We derive a reduced control system model for the dynamics of compressible gas flow through a pipeline subject to distributed time-varying injections, withdrawals, and control actions of compressors. The gas dynamics PDE equations are simplified using lumped elements to a nonlinear ODE system with matrix coefficients. We verify that low-order integration of this ODE system with adaptive time-stepping is computationally consistent with solution of the PDE system using a split-step characteristic scheme on a regular space-time grid for a realistic pipeline model. Furthermore, the reduced model is tractable for use as the dynamic constraints of the optimal control problem of minimizing compression costs given transient withdrawals and gas pressure constraints. We discretize this problem as a finite nonlinear program using a pseudospectral collocation scheme, which we solve to obtain a polynomial approximation of the optimal transient compression controls. The method is applied to an example involving the Williams-Transco pipeline.