A combined support vector regression with firefly algorithm for prediction of bottom hole pressure

Research Article A combined support vector regression with firefly algorithm for prediction of bottom hole pressure Menad Nait Amar1 · Noureddine Zeraibi1 Received: 30 August 2019 / Accepted: 2 December 2019 / Published online: 4 December 2019 © Springer Nature Switzerland AG 2019 Abstract Bottom hole pressure (BHP) is a fundamental parameter for the proper design of the production process and the development of reservoirs. BHP can be measured directly through the deployment of pressure down-hole gauges (PDG) or by the application of existing correlations and mechanistic models based on surface measurements. Unfortunately, these methods suffer from two main problems: the cost of measurement which is quite expensive mainly for PDG, and the inaccuracies for the correlations and mechanistic models, due to the limitation of their ranges of application. In this work, a new model based on support vector regression (SVR) optimized with firefly algorithm (FFA) is proposed to predict BHP of vertical wells with multiphase flow. Firefly algorithm is implemented for the optimal selection of SVR hyperparameters. SVR-FFA model development is done using real-life measurement datasets obtained from distinct Algerian oil wells. The performance of the SVR-FFA model is compared with another hybridization SVR-genetic algorithm, trial and error SVR and with existing correlations and mechanistic models. The results demonstrate that the SVR-FFA model outperforms all the other models. Keywords Flowing bottom hole pressure (BHP) · BHP correlations and mechanistic models · Support vector regression (SVR) · Firefly algorithm (FFA) 1 Introduction Bottom hole pressure (BHP) is an essential parameter for a well from its completion till its abandonment stage. It is used to establish the development strategies, design facilities (such as well head completion and tubing size), and also in predicting suitable time for implementing activation mechanisms. Two main categories of methods can be distinguished for estimating BHP: the first is by using a permanent gauge in the bottom hole or by applying well testing; and the second is by a direct calculation using wellknown empirical correlations and mechanistic models that are based on the available surface measurements. The most widely used correlations for BHP determination are those proposed by Hagedorn and Brown [1], Duns and Ros [2], Orkiszewski [3], Beggs and Brill [4], Aziz and Govier [5], Mukherjee and Brill [6]. The mechanistic models includes those of Ansari et al. [7], Chokshi et al. [8], Gomez et al. [9] and Gray [10]. Although the accuracy of the first category (i.e. gauge and well tests) and the simplicity of application of the second (i.e. the correlations and the mechanistic models), both of them present sensible limitations. These incudes the cost which is expensive for the first category, and the poor performances for the second, since all the existing correlations and mechanistic models were developed under a range of conditions, consequently, when their applications are out of these domains, their results became mediocre. During the last years, data-driven through its different methods has been increasingly introduced in several * Menad Nait Amar, ; m.naitamar@univ‑boumerdes.dz | 1Laboratoire Génie Physique des Hydrocarbures, Faculté des Hydrocarbures et de la Chimie, Université M’Hamed Bougara de Boumerdes, Avenue de l’Indépendance, 35000 Boumerdes, Algeria. SN Applied Sciences (2020) 2:23 | https://doi.org/10.1007/s42452-019-1835-z Vol.:(0123456789) Research Article SN Applied Sciences (2020) 2:23 | https://doi.org/10.1007/s42452-019-1835-z fields of science and technology including petroleum engineering, to resolve practical problems [11–13]. Accordingly, very attractive frameworks such as Artap, which is based on machine learning and nature-inspired algorithms have been implemented for practical applications [14]. Accurate prediction of BHP using data-driven techniques is one of these successful applications as we have demonstrated in our previously published work [15]. On the other hand, support vector regression (SVR) is one of the most popular data-driven methods. It is characterized by the high generalization capability that is assured by the exploitation of both structural risk minimization (SRM) and empirical risk minimization (ERM) principles [16]. It has been applied in various fields of science and technology, such as signal processing [17], finance [18], biology [19], biomedicine [20], engineering [21, 22], oil industry [23, 24] and others. Many articles shed light the successful application of this tool in petroleum and reservoir engineering. Ansari and Gholami [25] have applied SVR to estimate the saturation pressure of crude oils. Na’imi et al. [16] have used SVR to estimate reservoir porosity and water saturation distributions. Bian et al. [26] have employed SVR to predict minimum miscibility pressure (MMP) of the system CO2-oil. Fattahi et al. [27] have used SVR in the prediction of asphaltene precipitation. Recently, firefly algorithm (FFA), which is a population-based and a nature-inspired heuristic algorithm has been applied in many fields as a global optimization approach [28]. It is based on flashing behavior of fireflies Fig. 1  SVR-FFA flow chart Vol:.(1234567890) [29]. This algorithm often leads to a significant improvement for solving problems with multimodal functions. In this paper, it is applied as an optimization method to increase the accuracy and the prediction reliability of SVR by finding the optimum SVR hyper-parameters. This research aims to establish a robust and fast approach to estimate BHP in vertical wells with multiphase flow using hybridization SVR with firefly algorithm. 100 field data gathered from various Algerian fields and covering a wide range of variables are used for this purpose. The performance of the combined SVRFFA model is compared with SVR-GA (hybridization SVR and genetic algorithm), SVR-TE trial and error SVR) and existing correlations and mechanistic models. The rest of the paper is organized as follows. Section 2 briefs the implemented data-driven technique, i.e. SVR and the applied optimization algorithms. Section 3 describes the utilized data sets. Results are presented and discussed in Sect. 4. The paper ends with Sect. 5 which summarizes the main findings of the study. 2 Methodology 2.1 Support vector regression (SVR) SVR is a well-formulated supervised learning technique which was developed by Vapnik [30, 31]. SVR aims to identify a function that approximates the functional { } dependency between targets T = t1 , t2 , … , tm defined Research Article SN Applied Sciences (2020) 2:23 | https://doi.org/10.1007/s42452-019-1835-z { } on R , and inputs X = x 1 , x 2 , … , x m where x i ∈ Rn and m is the number of data points. This approximation is defined as follows [30]: f (x) = w𝜑(x) + b (1) where 𝜑(x) points out a mapping function that transforms the i (...truncated)