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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.

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.

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.

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.

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.

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.

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.

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.

Methane adsorption in shale is a gas–liquid–solid interaction rather than a gas–solid interaction by considering the initial water saturation in actual condition. As an important constituent of inorganic matter, clay minerals may affect gas-in-place of shale systems. Generally, Clay minerals are strongly hydrophilic with a water film bound on its surface, significantly reducing gas sorption capacity, which will lead to overestimate gas-in-place (GIP) of shale gas reservoir. In this work, we analyze the interactions between methane, water film and clay, and results reveal that: methane adsorption on clay (dry) is a typical gas–solid interaction; however, methane adsorption on clay bound water film should belong to gas–liquid interaction. Furthermore, a unified model is established to describe gas-water-clay interactions, in which, gas–solid Langmuir equation and gas–liquid Gibbs equation are integrated by water coverage coefficient. Meanwhile, a mathematical model is presented to quantify thickness of water films by considering surface force interactions between liquid film and clay. Our results show that, the water film thickness in shale clay pores mainly depends on relative humidity and pore size. Under a certain humidity condition (such as 0.98), the water saturation distribute in different sized pores mainly as: (i) capillary water in the small pores (

Based on the critical issues associated with shale permeability measurements, a new experimental approach by modifying the traditional pressure-pulse decay method was developed. In order to reduce the measurement error caused by the pore volumes of the traditional method, we made a new design that the upstream and downstream reservoir volumes can be changed, In addition, we added a by-pass pipe to measure the bidirectional permeability instantaneously, which can reduce the total test time significantly. Except for nitrogen or helium, methane was utilized to measure the shale permeability in this work, which can be more practical and better understand the real gas transport mechanisms in shale. Furthermore, we modified the conventional interpretation model of permeability measurements by incorporating the physical mechanism of gas adsorption. We also performed a series of experimental measurements and data analyses using different cores from pure shale, sand shale, to sandstone, which are from the Ordos basin (Chang 7 section) in China. The results show that: (1) the error caused by the pore volume errors of the traditional method is decreased by nearly half if variable reservoir volumes are used. The total test time is reduced by around 7 h by adding the by-pass pipe on the apparatus. The value of permeability measured with methane is higher than that measured with nitrogen while lower than that measured with helium. (2) The effective gas adsorption porosity increases with the increasing Langmuir pressure and decreasing pore pressure. If without considering gas adsorption, the measured permeability value will be underestimated, especially under lower pore pressure, higher adsorption capacity, and higher Langmuir pressure. (3) The total error is less than 10% using this new apparatus and the modified permeability interpretation method. The measured permeability values are reliable by comparing the measurements using the new apparatus and the standard instrument of ProPDP-200 under the same condition. (4) The influence of gas adsorption on permeability measurement in shale cannot be ignored, and the permeability is underestimated by up to 97% in pure shale while by only 7.5% in sandstone if the gas adsorption is not taken into account.

Despite the recent activities in ultra-thick gas reservoirs worldwide, accurate evaluation of gas wells deliverability remains technically challenging. The success of such evaluation efforts relies heavily on proper consideration of the impact of ultra-thick pay zones. Deliverability equations and corresponding test methods are necessary to predict the deliverability of gas wells in ultra-thick gas reservoirs. In this paper, we develop a new model for calculating the pressure drop along the wellbore with varying mass flow rates from gas production profile testing. A new set of deliverability equations is proposed for gas wells in ultra-thick reservoirs. The new equations incorporate production testing data and are applicable to a wide reservoir pressure range. Correspondingly the deliverability test method for ultra-thick gas reservoirs was proposed. The integrated approach of utilizing deliverability equations and the proposed test method were validated against reservoir simulations that incorporate wellbore pressure drop. Good agreements between simulation and current analytical results were obtained for both low-pressure and high-pressure gas reservoirs. It is appropriate to apply the proposed deliverability equations and the corresponding test method to predict the deliverability of ultra-thick gas reservoirs. Further, validations using field data are in progress.

Retrograde condensation occurs when the reservoir pressure falls below the dew point pressure in gas condensate reservoirs. Complex fluid phase behavior in the reservoir and the wellbore makes it challenging to predict the productivity of gas condensate wells. To date, the gas rate in the deliverability equation of gas well is assumed the gas rate at surface condition converted from that at the reservoir condition by using the volume factor. However, because of the complex fluid phase behavior in gas condensate wells, the gas rate at the reservoir condition cannot be directly changed to that at surface condition by using volume factor. Hence, the development of a new analytical model to accurately calculate the productivity of gas condensate wells is still required and necessary. In this work, we propose a new deliverability equation of gas condensate wells with a consideration of fluid phase behavior in both the reservoir and the wellbore. Also, several pseudo-pressure functions for different condensate distribution and flow models are examined systematically; these include the model before condensation, the model after condensation, but without condensate flow, the model after condensation and with condensate flow, and the model after re-vaporization. Two synthetic numerical simulation cases and two field case studies are performed to validate these deliverability equations for gas condensate wells. Results show that the phase behavior of gas condensate fluid in the wellbore plays a significant role in the deliverability evaluation and in the forecasting of gas condensate wells. If neglecting its effect on the deliverability, gas and condensate production rates could not be accurately predicted. The data from the proposed model have good agreement with the simulation and field production data of wells in Yakela Gas Condensate Reservoir and Yaha Gas Condensate Reservoir in China. If the conventional deliverability equation neglecting the effect of phase behavior in the wellbore was used, the predicted gas production will be higher than the actual value; even 50% higher than the actual value at high flow rates. Through these case studies, it can be concluded that the effect of condensate-gas phase behavior in the wellbore cannot be ignored in the deliverability equation for gas condensate wells. This work can provide a more accurate method of forecasting the gas and condensate production for condensate gas reservoirs and also guide optimization of single well production rate and gas recovery rate for gas condensate reservoirs.

