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The existence of water phase occupies oil flow area and impacts the confined oil flow behavior at the solid substrate in inorganic nanopores of shale oil reservoirs, resulting in a completely different flow pattern when compared with the single oil phase flow. This study proposes an analytical model to describe the water-oil two-phase flow. In this model, water slippage at the solid substrate is considered while oil slip is introduced to calculate the oil movement at the solid-oil boundary in dry conditions. It is proven that the oil flow profiles of both the two-phase model and single-phase model show parabolic shapes, but the oil flow capacity drops when water takes up the flow space and the impact of water is more significant when the pore dimension is smaller than 30 nm. Also, the oil flow velocity at a pore center is found to drop linearly given a larger water saturation in wet conditions. The effects of surface wettability and oil properties on water-oil flow are also discussed. Compared with the existing single-phase models, this model describes oil flow pattern in the wet condition with the incorporation of the influence of nanopore properties, which better predicts the oil transport in actual reservoir conditions. Water-oil relative permeability curves are also obtained to improve oil yield.

Summary Imbibition is one of the most common physical phenomena in nature, and it plays an important role in enhanced oil recovery, hydrology, and environmental engineering. The imbibition in a capillary is one of the fluid transports in porous media, and the effect of a dynamic contact angle that changes with the imbibition rate on liquid-liquid imbibition is not clear. In this paper, the molecular kinetic theory (MKT) is used to study the effect of a dynamic contact angle on spontaneous capillary-liquid-liquid imbibition at a micrometer scale. The results show that: Using a scaling time, the effects of various forces in different imbibition systems can be compared, the influence of a dynamic contact angle on imbibition can be characterized by a frictional effect of the three-phase contact line, and the proposed model considering the effect of a dynamic contact angle is better than the model neglecting the effect of a dynamic contact angle. As the displacing phase viscosity increases, the influence of a dynamic contact angle on imbibition strengthens, which is attributed to a decrease in the viscous effect and an increase in the frictional effect during the imbibition process; as the displaced phase viscosity increases, the influence of a dynamic contact angle on imbibition weakens, which is attributed to an increase in the viscous effect and a decrease in the frictional effect during the imbibition process. As the interfacial tension increases, the frictional effect increases, with the result that the effect of a dynamic contact angle on imbibition increases. As the capillary becomes more hydrophilic, the effect of a dynamic contact angle on imbibition becomes stronger because of a decreasing viscous effect and an increasing frictional effect. As the capillary length increases, the viscous effect increases, whereas the frictional effect decreases, leading to a decrease in the dynamic contact angle effect. As the capillary radius increases, the frictional force decreases, whereas its proportion in total resistance or the frictional effect increases, resulting in an increase in the effect of a dynamic contact angle. This work sheds light on the effect of a dynamic contact angle on capillary-liquid-liquid imbibition, including displacing phase viscosity, displaced phase viscosity, interfacial tension, capillary wettability, length, and radius. It will provide new insights into manipulating a capillary imbibition process and provide a fundamental theory for enhanced oil recovery by imbibition in conventional or unconventional reservoirs. Supplementary materials are available in support of this paper and have been published online under Supplementary Data at https://doi.org/10.2118/205490-PA. SPE is not responsible for the content or functionality of supplementary materials supplied by the authors.

Imbibition is very common, occurring in life, material, chemistry, and energy. It plays an important role in enhanced oil recovery (EOR). The development of many reservoirs is beneficial to the imbibition process, such as fractured reservoirs, conventional reservoirs developed by a water-injection mode of huff-n-puff in their later development, and unconventional reservoirs with abundant micro–nanopores developed by the fracturing technology. Here, we present a critical review of EOR through imbibition. First, the mechanisms of EOR through imbibition are reviewed, including the mechanical analysis of imbibition in a capillary, imbibition models for rocks, and the scaling law. Then, the governing factors of EOR by imbibition are summarized, including the properties of rocks and fluids and the effects of the temperature and pressure. Besides, the EOR by imbibition in the oil and gas development is discussed, including the roles of surfactants, nanofluids, salinity, shut-in time, and injection/production rates. Finally, conclusions and outlooks are presented. This review provides systematic and recent insights about EOR by imbibition and a direction for future research on this topic, which can help for a better understanding of EOR by imbibition.

