each other, resulting in a collective, fluid-like behavior. This regime is characterized by a relatively high density and low mean free path.
• Molecular Flow: At very low pressures, gas molecules collide predominantly with the walls of the vacuum system, rather than with each other. This regime is characterized by a low density and high mean free path.
• Transitional Flow: This regime exists between viscous and molecular flow, where both molecule-molecule and molecule-wall collisions are significant. It's the most complex regime to model accurately.

The Knudsen number (Kn), defined as the ratio of the mean free path (λ) to a characteristic dimension (e.g., pipe diameter D), is a dimensionless parameter used to determine the flow regime:

• Kn < 0.01: Viscous flow
• 0.01 < Kn < 1: Transitional flow
• Kn > 1: Molecular flow

The following equations provide approximations for conductance in different flow regimes for a long, straight, cylindrical pipe:

Molecular Flow:

For a long, straight, cylindrical pipe in molecular flow, the conductance (C) can be approximated by:

C ≈ 12.1 * (D^3 / L) (L/s)

Where:

• D = Pipe diameter (cm)
• L = Pipe length (cm)

This equation is a widely accepted simplification for air at 20°C and is valid when L >> D. For other gases, a correction factor based on the molecular weight ratio may be applied.

Viscous Flow:

For a long, straight, cylindrical pipe in viscous flow, the conductance (C) can be approximated by:

C = 135 * (D^4 / L) * P_avg (L/s)

Where:

• D = Pipe diameter (cm)
• L = Pipe length (cm)
• P_avg = Average pressure in the pipe (Torr)

This equation is valid when L >> D. Note the pressure dependence of conductance in this regime. The constant 180 is dependent on the gas viscosity and temperature and is typically valid only for air.

Transitional Flow:

The transitional flow regime is more complex, and no simple analytical formula exists for calculating conductance. In this regime, both molecular and viscous effects are significant. Numerical methods or empirical data are often used to estimate conductance in transitional flow. One common approach is to use more complex equations that interpolate between the viscous and molecular flow conductance values.

For more complex geometries, such as elbows, valves, or constrictions, the conductance is often determined experimentally or obtained from manufacturers' data. These values are typically provided for a specific gas and temperature.

It's crucial to select the appropriate equation based on the flow regime to get a reasonably accurate estimate of the conductance. Inaccurate conductance values will lead to errors in the calculation of effective pumping speed and, consequently, pumpdown time.

The next section will discuss how to combine conductances of multiple components in series and parallel to determine the overall system conductance.

4.2.2. Combining Conductances in Series and Parallel

How do you combine conductances in series and parallel?

When you have multiple components in the vacuum system, you need to combine their individual conductances to determine the overall system conductance.

• Series: For components connected in series (one after the other), the overall conductance (C_total) is calculated as:

1 / C_total = (1 / C_1) + (1 / C_2) + (1 / C_3) + ...

• Parallel: For components connected in parallel (multiple paths for gas flow), the overall conductance (C_total) is calculated as:

C_total = C_1 + C_2 + C_3 + ...

4.2.3. Calculating Effective Pumping Speed from Pump Speed and Conductance

How do you calculate effective pumping speed from pump speed and conductance?

Once you know the overall conductance (C) of the piping system, you can calculate the effective pumping speed (S_eff) at the chamber using this formula:

1 / S_eff = (1 / S) + (1 / C)

Or, equivalently:

S_eff = (S * C) / (S + C)

Where:

• S = Pump's rated pumping speed (L/s or m³/hr)
• C = Overall conductance of the piping system (L/s or m³/hr)

This equation highlights the importance of minimizing conductance limitations to maximize the effective pumping speed at the chamber.

4.3. Gas Load Calculation: Q_total = Q_leak + Q_outgassing

How do you calculate the total gas load?

The gas load (Q) is the total amount of gas entering the vacuum system from all sources. It's a critical factor in determining both pumpdown time and ultimate pressure. The total gas load (Q_total) is usually the sum of the contributions from leaks (Q_leak) and outgassing (Q_outgassing):

Q_total = Q_leak + Q_outgassing

4.3.1. Q_leak: Estimating Leakage Rate

How do you estimate the leakage rate?

