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Knowledge tracing (KT) is the task of modelling students’ knowledge state based on their historical interactions on intelligent tutoring systems. Existing KT models ignore the relevance among the multiple knowledge concepts of a question and characteristics of online tutoring systems. This paper proposes a neural Turing machine-based skill-aware knowledge tracing (NSKT) for conjunctive skills, which can capture the relevance among the knowledge concepts of a question to model students’ knowledge state more accurately and to discover more latent relevance among knowledge concepts effectively. We analyze the characteristics of the three real-world KT datasets in depth. Experiments on real-world datasets show that NSKT outperforms the state-of-the-art deep KT models on the AUC of prediction. This paper explores details of the prediction process of NSKT in modelling students’ knowledge state, as well as the relevance of knowledge concepts and conditional influences between exercises.

In this work, a flowing material balance equation (FMBE) is established for undersaturated coalbed methane (CBM) reservoirs, which considers immobile free gas expansion effect at the dewatering stage. Based on the established FMBE, five straight-line methods are proposed to determine the control area, initial water reserve, initial free gas reserve, initial adsorbed gas reserve, original gas in place, as well as permeability at the same time. Subsequently, the proposed FMBE methods for undersaturated CBM reservoirs are validated against a reservoir simulation software with and without considering free gas expansion. Finally, the proposed methods are applied in a field case when considering free gas expansion effect. Validation cases show that the straight-line relationships for the proposed five FMBE methods are excellent, and good agreements are obtained among the actual reserves and permeabilities and those evaluated by the proposed five FMBE methods, indicating the proposed five FMBE methods are effective and rational for CBM reservoirs. Results show that a small amount of free gas will result in a great deviation in reserve evaluation; hence, the immobile free gas expansion effect should be considered when establishing the material balance equation of undersaturated CBM reservoirs at the dewatering stage.

Capillary spontaneous imbibition mainly occurs in fractured reservoirs, low permeability reservoirs, and unconventional reservoirs, simultaneously accompanied by high temperature and pressure. In t...

Currently, a key scientific question has been urgently raised up by nanoscale associated industry that how to generate precise prediction results of transport capacity for nanoconfined water. The proper solution for the aforementioned issue will directly contribute to the development as well as economic interests of the related industry. Notably, unlike well-established theory for water transport through conventional pore scale, flow behavior of nanoconfined water remains unclear nowadays to a large extent resulting from the varying intermolecular interactions between water and pore surface. The interplay between water molecules and pore surface has tremendous effects on near-wall water physical properties, including viscosity, density as well as the boundary condition. These effects can be reasonably overlooked at the macroscopic scale, however, play crucial roles when it comes to nanoscale and should be properly treated. Herein, a novel model is developed to characterize water transport capacity within nanopores, in which above physical properties of nanoconfined water are related to surface wettability explicitly representing water-wall interactions. Meanwhile, apparent permeability, a concept from the petroleum industry is employed here to describe the transport capacity of nanoconfined water. Results show that (a) effect of surface wettability will become stronger within smaller pore dimension and enhance factor will increase with the increase of contact angle at a certain pore radius as a result from the stronger water slip phenomenon; (b) Due to the weak effect of surface wettability on nanoconfined water transport capacity at large pore size, enhance factor will close to one with the increase of pore size. (c) Through analyzing effect of critical thickness of the interfacial region, it can be demonstrated that the proposed model can be applied to the majority of pore surface of contact angle larger than 100° with high accuracy. Moreover, utmost caution should be paid when using the proposed model to pore surface with contact angle is relatively small (

As an unconventional gas resource, coalbed methane (CBM) reservoir has unique flow mechanism and production scheme compared with conventional and other unconventional gas reservoirs. At present, many investigators have done a lot of researches on CBM productivity prediction. However, few studies consider variable mass flow within hydraulic fracture and hydraulic fracture conductivity decrease in the model. Thus in order to accurately forecast gas productivity, the pressure propagation process, gas-water two phase flow in coal formation, stress sensitivity and coal matrix shrinkage in cleat system, variable mass flow within hydraulic fracture, and fracture conductivity decrease should be considered simultaneously when establishing gas production model of CBM wells. In this work, firstly the pressure propagation model is established for vertically fractured CBM wells and vertical CBM wells without fracturing. Secondly, the pressure drop model in the hydraulic fracture is developed considering variable mass flow and conductivity decrease in the hydraulic fracture. Thirdly, based on the pressure propagation model, the dynamic permeability model considering stress sensitivity effect and matrix shrinkage effect, the pressure drop model in the hydraulic fracture considering variable mass flow and conductivity decrease in the hydraulic fracture, a multi-factor coupled CBM well productivity equation is established and solved using numerical methods. Fourthly, the proposed models are validated by numerical simulation and compared with numerical simulation when variable mass flow and conductivity decrease in the hydraulic fracture are considered. Finally, the main factors influencing the productivity of CBM wells are analyzed. Excellent agreements between gas (water) production rate by the proposed models and simulations are obtained when variable mass flow and conductivity decrease in the hydraulic fracture are not considered, indicating that the degradation form of the proposed gas productivity model for CBM wells is rational and accurate to predict the gas production of CBM wells. More importantly, when variable mass flow and conductivity decrease in the hydraulic fracture are considered, the proposed model matches the actual data better than the commercial simulator, exhibiting the superiority of the proposed model in some cases. Preliminary study results show that: the cumulative gas production of CBM wells (CGPC) decreases sharply when permeability is less than 0.5 mD. CGPC increases with increasing the hydraulic fracture length but reaches a plateau after a given value. The stress sensitivity of the cleat system decreases early production, while, the matrix shrinkage improves the productivity of CBM wells at late production stage. The permeability decreasing index of the hydraulic fracture directly leads to the rapid decrease in gas production rate of CBM wells. Because the pressure propagation process, the dynamic permeability, the variable mass flow within the hydraulic fracture, and fracture conductivity decrease are accounted for in the productivity equation of CBM wells, it can predict the actual productivity of CBM wells more accurately and provide a theoretical basis for the development of CBM reservoirs.