The gas slippage phenomenon under dry conditions has been investigated extensively both numerically and experimentally. However, very limited research has focused on gas slippage behavior under wet conditions. Unlike conventional formation, the influence of water on the gas transport process cannot be neglected in tight formations due to the comparable amount of thin water film attached along the rock surface. It is found experimentally that the gas slippage factor is positively related to water saturation if the water saturation is small, while it decreases with water saturation if it is larger than a critical value. Most of the existing models failed to capture the measured downtrend of the gas slippage factor with increasing water saturation, which resulted from water blocking or gas trapping phenomenon. In this work, a pore-scale network model is proposed to look at the water distribution characteristic and investigate the effect of water on the gas slippage factor. The proposed pore-scale model incorporates the capillary dominated multiphase fluid distribution, real gas effect, and gas transport mechanisms at pore scale. On the basis of our pore network model, the effect of pore structure characteristics including the frequency of mean pore radius, size of mean pore radius, aspect ratio, and coordination number on the gas slippage behavior are investigated and discussed in detail. Similar to previous experimental observations, the simulated gas slippage factor shows a non-monotonic increase trend with water saturation; it starts to decrease under high water saturation, and the critical water saturation depends on the pore structure factors. It increases with the mean pore radius and coordination number but decreases with the aspect ratio. We used the pore network model to investigate the effect of the water phase on the gas slippage behavior at the pore scale for the first time. It emphasized the predominance of water blocking and the gas trapping phenomenon in the estimation of the gas slippage factor at high water saturation.

Understanding and controlling the interfacial tension (IFT) of nanoconfined fluids has tremendous implications in scientific research and engineering applications. On the basis of the physical mean...

Deepwater oil and gas exploitation has become an important field in the petroleum industry development. However, there are still no mature methods for hydrate prevention in the deepwater wells clea...

Gas mobility control is highly required to obtain a sufficiently-expanded and uniformly-developed steam chamber, which is conducive to steam-assisted gravity drainage (SAGD) production. Adding chem...

Summary A model for gas transport in nanoscale channels in shale-gas reservoirs (SGRs) is proposed using a new effective mean free path (MFP) model, which considers the effects of surface/gas interaction and the geometrical termination of a nanochannel boundary. In addition, the influences of the nanochannel dimension, formation-burial depth, surface type, and gas type on nanoconfined gas flow in slit channels are addressed. The nanoconfined gas-flow behavior is investigated for a wide range of temperature and pressure in this work because of the large prospects of shale gas in deep and ultradeep formations with pressure up to 100 MPa and temperature up to 480 K. The newly developed effective MFP model and the gas-flow-rate model are successfully validated with data from molecular dynamics (MD) simulations and experiments. Results show that the effect of surface force reduces the MFP and gas-flow capacity, which increases with a decreasing pressure, a decreasing channel size, and an increasing temperature; that the nanoconfinement effect has weaker influence on gas-transport capacity as the formation-burial depth increases and greater influence as formation pressure decreases during hydrocarbon production from SGRs; that a surface type affects the gas transport, and the gas-flow capacity in carbon (C) channels (organic channels) is stronger than that in silicon (Si) channels (inorganic channels) with the same size; and that the differences among the transport capacities of nitrogen (N2), argon (Ar), and methane (CH4) are not obvious, while the transport capacities of helium (He) are greatly lower compared with CH4 at both the SGR temperature and the laboratory temperature.

Solvent-Assisted Steam-Gravity Drainage (SA-SAGD) has lately been viewed as one of the most efficient alternatives to develop heavy oil reservoirs. However, there is strong evidence that reservoir ...

Summary Dual-pipe steam injection technique has currently demonstrated technical potential for improving heavy oil recovery. It can effectively delay the occurrence of steam fingering and homogenize the steam injection profile along the horizontal wellbore. In this paper, first, we built a cylindrical wellbore physical model to experimentally study the steam injection profiles of a single-pipe horizontal well and a concentric dual-pipe horizontal well. Thus, the heat and mass transfer behavior of steam along the horizontal wellbore with a single-pipe well configuration and a dual-pipe well configuration was addressed. Subsequently, considering the effect of pressure drops and heat loss, a semianalytical model for the gas/liquid two-phase flow in the horizontal wellbore was developed to numerically match the experimental observation. Next, a sensitivity analysis on the physical parameters and operation properties of a steam injection process was conducted. The effect of the injection fluid type was also investigated. Experimental results indicated that under the same steam injection condition, an application of dual-pipe well configuration can significantly enhance the oil drainage volume by approximately 35% than the single-pipe well configuration. During the experiments, both a temperature distribution and liquid production along the horizontal wellbore were obtained. A bimodal temperature distribution can be observed for the dual-pipe well configuration. From this proposed model, an excellent agreement can be found between the simulation results and the experimental data. Because of the effect of variable mass flowing behavior and pressure drops, the wellbore segment close to the steam outflow point can have a higher heating radius than that far from the steam outflow point. From the results of sensitivity analysis, permeability heterogeneity and steam injection parameters have a tremendous impact on the steam injection profile along the wellbore. Compared with a pure steam injection process, the coinjection of steam and noncondensable gas (NCG) can improve the effective heating wellbore length by more than 25%. This model is also applied to predict the steam conformance of an actual horizontal well in Liaohe Oilfield. This paper presents some information regarding the heat and mass transfer of a dual-pipe horizontal well, as well as imparts some of the lessons learned from its field operation.

