The demand for natural gas is expected to continuously increase due to its significant role in the transition towards a low-carbon energy structure. Based on the nonhomogeneous grey model, a new method for estimating natural gas production and consumption is developed, namely, the conformable fractional nonhomogeneous grey Bernoulli model (denoted as CFNHGBM(1,1,k) for short). In the new method, the Bernoulli equation is first introduced into the existing differential equation. The traditional accumulation is then replaced with conformable fractional accumulation. Finally, the moth flame optimization (MFO) algorithm is applied to determine the structural parameters for the novel model. Moreover, when taking different values, the novel model will be changed into the existing grey serial models. Based on natural gas production and consumption from 2008 to 2018, we use the proposed model to predict future data from 2019 to 2021 in North America, and the forecasts show that the novel model performs better than other competitors. Furthermore, natural gas production and consumption maintain steady increasing trends with average annual growth rates of 3.29% and 2.02%, respectively.

由于天然气在向低碳能源结构过渡中的重要作用，预计天然气需求将持续增长。基于非均质灰色模型，开发了一种估计天然气产量和消费量的新方法，即合格分数非均质灰色伯努利模型（简称CFNHGBM（1,1，k））。在新方法中，伯努利方程首先被引入到现有的微分方程中。然后将传统的累积量替换为合格的分数累积量。最后，应用飞蛾火焰优化（MFO）算法确定新型模型的结构参数。此外，当采用不同的值时，新模型将变为现有的灰色序列模型。基于2008年至2018年的天然气生产和消费量，我们使用提议的模型预测2019年至2021年北美的未来数据，并且该预测表明新模型的表现优于其他竞争对手。此外，天然气的生产和消费保持稳定的增长趋势，年均增长率分别为3.29％和2.02％。