Good knowledge of nanoconfined gas flow behavior will significantly contribute to advance ultimate gas recovery from shale gas reservoirs. However, up to now, it has still been extremely challengin...

Effect of pore geometry on nanoconfined gas transport capacity has not been clearly revealed. Elliptical cross-section can vary from circular to slit-like shape by adjusting the aspect ratio (AR), which covers a wide range of pore shapes and shares more research value over that of regular cross-section. In this paper, a novel analytical model for gas transport in elliptical nanopores is established based on weighted superposition of continuum flow and Knudsen diffusion, which possesses more solidified theoretical background than existed models for elliptical nanopores. Results show that contribution of Knudsen diffusion will increase with the increase of AR at a certain pore scale. For a certain pressure point, the contribution of continuum flow mechanism within large pore scale will be greater than that within small pore scale. The discrepancy of simplifying elliptical cross-section as circle is about 90% in continuum flow, 50% in slip flow and 10% in transition flow as well as Knudsen diffusion. The proposed model can advance current understanding of gas transport characteristics through realistic shale matrix.

To date, the development of coalbed methane (CBM) reservoirs has attracted a great deal of attention due to its considerable perspective reserves. As a result, nearly all research aspects of CBM reservoirs have been extensively investigated and expect to advance gas production performance as well as associated economic value. Notably, amongst the most significant issue influencing the production performance is the production strategy optimization, which however remains challenging because of the complex time-varying fluid flow performance during the development process of CBM reservoirs. It is always difficult but crucial to shed light on the optimal drawdown pressure within different production scenarios. According to the gas-water two-phase version productivity equations which have been proposed in our previous work, a set of quantified optimization criterion for production strategy within the entire CBM well production process is developed for the first time in this research paper. The proposed optimization criterion contains three procedures: (1) the gas well maintains the bottom-hole pressure (BHP) as critical desorption pressure until the pressure wave propagate to the boundary; (2) the BHP is set as the critical pressure, which is firstly proposed herein and determined by gas phase productivity equation, until the pressure at the boundary become below the critical desorption pressure; (3) the gas well maintains the BHP as the abandonment pressure. In order to clarify the validity of the proposed criterion, we applied the optimization criterion to an actual CBM well located in Hancheng field, China, and found the case with optimized production strategy achieved much better gas recovery compared with that based on the previous production strategy. Moreover, production evaluation work is performed based on the utilization of the proposed optimization method, it indicates that optimized gas production can attain relatively high gas production rate in the future three years. The optimization method possesses simple and easy-operation advantages, which shares great application potential in actual CBM fields and turns out to be practical. In addition, because a practical optimization method for scheduling production strategy of CBM wells has not been proposed before, this work is able to fill the knowledge gap and will contribute to the efficient development of CBM reservoirs.

Shale, known as the “tight” rock with abundant nanopores, exhibits extremely low permeability on the order of micro/nanodarcy. The classic Darcy law, being widely and successfully used in conventional porous media, becomes insufficient for the shale. In this work, on the basis of molecular dynamics (MD) simulations data available in the literature, a model for oil transport through a single nanopore is established by considering the boundary slip and the varying viscosity of the confined oil. Then, the established model for the single nanopore is integrated into the generalized lattice Boltzmann method (GLBM) to mimic the oil transport in the shale with nanopore networks, successfully scaled up to the nanoporous media. The results show that, to accurately predict the oil transport properties in inorganic and organic nanopores, the viscosity correction for the confined oil transport in the nanopores is necessary. The oil transport capability in organic nanopores is greatly enhanced compared with that predicted by the no-slip Poiseuille equation, significantly enhancing the flow capability in the scale of nanoporous media, while the small slip length in the inorganic matter (IOM) has neglected effect. The large liquid slip in organic matter (OM) also results in the apparent oil permeability of shale increases with the total organic content (TOC), although the fact that pore sizes within OM are universally smaller than that in IOM. This work provides a better understanding of the oil transport behaviors in a single nanopore and the nanoporous shale, and paves a feasible way to the exact numerical simulation for oil transport in nanoporous shale.

Precise characterization of dynamic desorption area is crucial for accurate production prediction, production strategy formulation, and well pattern optimization of coalbed methane (CBM) reservoirs. However, little attention has been focused on this topic and a handful of related previous researches suffer some fatal deficiencies. Thus, the objective of this work is to overcome these deficiencies and then extensively investigate the propagation behavior of desorption area during CBM recovery. During depressurization development process of CBM reservoirs, due to the effect of gas desorption, gas saturation takes place in the original water-saturated coal seams, which will decrease the expansion speed of desorption area. Moreover, saturation distribution in the whole coal seam is a dynamic parameter during CBM recovery, which plays an important role for the propagation behavior of desorption area but has not yet been captured in current models. Firstly, pressure-squared concept is utilized to describe pressure distribution within desorption area, which has been considered as an effective method. Secondly, based on the partial differential equation of subface fluid flow accounting for gas desorption, the formulas for pressure-saturation relationship are derived. Finally, according to material balance equation for infinitesimal coal seams, a novel mathematical model for desorption area is developed. Results show that: (a) shape of desorption area will transition from ellipse into a circle with production proceed; (b) matrix shrinkage effect has few influences on the expansion of desorption area at a certain cumulative gas production; (c) rapid decrease of BHP will result in a small desorption area for actual production of CBM wells. The research, for the first time, provides an accurate and fast semi-analytical model to simulate propagation behavior of desorption area. Also, the proposed model is easier to setup and less data-intensive than a numerical simulator. Considering the interests for development of CBM reservoirs, the research can serve as an effective tool for gaining a better understanding of the flow physics in the whole coal seam.

