## 1 Introduction
### Soft Computing Approaches  
The flexible computing approaches are useful and powerful tools that play an essential part in analyzing and solving problems in various fields related to engineering and technology. These computational approaches demonstrate superior performance by defining highly accurate hypothesis functions for approximate solutions when compared to many published analytical and empirical models [9; 10; 11]. Although different computational models are applied abundantly in the field of multiphase pipeline flow, the literature contains only a limited number of attempts to apply these soft techniques to model WAF pressure losses. [PERSON] and [PERSON] [12] propose an artificial neural network (ANN) model to estimate pressure gradients in horizontal and quasi-horizontal multiphase pipes. The model was constructed and then tested on more than 450 field-derived test data samples. Its accuracy  
Figure 1: Schematic presentation of water-assisted flow regime [8]. was then compared with the available correlations as well as mechanistic models to show the superiority of the used ANN technique. Similarly, [PERSON] and [PERSON] [13] also developed an ANN to estimate the pressure gradient losses for the non-Newtonian fluid food which was passing through a tube. The proposed model was able to predict the measured values of pressure gradients with an absolute average error of less than 5.44%. [PERSON] and [PERSON] [14] used ANN instead of a traditional modeling approach to investigate the flow types and also the frictional pressure losses of a mixture of two phases (gas and liquid) flowing within a horizontal ring-shaped conduit. The outcome showed that the ANN can predict flow patterns with errors of less than \(\pm\)5% and friction losses with an accuracy of \(\pm\)30%. [PERSON] et al. [15] tried to estimate the volume fractions of triphasic flows by applying ANN and the nuclear technique. From the three investigated flow regimes of oil-water-gas (stratified, annular, and homogeneous), the ANN model could adequately relate the measurements which simulate the MCNP-X aided code that uses volume fraction for each of the components in the three-phase flow system. [PERSON] et al. [16] also used ANN in genetic algorithms to estimate the pressure gradients in multiple flows under a Venturi scrubber based on a two-phase ring flow model. Successful implementations such as those described above strongly indicate that ANN approaches can be extended to other multiphase flow systems. [PERSON] et al., (2020) [17] applied a feed-forward neural network with a backpropagation technique to model water-lubricated flow of non-conventional crude. Even though it was a pioneering study, the authors used more than 20 nodes. The ANN model was complex and vulnerable to overfitting. Another soft computing approach involves the use of support vector machines (SVMs). This kind of model is commonly applied to problems related to prediction and classification. The use of SVMs is prevalent in the medical sciences for the prediction of illnesses and deficiencies [18]. SVMs can also categorize data into clusters or zones to identify problem areas. This ability has led to their application for leakage detection and monitoring in pipe networks [19]. Different SVMs have also been used in combination with ANNs in previous studies to predict pipe pressure [20]. Recently, [PERSON] et al., (2021) [21] utilized SVM along with other ML algorithms including ANN to model the pressure losses in WAF pipelines. It was a scenario-based exploratory study. Although they found ANN and SVM to perform better compared to other ML models, the nonlinear nature of the dataset did not allow those artificial intelligence tools to be pertained with self-reliance. They emphasized the requirement of further analysis. Following this, our current study aimed to employ easier and simpler ANN and SVM models for cost-effective solutions in long-distance transport of viscous crudes which will serve to enhance the water-lubricated flow technology knowledge area.