The flow characteristics, across a detonation flame arrestor in gas transport pipelines was studied in detail numerically. The pressure drop in the flame arrestor is predominantly associated with the crimp design of the flame arrestor element. The flow in the flame arrestor element is three dimensional, making it very challenging and computationally expensive for numerical modeling. To overcome the complexity of directly modeling the three-dimensional flow, a porous media model is developed using the Forchheimer equation. The coefficients of the Forchheimer equation were obtained from experiments and numerical simulation. The experimental method used test data on a small-scale crimped flame arrestor element. In the numerical method, a single triangular crimp-channel flow numerical simulation result was used to calculate the Forchheimer coefficients. Numerical solutions of flow across a small-scale flame element using the experimentally and numerically developed Forchheimer equations were verified experimentally. The result in both cases were validated to within five percent of experimental data. The flow characteristic result calculated using the numerically developed Forchheimer equation has similar accuracy as the experimentally developed coefficients. The simplification and advantages gained by developing the Forchheimer coefficients using numerical methods in flame arrestor applications is presented.