A well monitoring system, comprising: a well; a well system, the well system including at least one sensor (136,137) measuring at least one well condition; and a computing apparatus, including: a processor; a storage; a bus system over which the processor communicates with the storage; a data structure residing in the storage in which real-time data acquired by the sensor is stored; a well monitoring software component residing on the storage that, when executed by the processor over the bus system, performs a method to detect a kick in a well, the method comprising: storing a set of real-time data from a measurement of the well condition by the sensor, the well condition being correlative to an unplanned fluid influx into the well; modeling the operation of the well with a physics-based, state space model of the well system to obtain an estimate of the well condition; and accessing the stored real-time data set; characterised in that the method further comprises: applying the accessed real-time data set and the estimate to a probabilistic estimator to yield a probability of an occurrence of a kick and a confidence measure for the probability. a well; a well system, the well system including at least one sensor (136,137) measuring at least one well condition; and a computing apparatus, including: a processor; a storage; a bus system over which the processor communicates with the storage; a data structure residing in the storage in which real-time data acquired by the sensor is stored; a well monitoring software component residing on the storage that, when executed by the processor over the bus system, performs a method to detect a kick in a well, the method comprising: storing a set of real-time data from a measurement of the well condition by the sensor, the well condition being correlative to an unplanned fluid influx into the well; modeling the operation of the well with a physics-based, state space model of the well system to obtain an estimate of the well condition; and accessing the stored real-time data set; characterised in that the method further comprises: applying the accessed real-time data set and the estimate to a probabilistic estimator to yield a probability of an occurrence of a kick and a confidence measure for the probability. a processor; a storage; a bus system over which the processor communicates with the storage; a data structure residing in the storage in which real-time data acquired by the sensor is stored; a well monitoring software component residing on the storage that, when executed by the processor over the bus system, performs a method to detect a kick in a well, the method comprising: storing a set of real-time data from a measurement of the well condition by the sensor, the well condition being correlative to an unplanned fluid influx into the well; modeling the operation of the well with a physics-based, state space model of the well system to obtain an estimate of the well condition; and accessing the stored real-time data set; characterised in that the method further comprises: applying the accessed real-time data set and the estimate to a probabilistic estimator to yield a probability of an occurrence of a kick and a confidence measure for the probability. storing a set of real-time data from a measurement of the well condition by the sensor, the well condition being correlative to an unplanned fluid influx into the well; modeling the operation of the well with a physics-based, state space model of the well system to obtain an estimate of the well condition; and accessing the stored real-time data set; characterised in that the method further comprises: applying the accessed real-time data set and the estimate to a probabilistic estimator to yield a probability of an occurrence of a kick and a confidence measure for the probability.