Neural-Network based Sensitivity Analysis for Injector-Producer Relationship Identification

Abstract

Abstract Determining injector-producer relationships, i.e., to quantify the inter-well connectivity between injectors and producers in a reservoir, is a complex and non-stationary problem. In this paper, we present a neural-network-based sensitivity analysis approach to address this problem. To the best of our knowledge, sensitivity analysis has never been applied for identification of the injector-producer relationships, yet we show that it is an intuitive while fundamental approach to address this problem. Sensitivity analysis is based on a theory with which the functioning of a closed system is derived by analyzing the derivatives of the output with respect to each input combination. For the injector-producer relationship identification problem, we use sensitivity analysis to determine the injector-producer relationships by varying the injection rates, i.e., the inputs to a trained neural network model of the oilfield, and analyzing the outputs, i.e., the production rates. With our approach, we first generated a neural network to define the mapping function between each producer and its surrounding injectors based on the historical injection and production data. We employed Back-Propagation-Through-Time (BPTT) learning algorithm to train the three-layer feed-forward neural network using real data collected from 1911 to 2005. Next, we utilized the generated neural network model to apply sensitivity analysis in order to quantify the significance of the injectors on the corresponding producers. We evaluated our proposed injector-producer relationship identification technique by experiments with real oilfield dataset as well as field trials. Experimental results show that our sensitivity analysis approach is not only an efficient method for identifying injector-producer relationships but also reveals significantly higher correlation accuracy as compared to the correlation typically estimated by the field engineers. 1. Introduction Forecasting injector-producer relationships and modeling fluid flow in petroleum reservoirs is the key to recover maximum oil with reduced operation costs. Based on the analysis of the historical injection and production data from a reservoir, one can observe that the production performance is not only controlled by the injection rates itself but also may be affected by various other factors. For example, new fractures in underground structures, fluctuation in permeability, and changes in reservoir temperature can easily impact the oil recovery. Typically, certain parameters may affect the output to a larger extent as compared with others, whereas some may have no effect on the behavior of the system. This complex behavior of oilfields renders the identification of the allocation factors between injectors and producers as an extremely hard problem. Currently, reservoir engineers determine allocation factors between injectors and producers based on their past experience, production and injection historical data, numerical simulations. These approaches are not only time consuming but also error prone as they neglect non-linear interactions between various parameters. In this paper, we present a novel neural-network-based sensitivity analysis approach to identify the injector and producer relationships in oilfields. Neural networks are mostly used when analytical model of the system either is not known or does not exist. In addition, neural networks employ historical data to learn the underlying system by developing a function that maps the input vectors to output vectors without knowing the system characteristics. In a typical neural network, the response at a particular time depends not only on the observable event but also on the past events. Moreover, neural networks [1] are adaptive systems as they arrange their weight functions on the basis of external or internal information that flows through the network. All these features of neural networks allow us to capture the complex characteristics of an oilfield and thus motivating us to develop a neural network based approach.