Accurate determination of permeability is critical for the efficient development of coalbed methane (CBM) reservoirs. Permeability determination is mainly based on the feature straight-line analysis method and the plate fitting method requiring pressure build-up data. Although few analytical methods only require dynamic production data, they usually have limitations in application due to complicated solution processes or insufficient consideration of CBM reservoir characteristics. This study improves the previous method for determining the permeability of undersaturated CBM reservoirs. Firstly, mathematical models are established for calculating permeability of undersaturated CBM reservoirs with constant permeability and variable permeability due to pulverized coal output/blockage, matrix shrinkage, and stress dependence during the production process. Secondly, the proposed models are validated by numerical simulation, analytical, and pressure build-up test methods. Finally, the models are applied to the Muai CBM reservoir in Sichuan Basin, China. High-, middle-, and low-permeability zones of the Muai reservoir are classified. The results show that when bottom-hole pressure and water production data of CBM wells during single-phase water flow period are processed by the proposed method and plotted in a rectangular coordinate system, a strong linear relationship can be obtained for CBM reservoirs with constant permeability and variable permeability. The slope of the fitted equations can be used to determine permeability efficiently and accurately. Compared with previous methods, the new method provides better interpretation results for CBM wells with strongly fluctuating production data since the use of the integration of fluctuating data and cumulative water production reduce the effect of production fluctuation on the results. Due to its conciseness, this method can rapidly calculate reservoir permeability around a large number of production wells and obtain permeability distribution in the reservoir, providing guidance for CBM productivity forecasting and development policy adjustment.

The low permeability of unconventional gas reservoir makes it difficult to achieve good development effect. Hydraulic fracturing technology and multi-lateral well technology are usually adopted to increase the gas production. What's more, the permeability may change dynamically during the production process because of the effective stress, gas slippage and matrix shrinkage effect. In this paper, we first establish the productivity equation of radial multi-branch horizontal (RMBH) well in unconventional natural gas reservoirs, considering the dynamic change of permeability during the production process. Then, the productivity equation of radial horizontal well with 2 branches is compared with fractured vertical well and conventional horizontal well productivity equations proposed by former researchers. Finally, main factors influencing the productivity of unconventional natural gas RMBH well are analyzed, including well structure parameters, gas formation properties and production stage. Results show that the productivity equation of degenerated RMBH well with 2 branches is proven to be reasonable by comparison with those of vertically fractured well and horizontal well. RMBH well shows more advantage in the formation with relatively large difference between maximum and minimum stresses, indicating that this type of well configuration may be an alternative technique for improving gas production in unconventional gas reservoirs. Sensitivity analyses demonstrate that the gas production rate of RMBH well is sensitive to branch length, branch number, build-up section horizontal distance, and stress dependence effect. The radial horizontal well with 4 branches can achieve a best development effect and economical benefit.

The exploration and development of unconventional resources have been of growing interest in the industry in recent years. It is widely known that the adsorption and desorption mechanisms of unconventional gas have great significance for gas accumulation and exploration. However, major researches based on the mechanism of solid-gas interface have failed to reveal it completely, which introduce large discrepancies between actual and predicted production. In this paper, the mechanism of solid-liquid-gas adsorption and desorption interface is enlightened to describe the characteristics of unconventional gas. The validity of the proposal was verified preliminarily by building a conceptual model which redefines the gas-water distribution. Furthermore, the possibility of production of gas trapped in micropores was first investigated. The findings of this study can help for better understanding of the adsorption, desorption, and production mechanisms and in unconventional gas system. Accordingly, the explanation of variation between experiment result and actual production rate even with physical parameters was reasonable in theory. Therefore, this work should provide a basis for improving the accuracy of production predictions in actual reservoirs and should assist analysts in determining reasonable unconventional gas target.

Summary Low-permeability coalbed-methane (CBM) reservoirs possess unique pressure-propagation behavior, which can be classified further as the expansion characteristics of the drainage area and the desorption area [i.e., a formation in which the pressure is lower than the initial formation pressure and critical-desorption pressure (CDP), respectively]. Inevitably, several fluid-flow mechanisms will coexist in realistic coal seams at a certain production time, which is closely related to dynamic pressure and saturation distribution. To the best of our knowledge, a production-prediction model for CBM wells considering pressure-propagation behavior is still lacking. The objective of this work is to perform extensive investigations into the effect of pressure-propagation behavior on the gas-production performance of CBM wells. First, the pressure-squared approach is used to describe the pressure profile in the desorption area, which has been clarified as an effective-approximation method. Also, the pressure/saturation relationship that was developed in our previous research is used; therefore, saturation distribution can be obtained. Second, an efficient iteration algorithm is established to predict gas-production performance by combining a new gas-phase-productivity equation and a material-balance equation. Finally, using the proposed prediction model, we shed light on the optimization method for production strategy regarding the entire production life of CBM wells. Results show that the decrease rate of bottomhole pressure (BHP) should be slow at the water single-phase-flow stage, fast at the early gas/water two-phase-flow stage, and slow at the late gas/water two-phase-flow stage, which is referred to as the slow/fast/slow (SFS) control method. Remarkably, in the SFS control method, the decrease rate of the BHP at each period can be quantified on the basis of the proposed prediction model. To examine the applicability of the proposed SFS method, it is applied to an actual CBM well in Hancheng Field, China, and it enhances the cumulative gas production by a factor of approximately 1.65.

It is a well-established fact that mineral matter in actual ultra-tight gas reservoirs presents a strong affinity for water. However, the presence of water within nanopores has not drawn due attention and is generally overlooked by previous literature. Furthermore, the other key physics required to be captured is how to upscale the gas conductance from a single nanopore to a core scale, which greatly aggravates the complexity of the issue. To date, the comprehensive apparent permeability model considering the aforementioned features is still lacking and the intent of this research is to achieve this goal. Firstly, the Beskok’s model is utilized to characterize bulk-gas transport behavior through nanotubes. And Li’s model is employed to quantify water storage mechanisms, which are based on thermodynamic equilibrium theory between liquid and vapor. More features, such as stress dependence and real gas effect are incorporated. Thus, the apparent permeability model for a single nanopore is developed. Secondly, actual core sample is discretized to numerous little cells and the pores within each cell are assumed to possess uniform pore size, which are assigned by Monte Carlo sampling from pore size distribution (PSD). Thus, the transport capacity of each cell can be quantified by utilizing the aforementioned established model for a single nanopore. Finally, based on apparent permeability of each cell, a reliable geostatistical method is employed to calculate the effective permeability of the core sample. And the proposed apparent permeability model for actual ultra-tight gas reservoirs is successfully verified against experimental data collected from published documents. Subsequently, we identify the effect of PSD, relative humidity, real gas effect and stress dependence on the apparent permeability of actual ultra-tight gas reservoirs. Results show that the presence of heterogeneity in 2D will contribute to the increase of effective permeability and the influence of water condensation only works when the relative humidity is relatively high (>0.8). Moreover, the real gas effect has little effect on the gas transport behavior at a certain pressure and can be neglected.

