1. Introduction
In the oilfield development process, due to reservoir heterogeneity and different production modes, there often exist great amounts of remaining oil in reservoirs. As a result, the prediction of remaining oil or water saturation distribution is of great significance for oilfield future development [
1]. Accurate prediction of water saturation distribution in a reservoir facilitate to tap the remaining oil in the reservoir.
There are mainly two traditional methods to analyze and predict water saturation at the current time. On the one hand, some researchers calculate the water saturation in the reservoir based on petrophysical models. Archie [
2] used the formation resistivity and porosity to calculate water saturation
Sw in the reservoir. Some other researchers adopted saturation–height function like Leverett
J function [
3] and Heseldin method [
4] to formulate capillary pressure data and then water saturation could be obtained. These methods are relatively time-consuming, and their sample range is hard to reflect the reservoir heterogeneity. On the other hand, numerical simulation has been widely used in the petroleum industry. A variety of simulation techniques have evolved for different development conditions and reservoir types [
5,
6,
7,
8,
9]. Reservoir simulation plays a dominant role in formulating the reservoir development plan and improving oil recovery at the current stage [
10]. In this background, many researchers studied water saturation distribution utilizing numerical simulation for different type of problem, such as water imbibition [
11,
12,
13], performance of EOR (enhance oil recovery) methods [
14,
15], unconventional reservoir exploitation [
16,
17], etc. However, it will take a long time for history matching and forecast calculation, and the prediction cost is relatively higher.
In recent years, a data driven approach and artificial intelligence technology have been advantageous for quick exploitation determination with or without physical model. Take remaining oil saturation prediction in a reservoir as example, machine learning methods can show good ability to solve this problem. Reservoir engineers could propose rational scenarios for tapping of remaining oil and long-term healthy development of oilfields combining machine learning results with numerical simulation. In previous study, numbers of machine learning methods have already been applied into petroleum industry to analyze data, find patterns and predict target variables [
18]. The utilization of a machine learning method in petroleum industry often focus on two purposes. For one purpose, try to figure out the relationship between petrophysics and reservoir properties. Silpngarmlers et al. [
19] used the BP neural network method to learn different relative permeability curve data from a certain amount of papers and experiments, so as to develop a liquid/liquid and liquid/gas two-phase relative permeability predictors. Talebi et al. [
20] utilized two improved algorithms: Multilayer Perceptron (MLP) neural network and Radial Basis Function (RBF) for efficient estimation of saturation pressure of reservoir oil. Nouri-Taleghani et al. [
21] used three machine learning methods separately to predict the fracture density with full set log data as inputs. Masoudi et al. [
22] adopted Bayesian Network and K2 algorithm to find interrelationships between petrophysical parameters and optimum production feature. Hegde et al. [
23] conducted real time rate of penetration (ROP) optimization in drilling by utilizing Data-Driven model. Tian and Horne [
24] applied three machine learning methods as linear regression, convolution kernel and ridge regression to interpret flow-rate, pressure and temperature data from permanent downhole gauge. For another, try to forecast future well production performance. Gupta et al. [
25] forecasted gas production in unconventional resources using data mining and time series analysis. Schuetter et al. [
26] adopted simple regression random forest (RF), support-vector regression (SVR), gradient-boosting machine (GBM) and multidimensional Kriging to predict oil production in an unconventional shale reservoir focusing on establishment of robust predictive models. Ma et al. [
27] predicted the oil production using the novel multivariate nonlinear model based on traditional Arps decline model and a kernel method. Kamari et al. [
28] used least square support machine vector method (LS-SVM) to develop a robust model for predicting surfactant-polymer flooding performance. The prediction on well performance and reservoir characteristics including water saturation distribution tried by Gomez [
29] and Mohaghegh [
30] with a data-driven reservoir modeling was successful while without detailed implementation description. This attempt indicated the data driven method is feasible and effective to characterize reservoir and facilitate production. Actually, typical machine learning approach should be modified or selected properly in terms of practical production to produce best results. The specific process introduction on machine learning implementation must benefit reservoir engineers in the petroleum industry.
Combined with a specific machine learning approach, the aim of this study is to predict water saturation distribution in future production, which is a typically time-series problem. Recurrent Neural Network (RNN) was found to be good at solving these problems. The output of the previous moment is partial input of next time step of RNN which is appropriate for short-term prediction. However, long-term dependencies problem of RNN limits its further development. To overcome this drawback, a Long-Short Term Memory (LSTM) method was presented. As a variant of RNN, LSTM has gradually become a research hotspot in the field of machine learning in recent years. Significant results have been achieved in language translation, speech recognition and machine reading [
31,
32,
33,
34,
35]. As an improved form of RNN, LSTM solves the long-term dependencies due to its unique data preservation mechanism which could remember long-term data properties. This characteristic has great advantages in dealing with large-scale multi-dimensional data and time-series problems. In the petroleum industry, LSTM was used to perform secondary generation of well logging data [
36], forecast production decline of multiple wells [
37] and predict rate of penetration (ROP) based on recorded drilling data [
38]. However, this method has not been used for the prediction of water saturation distribution in reservoir yet. In terms of the huge scale of data amount and consistence between water saturation and time, LSTM is a comparatively appropriate machine learning method for water saturation prediction.
This paper was organized in four aspects. Firstly, a water saturation prediction model was established utilizing neural network LSTM with data processing, model training and testing. Then, the model was calibrated and validated quantitatively for further prediction. After that, the prediction and analysis of water saturation distribution were carried out to tap remaining oil. Finally, a comparison of accuracy and computational time between different machine learning methods was presented. In this study, we provide an alternative way for quick and robust prediction of water saturation distribution in a reservoir without empirical and numerical simulation.
4. Conclusions
This study presented an alternative way for quick and robust prediction of water saturation distribution in a reservoir besides of numerical simulation. A reservoir water saturation distribution predictor was developed utilizing a Long Short-Term Memory recurrent neural network. An actual reservoir dataset deriving from monitoring and simulating was utilized for model training and test. Through the trained model, it is accessible to forecast water saturation distribution, pressure distribution and oil production faster than with numerical simulation. After analyzing the calculation results, several conclusions can be drawn as follows:
The LSTM method has a good performance on the water saturation prediction. In the case of large data volume, the overall AARD can be controlled below 14.82%. It is proven that the model is valid and reliable. On the basis of model validation, the model can predict water saturation distribution and present suggestions for tapping remaining oil in future production. Compared with numerical simulation, machine learning methods have great advantages in computation time which could be exploited in the future. Different types of machine learning methods have distinct performance in water saturation prediction. The accuracy of LSTM is better than GRU and standard RNN. GRU is another choice, although the accuracy is slightly lower than LSTM.