Existing fouling monitoring of tubular heat exchangers relies heavily on historical operating conditions. Under fluctuating and variable operating states, significant deviations arise between the current and historical monitoring data, making it difficult to accurately capture fouling thickness and leading to false or missed alarms. This paper presents a study on digital twin-driven fouling monitoring and thickness quantification for tubular heat exchangers. First, a high-precision and high-fidelity finite element simulation model of the heat exchanger is developed. Through geometric modeling, unstructured tetrahedral meshing, and appropriate simulation assumptions, physical data from all nodes during operation are obtained. Second, key low-dimensional modes are extracted using proper orthogonal decomposition (POD), and parameter generalization is enhanced with radial basis function (RBF) interpolation. On this basis, a data-driven POD-RBF model order reduction method is proposed. An adaptive sampling layout optimization approach is also introduced to reduce computational costs while maintaining accuracy, enabling the generation of multiple training datasets and the construction of a digital twin model capable of real-time state prediction. Model errors are dynamically corrected via Kalman filtering to further improve prediction accuracy. Finally, a fouling detection and thickness quantification model is derived from the heat transfer coefficient formula. Fouling is identified by comparing overall heat transfer coefficient, inlet/outlet temperatures , and other parameters between the physical system and its twin. Thickness quantification is then achieved using the correlation between fouling thermal resistance and thickness. For experimental validation, a transparent-shell heat exchanger was used with saturated calcium sulfate solution as the cold fluid. By monitoring inlet/outlet pressures, flow rates, and temperatures, results show that under healthy conditions, the error between the digital twin and actual operation is within 1%. Under fouling conditions, the fouling detection rate reaches 100%, and the thickness sensing error ranges from 5%~25%, thus realizing reliable fouling monitoring and thickness quantification under variable operating conditions.