Estimating the leakage rate (Q_leak) can be tricky. It depends on the size and number of leaks, as well as the pressure difference across the leaks. In practice, you often determine leakage rate experimentally using a leak detector. However, for initial estimations, you can use these guidelines:

• Well-sealed system: Q_leak ≈ 10^-9 to 10^-6 Torr·L/s
• System with minor leaks: Q_leak ≈ 10^-6 to 10^-3 Torr·L/s
• System with significant leaks: Q_leak > 10^-3 Torr·L/s

These are rough estimates, and the actual leakage rate can vary a lot depending on the specific system.

4.3.2. Q_outgassing: Calculating Outgassing Load Based on Surface Area and Material

How do you calculate the outgassing load?

Outgassing is the release of adsorbed or absorbed gases from the surfaces of materials inside the vacuum chamber. You can estimate the outgassing load (Q_outgassing) using this formula:

Q_outgassing = A * q

Where:

• A = Surface area of materials inside the chamber (cm²)
• q = Specific outgassing rate of the material (Torr·L/s/cm²) - see Section 3.1 for typical values.

This equation highlights the importance of choosing materials with low outgassing rates and minimizing the surface area exposed to the vacuum.

4.4. Ultimate Pressure Calculation: P_ultimate = Q_total / S_eff

How do you calculate ultimate pressure?

The ultimate pressure (P_ultimate) is the lowest pressure a vacuum pump can achieve in a closed system. It's determined by the balance between the total gas load (Q_total) and the effective pumping speed (S_eff):

P_ultimate = Q_total / S_eff

This equation emphasizes the importance of minimizing the gas load and maximizing the effective pumping speed to achieve a low ultimate pressure.

5. Complete worked example step by step

Problem (restated + assumptions)

Calculate pumpdown time for a stainless-steel chamber:

• Chamber volume: V = 100 L

• Start pressure: P₀ = 760 Torr (atmospheric)

• Target pressure: P_f = 1×10⁻³ Torr

1. The chamber is connected by a straight pipe of D = 10 cm (100 mm) inner diameter and L = 1.00 m (100 cm) length to the pump inlet. (D and L in cm used in conductance formulas.)

2. The pump has a rated pumping speed S = 200 L/s (assumed constant for the illustrative calculation).

3. Chamber internal surface area ≈ that of a short cylinder containing 100 L: I choose radius r = 0.25 m which gives a realistic geometry for the volume; this yields surface area A ≈ 1.192 m² = 11 920 cm² (calculation shown below).

4. Outgassing specific rate: we take two illustrative values to show sensitivity

   • Case A (optimistic/clean/baked): q = 1×10⁻¹² Torr·L/s·cm²

   • Case B (less ideal, unbaked): q = 1×10⁻¹¹ Torr·L/s·cm²

5. Leak rate (assumed small): Q_leak = 1×10⁻7 Torr·L/s (rule-of-thumb small leak).

6. We assume single-stage pumping with a pump that (for simplicity of the analytic example) has constant S across the pressure range. Caveat: this is not fully realistic (see discussion at the end).

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Step 1 — Compute pipe conductance (molecular flow approximation)

For long cylindrical pipe in molecular flow, the standard formula (air at ~20 °C) is:

$$C_m \approx 12.1\;\frac{D^3}{L}\quad(\text{L/s})$$Cm​≈12.1LD3​(L/s)

with D and L in cm.

Using D = 10 cm, L = 100 cm:

• $D^3 = 10^3 = 1000$D3=103=1000

• $C = 12.1 \times (1000/100) = 12.1\times 10 = \mathbf{121\;L/s}$C=12.1×(1000/100)=12.1×10=121L/s.

(If the flow regime is not molecular, a different expression with the viscous coefficient 135 is used; see discussion below.)

