Horizontal well transient rate decline analysis in low permeability gas reservoirs employing an orthogonal transformation method

•A transient production decline analysis model which considering threshold pressure gradient is proposed.•Sturm-Liouville eigenvalue method and orthogonal transformation are employed to solve the mathematical model.•Type curves of production rate and derivate is plotted and five flow regimes of horizontal gas well are recognized.•The effect of threshold pressure gradient and other relevant influence factors on transient production rate decline are discussed.

Transient rate decline analysis (TRDA) is an important analysis in modern reservoir engineering and applications. Most studies have focused on the threshold pressure gradient (TPG) of low permeability reservoirs and have placed an emphasis on the transient pressure response or steady productivity, whereas transient production decline has not been a focus. This paper presents a transient production decline analysis model of a horizontal well in low permeability gas reservoirs considering the threshold pressure gradient. An accurate solution is determined by employing the Laplace transformation, Sturm-Liouville eigenvalue method, and orthogonal transformation. The bi-logarithmic type curves of dimensionless production and the derivative are plotted by the Stehfest numerical inversion method. Five different flow regimes were recognized, and the effects of the influencing factors, such as the threshold pressure gradient, wellbore storage coefficient, skin factor, horizontal section length, and formation thickness, are discussed. This research contributes to the understanding of transient flow behavior and provides the theoretical basis for efficiently exploiting low permeability reservoirs.