The petroleum geological features of hydrocarbon source rocks in the Oriente Basin in Ecuador are studied in detail to determine the potential of shale gas resources in the basin. The favorable shale gas layer in the vertical direction is optimized by combining logging identification and comprehensive geological analysis. The thickness in this layer is obtained by logging interpretation in the basin. The favorable shale gas accumulation area is selected by referring to thickness and depth data. Furthermore, the shale gas resource amount of the layer in the favorable area is calculated using the analogy method. Results show that among the five potential hydrocarbon source rocks, the lower Napo Formation is the most likely shale gas layer. The west and northwest zones, which are in the deep-sea slope and shelf sedimentary environments, respectively, are the favorable areas for shale gas accumulation. The favorable sedimentary environment formed thick black shale that is rich in organic matter. The black shale generated hydrocarbon, which migrated laterally to the eastern shallow water shelf to form numerous oil fields. The result of the shale gas resource in the two favorable areas, as calculated by the analogy method, is 55,500 × 108 m3. This finding shows the high exploration and development potential of shale gas in the basin.

An abnormality tends to occur in the productivity indicative curves in the process of productivity test interpretation of multi-layer gas wells, resulting in the failure of solutions to their productivity equations and absolute open flow rates. To figure out the reasons for such an abnormality, we established a full-hole calculation model considering the coupling of wellbore variable mass flows and reservoir seepages to calculate a gas production profile and wellbore pressure distribution of a multi-layer productive gas reservoir. Then, based on the analysis of the gas production profile and wellbore pressure distribution characteristics of gas wells at different gas production rates, the root cause for the abnormality in the productivity indicative curves of multi-layer gas wells was analyzed, and a corresponding correction method was proposed and validated based on some examples. And the following research results were obtained. First, there are two reasons for the abnormal productivity indicative curves of multi-layer gas wells. On the one hand, there is a variable mass pipe flow in the wellbore of multi-layer sections and a flowing pressure gradient decreases with the increase of well depth. And the flowing pressure in the middle of the reservoir which is converted based on the flowing pressure gradient above the pressure gauge is higher than the real value. On the other hand, the pressure in the multi-layer producing sections doesn't realize a balance after well shutdown for a short time, so the measured static pressure is greater than the one measured when the pressure of each layer gets balanced after well shutdown for a long time. Second, the flowing pressure obtained from the productivity test interpretation of multi-layer gas producer shall be converted based on the pressure measured by the pressure gauge within 200 m above the reservoir top and it is necessary to adopt the static pressure measured after the balance of wellbore pressure. Third, the reliability of the model, the rationality of the abnormality reason analysis and the validity of the correction method are verified based on calculation examples and cases. It is concluded that the research results provide a technical support for the productivity evaluation of multi-layer gas wells. Keywords: Multi-layer gas reservoir, Commingling, Productivity test, Indicative curve, Variable mass flow, Abnormality correction, Flowing pressure, Static pressure

Accurate acquisition of reservoir properties can provide an important basis for the evaluation of coalbed methane (CBM) reservoirs. To date, there are many methods that can be utilized to estimate reservoir properties. Analyzing production data by productivity equation has attracted attention of many researchers due to its simple and convenient characteristics. However, most of the productivity analysis methods are established for non-fractured wells in conventional sandstone gas reservoirs, and have restrictive requirements on boundary conditions, that is, the dominant flow-regime is boundary-dominated flow. Some CBM reservoirs have extremely low porosity and permeability, which need hydraulic fracturing to achieve greater yields. Furthermore, the reservoir fluid flow gradually changes from single-phase water flow to gas-water two-phase flow during the production process, which can increase seepage resistance and change the form of pressure propagation. Hence, there are some limitations for conventional method of productivity analysis when applying to CBM reservoirs, and the prediction results tend to have greater deviation. In this paper, a new method for evaluating formation properties of under-saturated CBM reservoirs is proposed. The method takes into account the characteristics of pressure propagation and only requires production data in single-phase water flow stage. In addition, some CBM wells are not appropriately controlled during dewatering process resulting in stress sensitive and permeability change. For this kind of wells, this paper also puts forward the relevant method to estimate the permeability change coefficient of reservoirs. The evaluation method is applicable to reservoirs which have long single-phase water flow period without well interference during the process and the pressure does not propagate to the flow boundary in dewatering stage. Hence, the greatest advantage of the proposed method is that the reservoir properties can be easily obtained only by using the water production and well bottom hole flowing pressure data at the early production stage of CBM wells. The proposed method is verified by numerical simulation data and production data calculated by analytical method, which show that this novel method is more appropriate to apply to CBM reservoirs. It is convenient and reliable in providing basic parameters for reservoir evaluation and production prediction.

The hydraulic fracturing fluid can easily infiltrate the ultra-tight shale matrix due to the remarkable slip feature of the liquid flow in nanoscale pores, showing a higher-than-expected fluid-loss in shale gas development. In this paper, a stochastic apparent liquid permeability (ALP) model is developed to reveal water transport mechanisms in dual-wettability nanoporous shale based on the transport behavior in a single nanotube. The present model considers the wettability and pore size related liquid slip effect, total organic carbon (TOC) content, and the structural parameters (maximum and minimum pore size of inorganic or inorganic matter, porosity) of shale matrix. The results show that the multilayer sticking effect (structural water molecules in the pore surface) constricts the flow capacity and slightly decreases the ALP for the inorganic hydrophilic matter, while, a large slip length for the water flow can be observed and the ALP is dramatically improved if the nanopores in the organic matter are strong hydrophobic, especially in organic-rich shale reservoir. The ALP can be reduced or enhanced with the increase of TOC content, which is determined by the relative importance of pore size difference (between organic matter and inorganic matter) and wettability of organic matter. Additionally, the sensitivity analysis of structural parameters on the ALP are examined.