Permeability is a fundamentally important parameter of hydrocarbon reservoir because it significantly impacts well productivity. In laboratories, it is measured under isotropic load which is equal to overburden pressure and it is often assumed to remain unchanged during production. In really however, stress arch forms above the reservoir and the overburden pressure drops during production. Consequently, there is a clear need to illustrate the stress arching effect on the stress sensitivity of permeability and well dynamic performance. Stress arching ratio, which is defined as the change in overburden pressure divided by the change of pore pressure from initial reservoir condition, is calculated for different reservoir shapes in Sulige gas field. Relationship between overburden pressure and effective stress considering stress arching effect in Sulige gas field has been established. Laboratory experiments following reservoir depletion path have been conducted under the stress arching ratio of 0.12 and 0.28 that the reservoir may follow. The results show that the stress sensitivity of permeability greatly depends on stress arching ratio. Permeability measured under nonzero stress arching ratio is larger than that obtained from the conventional experiments with the stress arching ratio of 0 under the same condition. At the pressure drop of 25 MPa, the measured permeabilities increase by 23% and 50% for the stress arching ratios of 0.12 and 0.28, respectively, compared with the values obtained by the conventional experiments when the initial permeability of the core is 0.098 md. In contrast, the permeability shows less dependence on stress arching ratio when the initial permeability of the core is large, such as 7.387 md. Furthermore, the effect of stress arching ratio is introduced into the calculation of well productivity based on the experiment results. The gas well productivities increase by 5.03%, 12.46% and 72.48% for stress arching ratios of 0.12, 0.28 and 1, respectively, when the reservoir initial permeability is 0.098 md. The impact of stress arching ratio on dynamic performance of gas well is generally incorporated via look-up tables of transmissibility multiplier in Eclipse, which is approximate to the ratio of the decreased permeability to the initial permeability for different stress arching ratio. The production decline rate and production decline type are closely related with stress arching ratio when the initial permeability is 0.098 md. This work investigates the stress arching effect on stress sensitivity of permeability for cores with different initial permeabilities. it can provide some insights into gas productivity calculation, production forecasting, and gas recovery determination

Permeability measurement is necessary in oil and gas fields. During the measurement, slippage, rock deformation, and water saturation affect apparent permeability of low permeability sandstones measured by different fluids. It is well known that gas slippage effect is very obvious and crucial in apparent permeability of low permeability sandstones measured for gas. Klinkenberg correlation was proposed to calculate gas permeability and absolute permeability for low permeability sandstones without considering rock deformation and water saturation. Most previous researchers modified the slippage factor b as a function of absolute permeability, porosity, and water saturation. However, few models were proposed for gas permeability calculation, simultaneously considering effects of rock deformation, gas slippage, and water saturation. In this work, Klinkenberg correlation was extended for permeability calculations measured by liquid and gases. The difference between apparent liquid permeability and apparent gas permeability was that gas slippage, which was much more evident from liquid slippage. An apparent gas permeability model was proposed for gas permeability and absolute permeability calculation simultaneously considering rock deformation, gas slippage, and water saturation in low permeability sandstones. The apparent gas permeability is proportional to the term T / p . Both the interception and the slope of the straight line in the T / p – k g plot with Cartesian coordinate were power law functions of net stress and gas saturation. Some experimental data from literature were applied to validate the proposed model. Good agreements between experimental data and those evaluated by the proposed model were obtained. The apparent gas permeability model proposed in this work will be useful to professionals involved in laboratory measurement of low permeability water-bearing rocks, modeling well performance, and gas production forecasting.

A detailed study for production prediction methods under various drainage schedules for under-saturated coalbed methane wells is performed. In terms of the relationship between the value of average reservoir pressure and the critical desorption pressure, whole production life of under-saturated coalbed methane wells is divided into two periods, and the material balance equation in each period is derived respectively. Combining the two-period material balance equation and productivity equation under pseudo-steady state, a novel production prediction method is developed. Excellent agreements between predicted water/gas production rates from the proposed method and those from numerical simulator clarify the reliability successfully. Results demonstrate that (a) matrix shrinkage effect and effective permeable capability can significantly contribute to the production rise; (b) For the drainage schedule (FWFB), with the increase of the fixed water production rate, the drainage period will shorten; (c) For the drainage schedule (RDFB), sharp decrease of formation pressure will take place.