Natural gas transmission is energy consuming due to significant pressure loss during the transportation process. Despite considerable effort to reduce its energy consumption in optimization study, the non convex behavior of mathematical models, mainly resulted from nonconvex pressure drop constraints, have made the problem challenging to tackle. To address this issue, this paper presents two convex formulation techniques to convexify the pressure drop constraints. The techniques use logical constraints to handle unknown gas flow direction to avoid absolute values and bilinear terms in the constraints. Modeling techniques are also presented to reformulate nonconvex compressor constraints into convex/concave ones. The proposed techniques are applied to two different scale natural gas transmission networks. Computational results suggest that the convexification relieves the models from local optima, and greatly improves solution quality and solution efficiency. (C) 2018 Elsevier Ltd. All rights reserved.