عنوان مقاله [English]
Water saturation is one of the key petrophysical parameters that mainly affects the accuracy of initial oil estimation related to a hydrocarbon reservoir. Approximation of this parameter is inevitable since it has a high effect on economic development of hydrocarbon reservoirs. In this paper, we propose a two-step approach using 2 well sets and core data to predict water saturation by means of Support Vector Machine (SVM) algorithm in one of the gas reservoirs in Persian Gulf. Due to inevitability of noise and outliers in measured data, SVM modified to Fuzzy SVM (FSVM). Support Vector Regression (SVR) roots from SVM for regression purposes. Considering data in fuzzy sets approaches the machine to reality. In this case, the user is able to give priority to each data point. As a result, noise and outliers can receive less priority which leads to creating better models. After receiving degree of membership, data points enter the algorithm for prediction of water saturation in core missing areas.
Water saturation is the fraction of water in a given pore space. It is expressed in volume/volume, percent or saturation units. This is one of the most applicable petrophysical parameters to evaluate petroleum reservoirs which directly affects success of drilling operations, complementary and production of oil well sets. Therefore, an accurate estimation of this parameter is necessary in exploitation of oil and gas reservoirs. There are two main methods to investigate reservoir parameters; first core data analysis as a direct method and second using well logs as an indirect method. Core data analysis to obtain water saturation information has been presented by different authors (Walther 1967, Morad Zadeh et al. 2011, Jia et al 2020). Measurement of this parameter in the laboratory is costly and takes lots of time. Moreover, core data is not always available for whole well sets. So, using algorithms to estimate reservoir parameters in wells missing core data is profitable. There are variety of formulas that estimate water saturation from other parameters such as resistivity and porosity (Luthi 1941, Archi 1942). But these formulas highly depend on lithology and formation type. So, they can not be generalized to variety of situations. Over the last decade application of machine learning methods has been widely used to estimate reservoir parameters (Zhang et al. 2018, Okwu et al. 2019, Li et al. 2021). Water saturation has been estimated using different algorithms (Adeniran et al 2009, Jafari Kenari et al 2013, Bagheripour et al 2014). Each algorithm has its pros and cons. This paper applies SVR algorithm on well logs to obtain water saturation. The superiority of SVR to other algorithms is the high capability of model generalization and low amount of model error. As the next step, membership functions was used to devote membership degrees to each data point. In other words, data is transformed to a fuzzy system in which each data in a (0,1) interval (Zadeh 1965). In this case, noise and outliers receive less degree of membership so their influence on the final model decreases. As a result, better output is produced and modification of SVR to FSVR notably improves the results (Lim et al. 2002, Le et al. 2009). In this paper 3 well sets of a gas reservoir was utilized, two well sets for training the algorithm and the third well for the testing purpose.
Well logs for this study include acoustic-DT, transit interval time or slowness, neutron porosity (NPHI), density log (RHOB), photoelectric absorption factor (PEF) and gamma ray, intensity of natural radioactivity (GR), resistivity log both shallow and deep (LLD, LLS) and Micro-Spherical Focused log (MSFL). Determination coefficient calculated for water saturation core data and predicted model obtained from FSVR illustrates better results compared to SVR. This study shows determination of coefficient measured from predicted water saturation and core data of SVR algorithm is 71% while for FSVR is 95%.