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Step 2 — Compute effective pumping speed at the chamber

Combine pump speed S and pipe conductance C:

$$\frac{1}{S_{\text{eff}}} = \frac{1}{S} + \frac{1}{C} \quad\Rightarrow\quad S_{\text{eff}} = \frac{S\,C}{S + C}$$Seff​1​=S1​+C1​⇒Seff​=S+CSC​

With S = 200 L/s and C = 121 L/s:

$$S_{\text{eff}} = \frac{200\times121}{200+121} = \frac{24200}{321} \approx \mathbf{75.39\;L/s}.$$Seff​=200+121200×121​=32124200​≈75.39L/s.

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Step 3 — Compute total gas load Q_total = Q_leak + Q_outgassing

Compute chamber surface area (approximation used):

• We used a cylinder with r = 0.25 m, h chosen so π r² h = 0.1 m³ (100 L). That gives h ≈ 0.51 m.

• Surface area $A = 2\pi r (r + h)$A=2πr(r+h) ≈ 1.192 m² = 11 920 cm².

Outgassing contribution Q_out = A × q. Using the two q cases:

• Case A (q = 1×10⁻¹² Torr·L/s·cm²):
  $Q_{\text{out}} = 11\,920 \times 1\times10^{-12} = 1.192\times10^{-8}\; \text{Torr·L/s}$Qout​=11920×1×10−12=1.192×10−8Torr\cdotpL/s.

• Case B (q = 1×10⁻¹¹ Torr·L/s·cm²):
  $Q_{\text{out}} = 11\,920 \times 1\times10^{-11} = 1.192\times10^{-7}\; \text{Torr·L/s}$Qout​=11920×1×10−11=1.192×10−7Torr\cdotpL/s.

Add the leak Q_leak = 1×10⁻7 Torr·L/s:

• Case A total $Q_{\text{total}} = 1.192\times10^{-8} + 1\times10^{-7} \approx \mathbf{1.1192\times10^{-7}\;Torr\cdot L/s.}$Qtotal​=1.192×10−8+1×10−7≈1.1192×10−7Torr⋅L/s.

• Case B total $Q_{\text{total}} = 1.192\times10^{-7} + 1\times10^{-7} = \mathbf{2.192\times10^{-7}\;Torr\cdot L/s.}$Qtotal​=1.192×10−7+1×10−7=2.192×10−7Torr⋅L/s.

(Notes on q: wide ranges exist depending on bakeout and material history. Use measurement if you need high accuracy.)

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Step 4 — Compute ultimate pressure P_ult = Q_total / S_eff (steady state)

Use consistent units: Q in Torr·L/s and S_eff in L/s → Pressure in Torr.

• Case A: $P_{\text{ult}} = 1.1192\times10^{-7} / 75.39 \approx \mathbf{1.48\times10^{-9}\;Torr}.$Pult​=1.1192×10−7/75.39≈1.48×10−9Torr.

• Case B: $P_{\text{ult}} = 2.192\times10^{-7} / 75.39 \approx \mathbf{2.91\times10^{-9}\;Torr}.$Pult​=2.192×10−7/75.39≈2.91×10−9Torr.

Both are much smaller than the target $P_f = 1\times10^{-3}$Pf​=1×10−3 Torr. That means the steady-state (ultimate) pressure will not limit reaching 1×10⁻³ Torr; the simplified transient formula (neglecting P_ult) is acceptable for a first estimate.

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Step 5 — Compute pumpdown time (simplified formula)

When $P_{\text{ult}} \ll P_f$Pult​≪Pf​ the standard simplified pumpdown equation is:

$$t \approx \frac{V}{S_{\text{eff}}}\,\ln\!\left(\frac{P_0}{P_f}\right)$$t≈Seff​V​ln(Pf​P0​​)

Units: V in L, $S_{\text{eff}}$Seff​ in L/s ⇒ t in seconds.

Calculate ln factor: $\ln(760 / 1\times10^{-3}) = \ln(7.6\times10^5) \approx 13.541$ln(760/1×10−3)=ln(7.6×105)≈13.541.

Then:

$$\frac{V}{S_{\text{eff}}} = \frac{100}{75.39} \approx 1.3264\ \text{seconds}$$Seff​V​=75.39100​≈1.3264 seconds $$t \approx 1.3264 \times 13.541 \approx \mathbf{17.96\ \text{seconds}.}$$t≈1.3264×13.541≈17.96 seconds.

