The mathematical model of composite reservoir has been widely used in well test analysis. In the process of oil recovery, due to the injection or replacement of the displacement agent, the model boundary can be moved. At present, the mathematical model of a composite reservoir with a moving boundary is less frequently studied and cannot meet industrial demand. In this paper, a mathematical model of a composite reservoir with a moving boundary is developed, with consideration of wellbore storage and skin effects. The characteristics of pressure transient in moving boundary composite reservoir are studied, and the influences of parameters, such as initial boundary radius, moving boundary velocity, skin factor, wellbore storage coefficient, diffusion coefficient ratio, and mobility ratio on pressure and production, are analyzed. The moving boundary effects are noticeable mainly in the middle and late production stages. The proposed model provides a novel theoretical basis for well test analysis in these types of reservoirs.

On the basis of the multiple velocity difference effect (MVDE) model and under short-range interaction, a new three-phase traffic flow model (S-MVDE) is proposed through careful consideration of the influence of the relationship between the speeds of the two adjacent cars on the running state of the rear car. The random slowing rule in the MVDE model is modified in order to emphasize the influence of vehicle interaction between two vehicles on the probability of vehicles’ deceleration. A single-lane model which without bottleneck structure under periodic boundary conditions is simulated, and it is proved that the traffic flow simulated by S-MVDE model will generate the synchronous flow of three-phase traffic theory. Under the open boundary, the model is expanded by adding an on-ramp, the congestion pattern caused by the bottleneck is simulated at different main road flow rates and on-ramp flow rates, which is compared with the traffic congestion pattern observed by Kerner et al. and it is found that the results are consistent with the congestion characteristics in the three-phase traffic flow theory.