基于随机稳健梯度优化算法的两相压缩系数相关性研究。

A. Sheriff
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摘要

准确估计两相压缩系数对利用物质平衡法预测凝析气藏动态具有重要意义。多年来,人们发展了几种估算气体压缩系数的关系式。其中一些相关性是;Standing和Katz, Rayes etal, Dranchuk和Abou-Kassem, Brill和Beggs以及Hall-Yarborough的相关性。然而,这些相关性在预测两相区域(低于露点压力)气藏流体的压缩系数方面并不成功,这就解释了为什么该行业仍然依赖于昂贵且耗时的恒定体积消耗(CVD)方法。因此,本文提出了基于随机鲁棒梯度的Newton-Raphson优化算法估计两相压缩系数的两种不同相关性。第一个关联表示两相z因子是伪还原压、伪还原温和比重的函数。另一方面,第二个相关性将两相z因子表示为单相z因子的函数(使用Standing和Katz方法获得)。这两种相关性是利用从世界各地的凝析气藏获得的50多个储层流体样本的恒定体积损耗(CVD)数据建立起来的。此外,为了发展这些相关性,提出了两种不同的模型,庚烷+ (C7+)和酸性气体馏分分别使用Sutton 's和Lee Kesler相关性。以拟还原压力、拟还原温度、比重和单相z因子期望值(均采用适当的概率分布得到)作为输入变量,采用随机鲁棒优化算法(该算法由误差函数的泰勒级数展开得到,本研究采用Octave编程语言实现)求得模型拟合参数的最优值,使误差平方和(SSE)最小。最后,使用70%的可用数据开发了相关性,使用30%的可用数据评估了这些相关性的性能,获得的结果表明,这些相关性优于其他预先存在的相关性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Development of Two-Phase Compressibility Factor Correlations Using a Stochastic and Robust Gradient-Based Optimization Algorithm.
Accurate estimation of two-phase compressibility factor is of great importance in predicting the performance of a gas condensate reservoir using the material balance approach. Over the years, several correlations for estimating gas compressibility factor have been developed. Some of these correlations are; the Standing and Katz, Rayes etal, Dranchuk and Abou-Kassem, Brill and Beggs’ and Hall-Yarborough’s correlations. However, these correlations have not been so successful in predicting the compressibility factor of gas reservoir fluids in the two-phase region (below dew point pressure) and this explains why the industry still relies on the expensive and time-consuming constant volume depletion (CVD) approach. Therefore, this paper presents two different correlations for estimating two-phase compressibility factor using stochastic and robust gradient-based Newton-Raphson optimization algorithm. The first correlation presents the two-phase Z-factor as a function of pseudo-reduced pressure, pseudo-reduced temperature and the specific gravity. The second correlation on the other hand presents the two-phase Z-factor as a function of the single-phase Z-factor (obtained using Standing and Katz approach). Both correlations were developed using over 50 constant volume depletion (CVD) data of reservoir fluid samples obtained from gas condensate reservoirs around the world. Furthermore, in order to develop these correlations, two different models were proposed and the heptane-plus (C7+) and acid gas fractions were accounted for using the Sutton’s and Lee Kesler correlations respectively. Moreover, using the expected values of the pseudo-reduced pressure, pseudo-reduced temperature, specific gravity and single-phase Z-factor (all obtained using appropriate probability distributions) as the input variables, the optimum values of the models’ fitting parameters that minimize the sum of squares of the errors (SSE) were obtained using the stochastic and robust optimization algorithm(an algorithm obtained from Taylor series expansion of the error function and implemented on Octave programming language for the purpose of this study). Finally, having developed the correlations using 70% of the available data, the performances of these correlations were evaluated using 30% of the available data and the results obtained shows that these correlations outperform other pre-existing correlations.
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