Robust Centrifuge Data Processing for Tight and Permeable Rock Samples

Ahmad M. AlZoukani, G. Aidagulov, Farhan Ali, Mohammed Al-Hamad, Wael Abdallah
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引用次数: 1

Abstract

Capillary pressure measurements are key to reservoir characterization. The centrifuge technique is the most used industrial laboratory method to obtain capillary pressure curves for rock samples. The generated experimental data, however, requires conversion of average saturation into local saturation to get correct capillary pressure curves, which is often complicated by the need of fitting of complex and noisy data. Therefore, the objective of this study is to construct a smooth, stable and physically-consistent data fitting model for complex centrifuge data, in order to deliver accurate local saturations for different capillary pressure curves. Drainage capillary pressure curves were generated by centrifugation. Isoparaffinic oil was used to displace brine from core samples at elevated capillary pressure steps. Average water saturation was determined at each capillary pressure step after attaining production stability. Hassler-Brunner and Forbes’s second approximate solutions were used to convert the acquired average water saturations into local saturations. For these two solutions, three analytical fitting techniques were compared on different sets of experimental data. These are power law, global polynomial and cubic spline fitting methods. Two carbonate samples of (96 md) and (0.7 md) permeability were evaluated to represent two distinct cases of a capillary pressure curves. Initially, the power law was used to fit the centrifuge data. For both permeable and tight samples, the resulting capillary pressure curves were found strongly biased by a choice of non-zero initial pressure point, which makes this technique not suitable for data interpretation. The second approach was to use the polynomial fitting method, which found unable to properly fit the tight sample data. It was, however, capable to fit the raw data of the permeable sample. The generated corrected capillary pressure curve, however, was unphysical at low water saturation ranges. Therefore, the raw data of the both samples required application of more complex fitting approach, i.e. the spline method. From the results, the spline function showed high degree of fitting and could account for irregularities of the experimental data. However, non-physical oscillations may occur during the data processing. Therefore, additional constraints of monotonicity of the fit and of the derived Forbes solutions were imposed on the optimal fitting spline. This approach was implemented using cubic splines and verified by equally good results obtained in processing experimental data sets for tight and permeable samples. Robust interpretation workflow to reconstruct capillary pressure curves from centrifuge experiment was built and verified on two limiting cases of tight and permeable samples. The approach is based on fitting of noisy experimental data with cubic spline, constructed using constrained optimization procedure to ensure monotonicity of the derived solutions. The latter physical consistency of the constructed spline fit returns correct capillary pressure curves required for accurate prediction of oil recovery and reservoir fluid distribution.
致密和渗透性岩石样品的稳健离心机数据处理
毛细管压力测量是储层表征的关键。离心技术是获得岩石样品毛细压力曲线最常用的工业实验室方法。然而,生成的实验数据需要将平均饱和度转换为局部饱和度才能得到正确的毛管压力曲线,这往往需要对复杂和有噪声的数据进行拟合。因此,本研究的目的是为复杂的离心机数据构建一个光滑、稳定、物理一致的数据拟合模型,以便为不同的毛细管压力曲线提供准确的局部饱和度。离心生成排水毛细管压力曲线。用异烷烃油在提高毛细管压力的步骤下取代岩心样品中的卤水。在达到生产稳定后,测定了每个毛细管压力步骤的平均含水饱和度。Hassler-Brunner和Forbes的第二近似解用于将获得的平均水饱和度转换为局部饱和度。针对这两种解,在不同的实验数据集上比较了三种解析拟合技术。它们是幂律、全局多项式和三次样条拟合方法。对渗透率为(96 md)和(0.7 md)的两种碳酸盐样品进行了评估,以代表毛细管压力曲线的两种不同情况。最初,幂律被用来拟合离心机的数据。对于渗透性和致密性样品,由于选择非零初始压力点,所得毛细管压力曲线存在强烈偏差,这使得该技术不适合数据解释。第二种方法是使用多项式拟合方法,这种方法发现不能很好地拟合紧样本数据。然而,它能够拟合可渗透样品的原始数据。然而,校正后的毛管压力曲线在低含水饱和度范围内是非物理性的。因此,两个样本的原始数据需要应用更复杂的拟合方法,即样条法。结果表明,样条函数具有较高的拟合度,可以解释实验数据的不规则性。然而,在数据处理过程中可能会出现非物理振荡。因此,在最优拟合样条上附加了拟合的单调性约束和推导出的福布斯解的单调性约束。该方法采用三次样条实现,并通过处理致密和渗透性样品的实验数据集获得了同样好的结果。建立了用于重建离心实验毛细管压力曲线的鲁棒解释工作流程,并在致密样品和渗透性样品两种极限情况下进行了验证。该方法基于用三次样条拟合有噪声的实验数据,采用约束优化程序构造,以保证导出解的单调性。后一种构造的样条拟合的物理一致性返回了准确预测采收率和储层流体分布所需的正确毛细管压力曲线。
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