Summary Vertically fractured wells are used widely to achieve efficient development of low-permeability reservoirs and unconventional tight reservoirs. Currently, there are some commonly adopted productivity models for a fractured vertical well, including the Giger (1985) model, the Economides model (Economides et al. 1989), the Joshi (1991) model, the Guo model (Guo and Evans 1993), the Zhang (1999) model, and others. However, these models are only suitable for either short fractures or long fractures, and thus cannot satisfy the need for arbitrary-length fracture selection. In addition, these models have certain requirements for boundary conditions, and few models consider the nonuniform flow in actual hydraulic factures. Therefore, it is desirable to establish a productivity model for vertically fractured wells with arbitrary fracture length under complex boundary conditions. In this paper, first, we evaluate the existing fractured-vertical-well productivity models in detail. After that, on the basis of the potential superposition principle and mirror-image method, we develop the productivity model for a fractured vertical well with arbitrary fracture length under different boundary conditions. Grounded in this model, further considering the frictional pressure drop caused by fracture-flow nonuniformity, we establish the productivity equation of a finite-conductivity-fracture vertical well with nonuniform flow in the fracture. Finally, after comparing with the existing model under certain conditions, the reliability of the proposed model is verified successfully. Results show that the Giger model assumes that the boundary in the fracture-extension direction is impermeable, and the pressure wave reaches the boundary earlier than the constant-pressure boundary, which is perpendicular to the extension direction of the fracture, whereas both the Economides model and the Joshi model assume that the boundary in the fracture-extension direction is far, and is always farther than the boundary perpendicular to the direction of the fracture extension. The results forecast by the previous models will deviate greatly from actual well-production performance, if the real field case cannot meet the requirements of these models. The proposed model is not only in good agreement with the previous models at given conditions, but is also suitable for fractured vertical wells under arbitrary-length fractures and complex boundary conditions. Compared with the existing models, the correctness and reasonableness of the model are shown, and the application of the proposed model is broadened. For the development of low-permeability and unconventional tight oil and gas reservoirs with fractured vertical wells or fractured horizontal wells, the establishment and application of this model have great theoretical significance and application value for production prediction. This model can be a foundation or reference for productivity prediction of low-permeability and unconventional tight oil and gas reservoirs with fractured vertical wells or fractured horizontal wells.

Although many breakthrough efforts have been made in recent years, it is still challenging to gain a clear knowledge of the variation regularities of effective gas/water phase permeability with the pressure depletion. The reasons behind this phenomenon can be attributed to the coexistence of multiple effects and the transition of the flow behavior at different production stages. To date, the fully-coupled model for effective gas/water phase permeability in coal-bed methane (CBM) reservoirs is still lacking and is significantly necessary to be developed. Firstly, the Palmer-Mansoori (PM) model is employed to represent the variation relationship between absolute permeability and pressure. Secondly, after rigorous derivation of the gas–water two phase partial differential equations in coal seams, the relationship between pressure and saturation in infinitesimal coal is obtained, which can be solved through an iterative algorithm. Subsequently, combined with the Corey relative permeability model, the relative gas/water phase permeability can be described as a function of pressure. Finally, coupling the absolute permeability model and relative permeability model, the effective gas/water phase permeability can also be quantified as a function of pressure or saturation. And the reliability and the accuracy of the proposed model is successfully verified through comparisons with experimental data and previous model collected from published literature. Furthermore, on the basis of the proposed semi-analytical model, the effects of critical desorption pressure, gas desorption capacity, stress dependence, and matrix shrinkage on effective permeability are identified. And many implications and direct insights are achieved through the sensitive analysis process. The semi-analytical model, for the first time, incorporates nearly all known mechanisms and can achieve more accurate characterization of effective permeability during the production process. Moreover, due to the concise form and precise feature, the proposed model will serve as a simple, practical and robust tool for the development of CBM reservoirs.

As one of the important unconventional resources, coalbed methane (CBM) can mitigate energy shortage issue, and its efficient exploitation has received widespread attention globally. The development of CBM is of great significance to coal mine safety and energy supply. CBM reserve evaluation provides a basis for selecting development zones and determining development strategies. However, most existing CBM reserve evaluation methods do not consider the effects of dissolved gas, free gas and the difference between initial reservoir pressure and critical desorption pressure. Thus, the predicted results usually deviate from the actual reserve. In this paper, firstly, the material balance equation (MBE) for early dewatering stage considering the effect of stress sensitivity on porosity is established, and the initial free gas and dissolved gas reserves of undersaturated CBM reservoirs can be obtained. Secondly, the MBE for gas desorption stage is derived, in which the effects of stress sensitivity, matrix shrinkage and dissolved gas are considered. So the original gas in place (OGIP) of CBM reservoirs can be solved. Next, the correctness and rationality of MBEs for early dewatering stage and gas desorption stage are verified against King's MBE method and CBM dynamic analysis software. Finally, this method is applied to actual production wells. The results show that in early dewatering stage, 1 − S wi α c p + α S wi c w p ¯ Z ¯ − p i − p ¯ p ¯ Z ¯ and W p B w − W e α p ¯ Z ¯ + G p p sc T Z sc T sc have a linear shape, and the control area of CBM reservoir can be calculated based on the slope of the straight line. In addition, the ratio of the intercept to the slope of the straight line can be used to calculate the initial free gas and dissolved gas reserves of undersaturated CBM reservoirs. During gas desorption stage, p/Z* and Gp have a linear relationship. OGIP of CBM reservoirs can be obtained by the ratio of y-intercept to the slope of the straight line. Using gas and water production data provided by CBM dynamic analysis software, the reserves of undersaturated CBM reservoirs evaluated by the proposed method are in good agreement with those from CBM dynamic analysis software, which proves that the proposed material balance equations and corresponding methods are reasonable and reliable. The material balance equations and methods presented in this paper take into account the effects of various factors such as the difference between initial reservoir pressure and critical desorption pressure, pore compressibility, water compressibility, coal matrix shrinkage, dissolved gas, and free gas. The proposed reserve calculation methods for undersaturated CBM reservoirs can provide an important basis for selecting dominant production area, determining well spacing and guiding development policy.