The formation of hydrate will lead to serious flow assurance problems in deepwater submarine natural gas transmission pipelines. However, the accurate evaluation model of the hydrate blocking risk for submarine natural gas transportation is still lacking. In this work, a novel model is established for evaluating the hydrate risk in deepwater submarine gas pipelines. Based on hydrate growth-deposition mechanism, the mathematical model mainly consists of mass, momentum and energy conservation equations. Meantime, the model results are obtained by finite difference method and iterative technique. Finally, the model has been applied in the production of deepwater gas field (L Gas Field) in China, and the sensitivity analysis of relevant parameters has been carried out. The results show that: (a). The mathematical model can well predict the hydrate blockage risk in deepwater natural gas pipelines after verification. (b). Hydrate is easily formed at the intersection of horizontal pipeline and vertical riser, and the maximum blocking position often occurs in middle of the riser. (c). The hydrate blockage degree and length of hydrate formation region (HFR) decrease with the increase of gas transport rate. (d). The hydrate blockage degree and length of HFR decrease with the increase of gas transport temperature. (e). The hydrate blockage degree and length of HFR increase with the extension of horizontal pipeline. (f). Injecting inhibitors can effectively inhibit hydrate formation and blockage, but the improvement of transmission measures can significantly reduce the dosage of inhibitor. It is concluded that measures such as increasing gas transportation rate and temperature, shortening horizontal pipeline length, optimizing inhibitor injection point and injection rate can play a safe, economic and efficient role in hydrate preventing and controlling.

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

Summary An excess adsorption amount obtained in experiments is always determined by mass balance with a void volume measured by helium (He) –expansion tests. However, He, with a small kinetic diameter, can penetrate into narrow pores in porous media that are inaccessible to adsorbate gases [e.g., methane (CH4)]. Thus, the actual accessible volume for a specific adsorbate is always overestimated by an He–based void volume; such overestimation directly leads to errors in the determination of excess isotherms in the laboratory, such as “negative isotherms” for gas adsorption at high pressures, which further affects an accurate description of total gas in place (GIP) for shale–gas reservoirs. In this work, the mass balance for determining the adsorbed amount is rewritten, and two particular concepts, an “apparent excess adsorption” and an “actual excess adsorption,” are considered. Apparent adsorption is directly determined by an He–based volume, corresponding to the traditional treatment in experimental conditions, whereas actual adsorption is determined by an adsorbate–accessible volume, where pore–wall potential is always nonpositive (i.e., an attractive molecule/pore–wall interaction). Results show the following: The apparent excess isotherm determined by the He–based volume gradually becomes negative at high pressures, but the actual one determined by the adsorbate–accessible volume always remains positive.The negative adsorption phenomenon in the apparent excess isotherm is a result of the overestimation in the adsorbate–accessible volume, and a larger overestimation leads to an earlier appearance of this negative adsorption.The positive amount in the actual excess isotherm indicates that the adsorbed phase is always denser than the bulk gas because of the molecule/pore–wall attraction aiding the compression of the adsorbed molecules. Practically, an overestimation in pore volume (PV) is only 3.74% for our studied sample, but it leads to an underestimation reaching up to 22.1% in the actual excess amount at geologic conditions (i.e., approximately 47 MPa and approximately 384 K). Such an overestimation in PV also underestimates the proportions of the adsorbed–gas amount to the free–gas amount and to the total GIP. Therefore, our present work underlines the importance of a void volume in the determination of adsorption isotherms; moreover, we establish a path for a more–accurate evaluation of gas storage in geologic shale reservoirs with high pressure.

