The prediction of leakage is one of the most challenging tasks when designing bolted flanged connections and industrial valves. Failure of these pressure vessel components can cause shutdowns but also accidents, loss of revenue, and environmental damages. With the strict regulations on fugitive emissions and environmental protection laws new tightness-based standards and design methods are being adopted to improve the sealing performance of bolted joints and valves. In addition, there is a practical interest in using a reliable correlation that could predict leak rates of one fluid on the basis of tests carried out with another on compressed packings. The paper presents an innovative approach to accurately predict and correlate leak rates in porous braided packing rings. The approach is based on Darcy–Klinkenberg to which a modified effective diffusion term is added to the equation. Experimentally measured gas flow rates were performed on a set of graphite-based compression packing rings with a large range of leak rates under isothermal steady conditions. Leakage from three different gases namely helium, nitrogen, and argon were used to validate the developed correlation. In the presence of the statistical properties of porous packings, the leak rates for different gases can be predicted with reasonable accuracy.