The complex nonlinear effects in the production process of shale gas wells have brought great difficulties to the accuracy of productivity evaluation. Nowadays, the nonlinear effects of the multi-scaled gas production process can be considered incomplete in most shale gas production prediction models, resulting in the inaccuracy of the production prediction of gas wells and errors in the dynamic production analysis of gas wells. Based on the conventional five-zone composite linear flow model, the comprehensive gas nonlinear effects were upgraded and an improved compound linear flow model was established in the paper. Subsequently, a semi-analytical solution of the proposed production model was obtained to verify the reliability of the model with practical production data. Ultimately, the gas well dynamic production analysis was developed. The research results show that:1) the more complete the various nonlinear effects in the gas production process, the more accurate the production prediction value and the greater the calculation accuracy;2) Adsorbed gas is a key component of shale gas wells long-term stable production, with an annual adsorption contribution rate exceeding 50%. When the pressure drops below the critical desorption pressure, the utilization of the adsorbed gas reserves will increase significantly, and the cumulative gas production under unit pressure drop will increase significantly. The final adsorbed gas volume will account for more than 20% in the cumulative gas production composition. The research results of this paper provide some theoretical reference for the accurate evaluation of shale gas reservoir utilization effect and the improvement of gas reservoir utilization rate and final gas recovery degree.