Water injection is widely performed to enhance oil recovery in fossil energy development. The fracture initiation pressure (FIP) is a key parameter for designing the reasonable injection pressure for micro-fracturing water injection (MFWI). In this work, a modified method was presented to accurately predict the FIP, in which the thermal effect and plugging effect were considered; moreover, the stress around perforations was analyzed. To validate our method, the field tests, including a step rate test (SRT) and a well test, were conducted to obtain the actual FIP for perforated water injection wells, and then the FIP calculated by our method was compared with a low relative error of about 1.7%. Results show that (i) a greater temperature difference between the injected water and the formation forms a greater thermal stress around perforations, resulting in a greater change in the FIP; (ii) a larger skin factor causes a greater pressure drop for the injected water flowing through a plugged area, resulting in a stronger effective stress reduction around perforations and further producing a larger FIP. Therefore, our present work illustrates a better understanding of the stress distribution around a perforated wellbore, and paves a path for a more accurate prediction of the FIP in perforated water injection wells.

With the consideration of a mobile high-viscosity water film and a bulk water layer, an analytical model is proposed to predict gas flow behaviors and gas apparent permeability in nanopores. Physical molecular forces are analyzed to determine the properties and formation of the high-viscosity water film and the bulk water layer. Boundary conditions at a solid-liquid interface and a liquid-gas interface are modified to account for water slippage and gas slip. How mobile bulk water molecules influence gas transport capability in pores of different geometry is investigated with different pore sizes and pressure for the whole range of water saturation, which has been validated with experimental data and simulation results. Besides, the effect of a wedged pore structure on multiphase flow behaviors is also investigated to figure out the influences of pore shape.

Hydrate formation and blockage in gas-dominated pipelines has always been an important issue in research of pipeline flow assurance. In this work, a novel hydrate deposition prediction model consid...

To commercially develop shale gas reservoirs, multi-fractured horizontal wells are widely employed in the industry. A number of analytical models have been proposed to evaluate and forecast production from fractured horizontal wells. However, the water film adsorbed in inorganic pores of shale matrix is often neglected and its effect on gas production has never been focused on. Moreover, the effect on gas production caused by the characteristic of a well not located in the center of drainage area has not been drawn much attention. In this work, on a basis of enhanced-fracture-region (EFR) model, a new model is put forward to conduct production prediction of multi-fractured horizontal wells from shale gas reservoirs. This novel approach incorporates critical gas transport mechanisms in shale, and considers the characteristic of a well not located in the center of drainage area. Specifically, this model takes the bulk-gas transport regimes, water film effect, stress dependence and real gas effect into account, which matches well with the real shale reservoirs. The analytical solution of the proposed model is deduced by employing the Laplace transformation approach, and then introducing the numerical algorithm put forward by Stehfest to invert to the real time domain. This presented model is verified by both numerical simulation cases and actual field applications. In addition, a sensitivity study is performed to illustrate various parameters on flow-regime and production curves. Results illustrate that both the size of stimulated zone and distance from the well to the outer boundary contribute to the well performance. A larger size of the stimulated zone increases the duration of the first linear flow period, whereas will shorten the duration of the third boundary dominated flow period. A larger distance from the well to the outer boundary leads to stronger gas production. The real gas has non-obvious effect on gas production. Both the stress dependence and humidity have negative effects on production curves, which are induced by the decrease of the effective pore radius. Specifically, compared with the gas production without considering water film effect, when the humidity value is 0.1, gas production can achieve an average decrease of 18.57%. When the humidity value is 0.3, gas production can reach an average decrease of 26.10%.

The hydraulic fracturing is extensively used to stimulate the production of fossil hydrogen energy. Perforation parameters have a great influence on the performance of hydraulically fractured horizontal wells in fossil hydrogen energy development. In this work, a practical model to study the effect of a completion scheme on simultaneous fracture propagation is proposed, in which the coupling fluid flow and stress interaction is considered, and a fracture propagation uniform index model is used to optimize the completion strategy. Moreover, this model is well validated by Wu's model and Zhang's model. The numerical study results indicate that a uniform completion scheme causes a non-uniform fracture development; an optimal completion method is proposed by reducing the cluster number, non-uniform spacing, and practical limited entry technique in a fracturing stage. Furthermore, the combined use of unequal cluster spacing and a limited entry strategy can significantly reduce the suppression effects between multiple clusters, improve the fluid flow into each cluster, and enhance the uniform propagation to achieve the maximum production. Our present work illustrates a better understanding of the effect of the completion strategy on the multiple fracture propagation, and paves a path for a more optimal completion design for fossil hydrogen energy development.

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.