Understanding mechanisms of gas transport in shale matrix pores is of great importance for more accurate production prediction of shale gas wells. Shale matrix is generally considered to be composed of organic matrix and inorganic matrix, and the gas transport mechanisms in different types of matrix pores are different. To date, most of the gas transport models assume that the gas transport channels in shale porous media are cylindrical capillaries or slits with uniform pore size, which ignore the effect of pore size distribution (PSD) on gas transport capacity. In addition, there are few transport models considering the presence of water in inorganic matrix, and the gas transport capacity will be overestimated ignoring this factor. Therefore, a real gas transport model for shale matrix pores is proposed so that the shale gas transport behavior can be analyzed more accurately. First, the nanopores in shale matrix is represented by cylindrical capillaries, and a logarithmic normal distribution function is utilized to characterize the PSD in shale organic and inorganic porous media. Then, the gas transport models are constructed for organic porous media and inorganic porous media, respectively. The total transport model can be obtained by coupling the two types of models. What is more, the influence of stress dependence and real gas effect are taken into account in the models. After that, the models are validated, which show that the proposed models fit well with published experimental data. Finally, the influence of multiple factors on gas transport capacity is analyzed, the results show that the total apparent permeability increases with the increase of total organic carbon (TOC) when the pressure is higher than 5 MPa, and it decreases with TOC as the pressure is lower than 5 MPa. The adsorption and desorption of gas in organic nanopores cannot be neglected, and its influence on slip flow is greater than that on Knudsen diffusion. The apparent permeability of inorganic nanopores decreases with relative humidity (water film thickness), and it decreases more rapidly when the relative humidity is higher than 0.5. The PSD has a great influence on shale gas transport capacity of porous media, especially for inorganic porous media.

To date, much attention has been focused on the high-permeability CBM reservoirs, which results in ignorance of pressure and saturation gradients in the coal seams of previous productivity equations. However, for the low-permeability CBM reservoirs (

The flowing material balance (FMB) equation is a frequently-utilized engineering tool to extract reservoir information according to production performance of producing wells. At present, it is still significantly challenging to adapt the FMB equation to CBM reservoirs due to the existence of gas-water two phase flow, stress dependence, matrix shrinkage and gas desorption. With all my respect to previous FMB equations for CBM reservoirs, a great deal of attention has been drawn to the single water/gas flow, which can only be applied for early production stage or cannot capture the gas-water two phase flow features of general CBM reservoirs. The most recent and comprehensive research effort of FMB equation for CBM reservoirs is performed by Clarkson and Salmachi (2017), which takes the aforementioned characteristics into account. However, suffering the limitation that the pressure-saturation relationship is not available, Clarkson and Salmachi (2017) assume the saturation and pressure gradients in coal seams are negligible, i.e., the relative permeability is not incorporated in the pseudo-pressure calculation, which will inevitably lead to large deviation compared with the precise results. Notably, during the depressurization development process of low-permeability CBM reservoirs, the pressure and saturation gradients are large enough and cannot be overlooked. Thus, a robust FMB equation for gas-water two phase flow in low-permeability CBM reservoirs is still lacking in the petroleum industry and is significantly necessary to be developed. In this study, the important pressure-saturation relationship is rigorously derived in terms of the conservation of mass and momentum equations, in which the gas desorption, matrix shrinkage and stress dependence are fully coupled. Next, the developed relationship is used to calculate the gas/water phase pseudo-pressure and subsequently the previous FMB equation for CBM reservoirs is modified. Finally, reliability of proposed FMB equation is successfully verified against the numerical simulation with excellent agreements compared with the input reservoir properties. In addition, with the intent of further solidifying the field applicability of the modified FMB equation, the production performance of an actual low-permeability CBM well in Hancheng field, China is analyzed through the proposed FMB equation and desirable interpretation results are achieved. Incorporating the pressure-saturation relationship for the first time, the modified FMB equation can serve as a practical and robust tool to extract valuable information regarding the low-permeability CBM reservoirs.

Although considerable advances have been achieved in recent years, it is still challenging to describe gas-water two phase flow behavior in low-permeability CBM (Coalbed methane) reservoirs. The pressure propagation characteristics at different production stages are generally overlooked, which play a crucial role to affect overall productivity and are required to be incorporated. In this work, a completely new production prediction model is established. Firstly, to consider pressure and saturation gradients, the pressure-saturation relationship is developed after rigorous derivation process in terms of partial differential equations for gas-water two phase flow. Subsequently, the gas/water phase productivity equations are modified on the basis of the key relationship. Secondly, according to the relationship between formation pressure and critical desorption pressure, the whole coal seam is divided into desorption area and without-desorption area. Moreover, pressure distribution features in desorption area and that in without-desorption area are characterized. Finally, an efficient iterative algorithm is present to predict the production performance and quantify the expansion regularities of drainage and desorption area at different production stages. The proposed model is utilized to shed light on the optimization of production strategy as well. Some meaningful conclusions and practical insights are drawn.

Previous attempts to characterize the gas transport through inorganic nanopores were not fully successful. The presence of an adsorption water film within nanopores is generally overlooked. Moreover, the compound influences of moisture content and confinement effect on critical properties of the gas phase have not been considered before. With the intent of overcoming these deficiencies, a fully coupled analytical model has been developed, in which complex bulk-gas transport mechanisms, moisture content, confinement effect, and various cross-section shapes of nanopores are incorporated. Results show that the confinement effect will significantly enhance the apparent gas permeability when the pore radius is smaller than 5 nm, and the real-gas effect can achieve an average increase of 4.38% when the pore radius falls in the range 1–2 nm. The stress dependence will greatly decrease the apparent gas permeability and the corresponding degree for slitlike inorganic nanopores will slightly increase with the incre...

