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Primary porosity is an important parameter in studies of reservoir and porosity evolution. However, the applicable conditions for the few existing mathematical models of primary porosity have yet to be clarified. A mathematical model based on the packing texture was proposed by the authors in a previous study; however, the proposed model was only applicable to well-sorted and well-rounded modern beach sands. In this study, the model was modified and applied to poorly-sorted and poorly-rounded braided river sands. The applicable conditions for the proposed models and the previous empirical formula were investigated based on 41 modern braided river sand samples from the Kuqa River in the Tarim Basin and 40 modern beach sand samples from eastern China. Modern sands can be divided into three types based on the particle size distribution. Modified mathematical formulas were derived for each type of sands. The constant parameters in the mathematical model, such as the filling coefficients, embedment coefficients, and packing void ratios were obtained through experiments and through linear fitting. Based on the mathematical model, the errors between the measured and the calculated primary porosities ranged from −3% to 3% for the modern braided sands and from −2% to 2% for the modern beach sands. Using the empirical formula, the primary porosity errors in the modern braided river sands were large, and the formula could not be appropriately applied except to well-sorted and well-rounded modern beach sands. Compared with the modified mathematical model, the original mathematical model could not be applied well to braided river sands owing to the additional errors caused by e f1. The modified mathematical model based on the packing texture was more credible when applied to poorly-sorted and angular braided river sands; further, it was applicable to all types of unconsolidated sands. • A modified model based on packing texture is applied to braided river sands. • Braided river sands are divided into three types by grain size distribution. • The effect of grain shape on primary porosity error is avoided by the new models. • The modified model is found to be more credible over a wider application range. [ABSTRACT FROM AUTHOR]