API 2000 Insulation Factor (Ri) Explained

Understanding Thermal In-Breathing in Fixed Roof Tanks

When sizing pressure and vacuum relief valves according to API 2000, engineers often encounter the insulation reduction factor (Ri) in the context of thermal in-breathing.
This factor is frequently misunderstood, leading to either unnecessary oversizing or unsafe underestimation of vacuum relief capacity.

This article explains what Ri really represents, how it is applied to fully insulated and partially insulated tanks, and how it affects API 2000 vent sizing in real engineering practice.

Thermal In-Breathing Is Driven by Heat Transfer, Not Airflow

Thermal in-breathing does not occur because air “flows into” the tank by itself.
It occurs because the vapor space inside the tank cools down, causing gas contraction and sometimes condensation.

From basic thermodynamics:$$\frac{\Delta V}{V} \approx \frac{\Delta T}{T}$$

This means the rate of vapor volume contraction is directly related to the rate of temperature change inside the vapor space.
The faster the vapor space cools, the higher the instantaneous in-breathing flow rate required to prevent vacuum collapse.

Therefore, thermal in-breathing is fundamentally a heat-transfer-driven phenomenon, not a flow-control issue.

What Tank Insulation Actually Does

Tank insulation does not block breathing air or restrict the vent path.
Its function is to reduce the rate of heat transfer between the tank wall and the environment.

By adding thermal resistance, insulation:

• Reduces heat flux through the tank wall
• Slows down vapor space temperature change
• Reduces the rate of vapor contraction

This does not eliminate thermal breathing, but it spreads the same thermal effect over a longer time, lowering the peak in-breathing rate expressed in Nm³/h.

The Physical Meaning of the Insulation Reduction Factor (Ri)

In API 2000, Ri is a heat-transfer reduction factor, not a valve factor.

For a fully insulated tank, API 2000 defines Ri as:$$R_{in} = \frac{1}{1 + \dfrac{h \cdot l_{in}}{\lambda_{in}}}$$

Where:

• $h$ is the internal heat-transfer coefficient
• $l_{in}$ is insulation thickness
• $\lambda_{in}$ is insulation thermal conductivity

Physically, Ri represents:

The ratio of heat transfer with insulation to heat transfer without insulation

API 2000 then makes a deliberate engineering simplification:

Thermal breathing rate is proportional to the rate of heat transfer into or out of the vapor space.

As a result, thermal in-breathing is reduced proportionally by Ri.

For a fully insulated tank, the theoretical Ri calculated using API 2000 Eq.(11) is typically around 0.2 for 50 mm mineral wool insulation.
In engineering practice, however, a higher effective Ri (often 0.4–0.5) is frequently adopted to account for partial insulation coverage, thermal bridges, and construction tolerances.

Fully Insulated vs. Partially Insulated Tanks

Fully Insulated Tanks

If all relevant tank surfaces contributing to heat transfer are insulated, the reduction factor from the equation above can be applied directly to thermal in-breathing.

This represents the maximum achievable reduction for a given insulation thickness and material.

Partially Insulated Tanks

In real installations, tanks are often only partially insulated, such as:

• Insulated shell with uninsulated roof
• Insulated lower shell with exposed upper shell

In these cases, applying the fully insulated formula directly would overestimate the insulation effect.

API 2000 therefore introduces an area-weighted correction:$$R_{inp} = \frac{A_{inp}}{A_{TTS}} \cdot R_{in} + \left(1 – \frac{A_{inp}}{A_{TTS}}\right)$$

Where:

• $A_{inp}$​ is the insulated surface area
• $A_{TTS}$​ is the total surface area contributing to heat transfer

This equation reflects the fact that uninsulated surfaces still allow full heat transfer, and the vapor space responds to the net heat input, not the best-insulated section.

Engineering Implications for Vent Sizing

Several practical conclusions follow directly from API 2000:

1. Thermal in-breathing must always be evaluated, even when insulation is present
2. Insulation provides a quantifiable, legitimate reduction, not an arbitrary discount
3. With sufficient insulation, liquid emptying often becomes the governing in-breathing case
4. Partial insulation provides less reduction than full insulation of the same thickness
5. Insulation affects thermal breathing only, not liquid movement or fire emergency venting

This explains why vacuum relief capacity is often significantly larger than pressure relief capacity in fixed roof tanks, especially in hot climates.

Common Misunderstandings to Avoid

• Ri is not a valve efficiency factor
• Ri does not block airflow
• Ri does not reduce total volume change, only the rate
• Insulation does not eliminate the need for vacuum relief devices

Understanding these points is essential for correct and defensible API 2000 vent sizing.

Summary

In API 2000, the insulation reduction factor Ri represents reduced heat transfer, not reduced airflow.

By slowing vapor space temperature change, insulation lowers the instantaneous thermal in-breathing rate, allowing engineers to size vacuum relief devices realistically while maintaining structural safety.

Correct application of Ri—especially for partially insulated tanks—ensures compliance with API 2000 and avoids both unnecessary oversizing and dangerous underdesign.