A reliable gas–water relative permeability model in shale is extremely important for the accurate numerical simulation of gas–water two-phase flow (e.g., fracturing fluid flowback) in gas-shale reservoirs, which has important implication for the economic development of gas-shale reservoir. A gas–water relative permeability model in inorganic shale with nanoscale pores at laboratory condition and reservoir condition was proposed based on the fractal scaling theory and modified non-slip boundary of continuity equation in the nanotube. The model not only considers the gas slippage in the entire Knudsen regime, multilayer sticking (near-wall high-viscosity water) and the quantified thickness of water film, but also combines the real gas effect and stress dependence effect. The presented model has been validated by various experiments data of sandstone with microscale pores and bulk shale with nanoscale pores. The results show that: (1) The Knudsen diffusion and slippage effects enhance the gas relative permeability dramatically; however, it is not obviously affected at high pressure. (2) The multilayer sticking effect and water film should not be neglected: the multilayer sticking would reduce the water relative permeability as well as slightly decrease gas relative permeability, and the film flow has a negative impact on both of the gas and water relative permeability. (3) The increased fractal dimension for pore size distribution or tortuosity would increase gas relative permeability but decrease the water relative permeability for a given saturation; however, the effect on relative permeability is not that notable. (4) The real gas effect is beneficial for the gas relative permeability, and the influence is considerable when the pressure is high enough and when the nanopores of bulk shale are mostly with smaller size. For the stress dependence, not like the intrinsic permeability, none of the gas or water relative permeability is sensitive to the net pressure and it can be ignored completely.

At present, analyzing and predicting CBM production performance remains challenging, which can be attributed to the complex gas-water two phase flow and dynamic nature of petro-physical properties. For the sake of simplicity, the saturation distribution in coal seams is generally overlooked and characterized by average water saturation in previous literature, which one can easily handle analytically, semi-analytically, and numerically. However, average water saturation is inadequate to obtain the precise value of pseudo pressure for water/gas phase, which may generate large deviation compared with actual production behavior. To our best knowledge, the relationship between pressure and saturation in coal seams is still lacking in the petroleum industry. Thus, the main objective of this research is to gain a clear understanding of this issue. In this work, on the basis of rigorous derivation, a semi-analytical model for the relationship between pressure and saturation is developed, which comprehensively accounts for the presence of free gas at the early production stage, matrix shrinkage and gas desorption. Notably, the stress dependence effect is incorporated during the entire production process of CBM wells. Subsequently, employing the gas-water two phase relative permeability data, we present an iterative numerical algorithm to solve the model. Moreover, the proposed semi-analytical model is successfully verified against a numerical reservoir simulator. After that, we shed light on the influences of physical parameters upon the saturation distribution versus pressure and achieve a variety of new insights. This research, for the first time, presents a semi-analytical model to quantify the relationship between pressure and saturation, which fills the gap for the theory of gas-water two phase flow in CBM reservoirs. The proposed model is less data-intensive than performing a numerical simulation and turns out to be simple and powerful in the application. In addition, the new model can significantly contribute to the obtainment of precise pseudo pressure for water/gas phase, therefore lays the theoretical basis for the accurate production prediction for CBM wells.

The accurate knowledge of gas transport mechanisms through shale matrix will significantly advance the development of shale gas reservoirs. At present, the different cross-section shapes for organic and inorganic pores have not drawn much attention. In terms of current literatures, the organic pores are considered as hydrophobic and the inorganic pores is hydrophilic, thus the water film can be adsorbed on the surface of inorganic pore. However, the volume occupied by water film is overlooked and its effect on gas transport capacity has not been investigated ever. In this work, the Beskok’s models are employed, which can be applied to characterize the bulk-gas transport mechanisms through circular nanotubes or slit nanopores with arbitrary aspect ratio. In addition, the organic and inorganic nanopores in shale matrix are assumed as nanotubes and slit nanopores respectively. Considering the presence of adsorbed gas phase, the apparent permeability model for organic pores takes bulk-gas transport regimes, surface diffusion and gas desorption into account. Considering the thickness of adsorbed water film, the apparent permeability model for inorganic matter incorporates the bulk-gas transport mechanisms and effect of water film. More features, such as stress dependence, real gas effect, are included in both models. Based on the proposed permeability models, the influences of pore size, formation pressure, and humidity on apparent permeability for organic/inorganic pores are seriously analyzed. Results show that the surface diffusion will dominate the transport capacity when the organic pore size is less than 2 nm. For inorganic pores, it can be concluded that the larger pore radius will obtain the stronger transport capacity. The real gas effect has little influence on apparent gas permeability which can be neglected. The stress dependence, humidity and gas desorption influence the effective radius of nanoscale pores, which have significant effects on transport capacity.

In coal-bed methane (CBM) field development plan, more attention is paid to production forecasting, well spacing optimization, pressure transient analysis and adsorption/desorption mechanism within coal matrix. Few studies were carried out to investigate the expansion of drainage and desorption area based on the characteristics of pressure propagation in CBM reservoir. Moreover, the production rate and bottom-hole pressure (BHP) are usually variable, while the production system in current analytical models are either at constant production rate or constant BHP. When optimizing the production system of CBM well, the knowledge of expansion principle of drainage and desorption area can help obtain the critical time of interference and its intensity, which are both key factors for efficient development of CBM reservoirs. In this paper, a comprehensive method for drainage and desorption area expansion during coal-bed methane production is proposed, in which the variable rate and BHP in different production stages and saturation distribution are considered. The coal seam is divided into two areas, namely desorption and without-desorption area, and the production life is divided into five stages. The pressure profiles at different production stages are detailed investigated utilizing diffusivity equation which is solved by the continuous succession of steady states. By assuming the desorption area with low water-gas ratio and without-desorption area with high water-gas ratio, the pressure-squared approach is applied in desorption area and pressure approach is employed in without-desorption area. Finally, a model for predicting drainage and desorption area is developed by generating pressure profile and material balance equation. The proposed semi-analytical model is verified by numerical simulation with excellent agreement with the simulation data. Results show that the drainage area expands much faster at early production stage than that at late stage when desorption area starts expanding in the coal-bed reservoir. In addition, the production system of CBM well is found to play a significant role in the expansion characteristics of desorption area. Considering these characteristics of CBM, we shed light on the production system optimization in different production stages and apply the developed production system to a CBM well in Qinshui field, China. In summary, this method only requires BHP, gas and water production, and turns out to be simple, reliable and powerful in application.