Result (simplified, under assumptions above):

about 18 seconds to pump 100 L from 760 Torr to 1×10⁻³ Torr

Remarks

• Two-stage pumping in practice. Most high-vacuum systems are pumped in stages: a roughing/backing pump (rotary vane, dry scroll, roots, etc.) evacuates the chamber from atmosphere down into the rough/vacuum region (mbar → 10⁻³ mbar), then a turbomolecular or diffusion pump takes over for high vacuum. The pumping speed and behavior differ greatly between roughing and high-vacuum pumps. Our single-S assumption across the whole range is only an illustrative simplification.

• Flow regime and conductance change with pressure. The conductance expressions differ in viscous vs molecular regimes. At high pressure (viscous), conductance is higher (and depends on pressure) and is given by formulas involving the coefficient 135 (not 180) for air at 20 °C. A correct pumpdown calculation that crosses regimes should either (a) use the full Knudsen interpolation formula (Leybold) or (b) split the pumpdown into intervals and use the appropriate conductance expression in each interval. Using the molecular C for the entire pumpdown (as we did) tends to underestimate the conductance at high pressures and thus underestimate the early-time pumping speed — paradoxically this gives a shorter time in the simplified math, but the biggest practical error comes from pump type limitations at high pressure.

• Pump operability at high inlet pressure. Many high-vacuum pumps (e.g., turbo) cannot be run at atmospheric inlet pressure — they need a roughing pump to bring the pressure down to their operating range. A practical pumpdown time is usually dominated by the roughing stage if the roughing pump speed is much lower than the high-vacuum pump speed. In other words, the ~18 s result above is optimistic because it assumes a single 200 L/s pump active from 760 Torr downwards. In reality, a roughing pump with significantly lower speed and different conductance will govern the time from 760 Torr to, say, 10⁻²–10⁻³ Torr.)

• Outgassing and time dependence. Outgassing rates q are time-dependent (high initial desorption then decay) and temperature dependent (bakeout reduces q dramatically). If you have a lot of adsorbed water or organics, reaching 1×10⁻³ Torr may take longer than the simple model predicts. Measure q (rate-of-rise or throughput) for best results.

6. Applications

Pumpdown time calculations are widely used across industries where vacuum systems are critical to product quality, process efficiency, or research accuracy. In semiconductor manufacturing, they help engineers optimize wafer-processing cycles by minimizing idle time between batches. In materials science laboratories, accurate pumpdown estimations enable researchers to plan experiments with high-vacuum chambers for surface analysis or thin-film deposition. In industrial coating applications—such as PVD (Physical Vapor Deposition) or sputtering—predicting pumpdown time ensures consistent throughput and energy efficiency. Even in large-scale systems like particle accelerators or space simulation chambers, these calculations play a vital role in balancing pump capacity, chamber design, and operational costs. Ultimately, understanding and predicting pumpdown time allows engineers to design more efficient systems, reduce downtime, and achieve the required vacuum levels reliably.

7. Vacuum pump down time : Calculator

Warning : this calculator is provided to illustrate the concepts mentioned in this webpage, it is not intended for detail design. It is not a commercial product, no guarantee is given on the results. Please consult a reputable designer for all detail design you may need. 

Source

    https://www.engineeringtoolbox.com/vacuum-evacuation-time-d_844.html
    https://www.leybold.com/en-us/knowledge/vacuum-fundamentals/vacuum-generation/calculating-pump-down-time
    https://www3.nd.edu/~wzech/Resources_LEYBOLD_FUNDAMENTALS.pdf
    https://www.leybold.com/en-us/knowledge/vacuum-fundamentals/fundamental-physics-of-vacuum/how-to-calculate-vacuum-conductance
    https://www.normandale.edu/academics/degrees-certificates/vacuum-and-thin-film-technology/articles/how-to-match-pumping-speed-to-gas-load.html
    https://fit-vac.com/resources/calculator/pump-down-time