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Accurate calculation of flow discharge for sluice gates is essential in irrigation, water supply, and structure safety. The measurement of discharge with the requirement of distinguishing flow regimes is not conducive to application. In this study, a novel approach that considers both free and submerged flow was proposed. The energy–momentum method was employed to derive the coefficient of discharge. Subsequently, the discharge coefficient was determined through the experiment which was performed on the physical model of a vertical sluice gate with a broad-crested weir. Feature engineering, incorporating dimensional analysis, feature construction, and correlation-based selection were performed. The best subset regression method was employed to develop regression equations of the discharge coefficient with the generated features. The derived formula was applied to compute the discharge coefficient in the vertical sluice gate and determine the flow discharge. The accuracy of adopted method was assessed by comparing it with recent studies on submerged flow, and the results demonstrate that the developed approach achieves a high level of accuracy in calculating flow discharge. The coefficient of determination for the calculated flow rate is 0.993, and the root mean square percentage error is 5.04%. HIGHLIGHTS The feature combination with efficient interpretability of free-submerged flow discharge coefficient was proposed.; The computational equation applicable to free-submerged flow regimes based on the EM method was established with high accuracy.; The process of feature selection and calculation is not complicated and has potential for automated calibration.;

Multi-stage hydraulic fracturing is a crucial technique in the development of horizontal shale gas wells. After fracturing and shut-in for several days, the well would be opened and the fracturing fluid injected into the gas formation would flow back to the ground along with extracted gas. Field experts suggest fracturing fluid flowback plays a key role in the production of shale gas and hope to find the relationship between flowback and production. However, the flowback and production data we collected from 161 wells in one shale gas field in China illustrate that there is no general relationship between flowback and production. The main reason we deduce is that the commonly-used cumulative flowback amount is not a good indicator to represent shale gas wells’ flowback situation. Therefore, we propose a new flowback indicator based on filed data and a shale gas flow model. The proposed indicator is the cumulative flowback ratio per fracturing cluster calculated on production days, where production day is a newly proposed time measurement substituting the calendar day. Further study illustrates that the proposed indicator can be easily predicted using a random forest model with engineering parameters, geological parameters, and well operation parameters. Besides, fracturing scale parameters and brittle mineral proportion are identified as the most important controlling factors of the proposed indicator. With the help of the newly proposed flowback indicator, field experts can have a new way to comprehend each well’s flowback characteristics and make better development plans.

The collapse mechanism of dual-structure vegetation riverbanks at different water levels is unclear. A method for calculating the critical collapse width of a dual-structure vegetation bank under different failure modes that consider the variations in river and groundwater levels and the influence of vegetation roots is proposed. Combined with the influence of flow lateral erosion and slope toe accumulation, a calculation model of riverbank stability was established. The results show that shear failure is the main failure mode when the cohesive soil layer on a dual-structure bank is thick, and the critical collapse width of the bank with root soil is higher than that of the soil bank. The critical collapse width of the bank varied with the water level during different water level periods. Compared with a soil riverbank, a rooted soil riverbank can significantly prolong the bank collapse time. The collapse width of a soil bank without vegetation roots is smaller than that of a rooted soil bank, and the cumulative collapse width is related to calculation time. The greater the thickness of rooted soil, the slower the decay rate of bank stability under water flow erosion. HIGHLIGHTS The collapse mechanism of riverbanks with a dual structure under the influence of water level and vegetation was revealed.; The collapse process analysis and stability calculation model of dual-structure bank with vegetation were established.; The stability analysis and prediction of the dual-structure bank with vegetation in the lower reaches of the Yangtze River were carried out.;

Well shut-in and drainage after shale gas fracturing are important factors affecting the productivity. Due to the imperfect optimization method of shale gas flowback, there has been no clear explanation for the problems such as “formulation of reasonable well shut-in time” and “less fracturing fluid flowback but high-gas production phenomenon” during shale gas drainage. In this paper, the double pressure funnels (one funnel is formed during fracturing by pressure difference from wellbore to formation, and two funnels are formed during flowback by pressure difference from fracture to formation and from fracture to wellbore) and gas-liquid two-way mass transfer (gas transfer by diffusion and liquid transfer by pressure difference) in shale gas drainage are investigated by calculating the pressure distribution after fracturing shale gas wells. The discrete numerical simulation by using unstructured PEBI grid is conducted, and the result is as follows: when shale gas well is shut-in for 20 days and produce for 1 year, the daily gas production corresponding to fracturing fluid flowback rates of 20%, 10%, and 5% are 47700 m3, 5800 m3, and 72700 m3, respectively. The investigation of double pressure funnels and gas-liquid two-way mass transfer explains clearly the phenomenon “less fracturing fluid flowback but high-gas production.” Meanwhile, the two conditions for optimizing the well shut-in time after fracturing are presented. That is, as for the studied case, the moving speed of the pressure boundary line should be less than 0.1 m/d, and the water-gas ratio near the fracture should be less than 1/d with time. Consequently, the reasonable well shut-in time is optimized to be 20-25 days. The findings in this work are of benefit to enrich the flowback theory of shale gas after fracturing and provide a theoretical basis for the optimization technology of shale gas drainage after fracturing.

Fracture-vuggy oil reservoirs contain micrometer-sized dissolved secondary pores, fractures, and meter-sized karst caves. Generally, the researches on the flow mechanism of fractured-vuggy reservoirs are based on the assumption of karst cave-fracture-matrix triple medium that gives a partial differential equation which the pressure satisfies. This triple medium flow equation lays the basics for the well testing theory of fractured-vuggy reservoirs. However, the triple medium equation cannot reflect the actual existence of the karst cave volume in geology. Recently, we proposed a theory of fracture-cave seepage flow coupled with vug pressure wave which takes the vug size into consideration and thus can better describe the fracture-vuggy reservoirs. On the basis of this theory, this work combines the change of formation pressure with time, Duhamel’s theorem, and well testing theory to obtain the mathematical expression of time-varied bottom hole pressure and flow rate in Laplace space. Then, the dynamic inflow performance relationship (IPR) curve of fractured-vuggy reservoir is obtained by inverse Laplace transformations. This dynamic IPR curve can predict the productivity for fractured-vuggy reservoirs using parameters from well test interpretations of pressure recovery. The correctness of this productivity prediction method is verified by filed fractured-vuggy oil well. This productivity prediction method not only utilizes and expands the application of well test interpretation data but also shortens the test time and reduces test costs, which is important for oil development.

Based on the results of molecular dynamics simulation, in a gas-water miscible zone, the velocity profiles of the flowing water film do not increase monotonously but increase first and then decrease, which is due to the interaction between water and gas molecules. This exhibits a new physical mechanism. In this paper, we firstly propose a gas-water flow model that takes into account the new physical phenomena and describes the distribution of gas-water velocity in the whole pore more accurately. In this model, a decreasing factor for water film in the gas-water miscible zone is used to describe the decrease of water velocity in the gas-water miscible zone, which leads to the gas velocity decrease correspondingly. The new flow model considers the interaction among gas and water molecules in the miscible zone and can provide more accurate velocity profiles compared with the flow models not considering the miscible region. Comparison calculation shows that the previous model overestimates the flow velocity, and the overestimation increases with the decrease of the pore radius. Based on the new gas-water flow model, a new permeability correction factor is deduced to consider the interaction among gas and water molecules.