# A New Algorithm Model Based on Extended Kalman Filter for Predicting Inter-Well Connectivity
The well-logging curve method primarily determines the locations of ineffective circulation channels in reservoirs by analyzing well-logging data. However, this method is relatively simple and cannot accurately reflect reservoir changes [9]. The well-testing analysis method uses interference well testing, but it has long testing periods and high costs [10; 11]. The geochemical method identifies ineffective circulation channels through chromatographic fingerprinting techniques. Although the identification results are relatively accurate, the high costs make it unsuitable for large-scale application [12]. The tracer testing method involves injecting tracers into injection wells and monitoring their output from production wells. By plotting the tracer output curves, reservoir conditions can be assessed accurately, but the method is time-consuming and expensive, making it unsuitable for large-scale deployment [13; 14]. The fuzzy comprehensive evaluation method determines the evaluation indicators for inefficient circulation of oil and water wells by analyzing the influencing factors of ineffective circulation channels and their characteristics during development. While the results are objective and accurate, developing the evaluation indicators is time-consuming, and subsequent dynamic adjustments are challenging [15; 16]. Machine learning algorithms such as support vector machines, random forests [17], and neural networks have also been applied to the study of ineffective circulation channels [18] ([PERSON] et al., 2020). These methods save significant human and material resources, offer higher identification accuracy, and are suitable for widespread adoption. However, the accuracy and generalization capabilities of these models still need improvement. They face challenges in learning and adapting to unobserved tasks and have a high dependency on the training dataset [19]. The CRM analysis method for oil reservoirs has inherent advantages in quantitatively identifying ineffective circulation channels. CRM is a nonlinear, data-driven approach designed to precisely estimate the inter-well connectivities between production and injection wells under various conditions. CRM accounts for the effects of capacitance (compressibility) and resistance (transmissibility), which are represented by two key parameters: the degree of fluid storage (time constant, \(\tau\)) and the degree of connectivity (weight coefficient, \(\lambda\)) between wells. The model utilizes injection rates as input data and production rates as output, deriving the CRM from the overall fluid mass balance within the control volume. At present, there are many studies on the use of CRM to carry out ineffective circulation channels. [PERSON] et al. (2006) introduced a nonlinear data-driven CRM to accurately estimate the inter-well connectivities between production and injection wells under various conditions [20]. [PERSON] et al. (2008, 2009) presented three branches of CRM based on attributing model parameters to different control volumes: CRMT (control volume is the whole field), CRMP (each producer has a drainage volume), and CRMIP (a control volume for each injector-producer pair) [21]. [PERSON] (2011) presented an integrated capacitance-resistance model (ICRM) that fits cumulative total production using cumulative water injection rates as inputs [22]. This approach reduces computation time by avoiding local minima issues in previous nonlinear CRMs. [PERSON] et al. (2018) improved the matching performance of ICRM by employing two consecutive objective functions for monthly and cumulative liquid production matches, extending CRM applications to more realistic reservoir conditions [23]. Recently, various efforts have been made to characterize layered reservoirs using different types of CRM and their applications to conventional and smart reservoirs [24; 25; 26; 27; 28].