Much attention has been attracted by the successful development of shale gas reservoir in recent decades. Correspondingly, research aspects of shale gas reservoirs become more and more heat among the academic community, especially in the fields of nanoscale gas transport mechanisms as well as the storage modes. Fascinated by the craft interactions exerted by organic or inorganic shale surface, drastic discrepancy takes place in terms of the gas behavior inside the nanoscale dimension and that in conventional dimension. It is crucial to figure out the exact influence on shale gas recovery and overall production efficiency due to the above large difference. Notably, this paper is designed to comprehensively explore the methane storage behavior in shale nanopores, expecting to provide the direct relationship between adsorption gas and free gas content under various environmental conditions. Also, a novel and simple prediction method with regard to ultimate gas recovery is proposed, which is connected to the pore size distribution and formation pressure. First of all, the gas storage modes in a single nanopore with defined pore size are analyzed seriously. As a result, the evaluation model is constructed for adsorption gas and free gas content in a single nanopore. After that, an upscaling method is applied to extend the adaptiability of the model from single nanopore to nanoporous modia. Finally, sensitivity factor analysis work is performed and a recovery prediction methodology is developed. Results suggest that the adsorption gas content will be a larger contribution to total gas content when it comes to small pore radius and low formation pressure. In contrast, free gas content will increase with the increasing pressure and pore size. More importantly, pore size distribution characteristic has a key impact on gas storage modes and ultimate gas recovery. The high proportion of small nanopores plays a detrimental role on gas recovery, resulting in large content of adsorption gas at low pressure, which will not be produced and remain in shale gas reservoirs.

A great deal of attention has been attracted to the exploitation as well as the development of unconventional gas reservoirs, which expect to act as an essential role in counterpoising the daily increasing energy demand around the world. In this research, with the intent of contributing to the successful development of coalbed methane (CBM) reservoirs, which is an indispensable member of the family of unconventional gas reservoirs, a novel production prediction model is proposed for fractured vertical CBM wells. The main difference of the research compared with previous excellent documents is taking the effect of pressure propagation behavior on production performance of CBM wells into account. In general, CBM reservoirs possess the low-permeability (

In the early production stage of coalbed methane (CBM) wells, especially in low permeability reservoirs, the method of shutting in casing annulus is usually adopted. However, the current commercial numerical simulation software fails to predict the dynamic performance of CBM wells under the control of both bottom-hole pressure and casing pressure. In this work, the calculation models of wellbore-pressure distribution and formation pressure distribution are derived firstly. Then, the above two models are coupled with several CBM dynamic performance analysis (CBMDPA) models developed in our previous researches, including pressure propagation model, water/gas productivity equations, dynamic permeability model, and material balance equation. A new CBMDPA program is developed with the coupling model, which can simulate the dynamic production performance of CBM wells after inputting the basic reservoir and fluid parameters, casing pressure, and bottom-hole pressure. Next, the newly developed CBMDPA program is validated against four field cases in China, and excellent agreements are obtained. The inputs of our CBMDPA program include casing pressure, bottom-hole pressure, and some deterministic and uncertain reservoir and fluid parameters. By adjusting the uncertain parameters, the gas production history can be fitted, and the uncertainty on the determination of reservoir properties can be addressed. On this basis, the future gas production is predicted using the determined parameters and the scheduled bottom-hole pressure and casing pressure. Finally, the influence of casing pressure on gas production is studied. Results show that high casing pressure has detrimental impact on the maximum daily gas production, while, it plays a positive role to achieve great desorption area, which will further prolong the stable gas production period. Under the high casing pressure of 2.5 MPa, the maximum daily production is decreased by about 54%, but the stable production stage is prolonged to more than 3000 days. It indicates that an appropriate range for casing pressure is favorable, considering both the accumulative gas production and the desorption area. For the case with representative properties from Muai block, the casing pressure is suggested to be 1–2 MPa, and the range between 1 MPa and 1.5 MPa is recommended for Hancheng block.

A material balance equation (MBE) is usually used to estimate hydrocarbon reserves, to judge driving mechanism, and to predict the dynamic performance of oil and gas reservoirs. Few straight-line methods have been proposed for estimating original gas in place (OGIP) of water bearing gas reservoirs with high water production until now. For this type of gas reservoir, gas and mobile water mostly coexist in the same formation because of low permeability. Lots of water is produced even though there is no bottom or edge aquifer. Thus, the effect of water production on average pressure should not be ignored. In this work, an MBE for water bearing gas reservoirs considering the effects of water compressibility, pore compressibility, and water production, is derived step by step from the basic material balance principle, and the corresponding straight-line reserve evaluation method is developed. Then the proposed reserve evaluation method is validated against a computer modelling group (CMG) simulation case and two field cases using pressure transient analysis (PTA) method in the dynamic data analysis software KAPPA Ecrin. Finally, the necessity and importance of the proposed reserve evaluation method in water bearing gas reservoirs are discussed. Validation cases prove that the proposed straight-line reserve evaluation method for water bearing reservoirs is reliable and rational. The OGIP of water bearing reservoirs can be evaluated directly using the y-intercept divided by the minus slope of the straight line. If ignoring the effect of water production, the OGIP of water bearing gas reservoirs will be underestimated, especially for gas wells with high water production rate and short producing time.

Characteristics of sorption and distribution of water in nanoporous shale are topics of great interest to evaluate unconventional reservoirs. Also, a study of surface force of water/solid interaction at nanoscale is significant for understanding the storage of initial water and the fate of residual treatment liquid in shale systems. In this work, the thickness and stability of water film were investigated by vapor sorption experiments on clay and shale samples. Meanwhile, an approach based on surface forces (disjoining pressure), which resulted in the instability of adsorbed film transition into condensed bulk liquid, was developed to describe molecule/pore wall interactions. Our experimental results directly demonstrated the occurrence of capillary condensation in hydrophilic clay minerals; however, water would not entirely fill in shale nanopores even under high-moisture conditions. This remarkable finding is mainly due to the inaccessibility of water molecules to micropores of hydrophobic organic matte...