We explored the dynamics of the two interacting information systems. We show that for the Markovian marginal systems the driving force for information dynamics is determined by both the information landscape and information flux. While the information landscape can be used to construct the driving force to describe the equilibrium time reversible information system dynamics, the information flux can be used to describe the nonequilibrium time-irreversible behaviours of the information system dynamics. The information flux explicitly breaks the detailed balance and is a direct measure of the degree of the nonequilibriumness or time irreversibility. We further demonstrate that the mutual information rate between the two subsystems can be decomposed into the equilibrium time-reversible and nonequilibrium time-irreversible parts respectively. This decomposition of the mutual information rate (MIR) corresponds to the information landscape-flux decomposition explicitly when the two subsystems behave as Markov chains. Finally, we uncover the intimate relationship between the nonequilibrium thermodynamics in terms of the entropy production rates and the time-irreversible part of the mutual information rate. We found that this relationship and MIR decomposition still hold for the more general stationary and ergodic cases. We demonstrate the above features with two examples of the bivariate Markov chains.

The western Sulige gas field is a new and key reserve area for the rolling development of the Sulige gas field in China. However, due to the complex gas–water relationship and the difficulty in identifying gas and water formation, the scale and benefit deployment of the gas field are seriously restricted. In particular, almost all of the wells in the area produce water and no water measurement has been carried out for any single well, which leads to an unclear understanding of the dynamic characteristics of the production wells, thus affecting the productivity calculations of the gas wells and the overall regional productivity evaluation. Based on the testing data for a gas well, the impacts of the reservoir property parameters on the gas and water production were analyzed by combining the production performance and static geological characteristics. It was determined that the physical parameters K, Kh, and φSg had good positive correlations with gas production but not with water production; thus, effective prediction cannot be obtained for water production in gas well testing. After the analysis of the liquid loading law, the gas wells were classified into three types: continuous liquid carrying production, slight liquid loading, and liquid loading wells. In general, up to 96% of the gas wells were liquid loaded. According to the different production performances exhibited in the different stages of the gas wells, five types of methods for diagnosing water production wells were proposed (gas testing, pilot production, gas–liquid two-phase measurement testing, liquid level detection, and production performance analysis), as well as the diagnostic criteria and corresponding solutions. To obtain real-time water production data for each well and investigate the change of water-gas ratio (WGR) during the whole production process, a water production splitting method for gas wells based on three-dimensional geological modeling and numerical simulation combined with the constraints of the total water production of gas gathering stations was explored and established. The splitting results can be used to evaluate the water and gas productivity of gas wells and determine the best deliquification period. The gas well productivity when water production was considered was about 10% lower than that when water production was not considered. The best deliquification period was determined to be 125 days for wells with small water production, 20 days for wells with moderate water production, and 3 days for wells with serious water production. The results of this study could provide technical support for the scientific evaluation of gas well production indicators, reduction of development costs, and improvement of oil recovery.