Adsorbed gas is a significant component of shale gas due to the abundant nanopores of organic matter in shales. Methane adsorption behavior on shale matrix is complex considering the geochemical properties, lithology, pore structure and pressure-temperature conditions. In this work, methane adsorption experiments were conducted through a gravimetric method for shale samples at reservoir pressure and temperature conditions. Meanwhile, total organic carbon (TOC), mineral contents and pore structure parameters of samples were measured, respectively. Experimental results show that (1) an excess adsorption phenomenon is obvious at high-pressure and high-temperature conditions; (2)methane adsorption capacity of shale tends to increase with an increase of TOC; (3) lithology and pore structure also affect the methane adsorption capacity of shales, inducing the different adsorption results of two samples with similar TOC; (4) a shale with a large TOC, a low illite content, a large specific area, a large pore volume and a small average diameter would have a strong methane adsorption capacity, nevertheless the effect of TOC is generally dominant. In order to further investigate the methane adsorption behavior on shales, a simplified local density adsorption model considering the cylindrical pore geometry is established, and is regressed and verified by the experimental data. The modeling results indicate that a sample with a large TOC would have a strong fluid-solid interaction energy and a large surface area of methane adsorption. At last, the mechanism of methane adsorption on shales at in-situ conditions is summarized. This work is beneficial for an accurate shale gas reservoir modeling.

Gas slippage phenomenon in single phase gas flow conditions has been extensively investigated. However, only a few researchers have focused on gas slippage in gas/water two-phase flow conditions. Unfortunately, initial water saturation always exists in tight gas reservoirs, and its impact on gas slippage and flow capacity should not be neglected. In this work, gas slippage for single phase and two-phase flows in tight rocks were experimentally investigated, and our results directly demonstrated that gas slip factors increase with an increase in water saturation. But interestingly, the measured values were significantly higher than those predicted by the Klinkenberg idealized model. This finding indicated that the heterogeneous pore-network structure could largely affect the gas/water distribution characteristics, e.g., leading to ‘water blocking’ or ‘gas trapping’ inside actual samples, which further influenced the two-phase gas slippage behaviors. Thus, a heterogeneity coefficient χ was proposed to correct the deviation between actual cases and the Klinkenberg’s ideal model (χ = 0.5 is for the ideal case, and χ ranges from 0.5 to 2.0 for actual tight sandstones), and thus the two-phase gas slippage for actual tight rocks could be well characterized. Besides, the impact of two-phase gas slippage on the relative gas permeability also needs to be paid more attention. Without a correction of gas slippage, the relative permeability for gas flow in a high-pressure reservoir condition would be overestimated, and this error could be up to 20% for our studied samples. Our present work illustrates a better understanding on how water saturation affects gas slippage in a two-phase flow condition, and paves a path for a more accurate evaluation of the gas flow capacity in actual reservoir systems.

The addition of hydrocarbon solvents to the steam injection, known as Solvent-Assisted Thermal Gravity Drainage (SA-SAGD), has recently been proven to be a more energy saving and environmentally friendly method for heavy oil recovery. Nevertheless, the relationship between injection parameters and heavy oil production in conventional SAGD were always introduced to analysis the performance of SA-SAGD, which makes many confusing in the interpretation. In this paper, the heat lost to the cap rock of the reservoir is determined by taking into account not only the chamber-edge velocity, but also the temperature and mass distributions inside the chamber. Besides, by implicitly characterizing the chamber-edge shape and considering heat and solvent diffusion beyond the chamber edge, the oil rate is calculated. Then, the model couples heat and mass balance equations in the whole oil sand dynamically by considering the effect of liquid pool. This comprehensive method enables us to clearly examine the relationship between the Production-Injection Ratio (PIR) and the height of liquid pool. Lastly, the new model is verified by comparing predicted results with that of numerical simulation. The results show that, the oil rate of SA-SAGD is improved by both of the diluting effect of solvent on bitumen viscosity and a more reasonable chamber shape formed by co-injection solvent with steam. In addition, although heat-loss rate of SA-SAGD is generally smaller than that of conventional SAGD, the Steam-Oil Ratio (SOR) of SA-SAGD may even higher than that of SAGD in the late period of the process if the liquid level is extremely high. Moreover, the liquid-pool height for SA-SAGD is more sensitive to the PIR than for SAGD. Accordingly, when the effect of liquid pool on the production is considered, the PIR of SA-SAGD must be selected carefully.

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.

A real gas transport model in shale matrix with fractal structures is established to bridge a pore size distribution and multiple transport mechanisms. This model is well validated with experiments. Results indicate that different pore size distributions lead to various transport efficiencies of shale matrix. A larger fractal dimension of the pore size and a smaller minimum pore size yield higher frequency of occurrence of small pores and a lower free gas transport ratio, which further results in lower transport efficiency. Gas transport efficiency due to pore size distribution parameters (a fractal dimension and a minimum pore size) varies with different porosities and pressures. Increasing fractal dimension and decreasing minimum pore size result in a higher contribution of Knudsen diffusion to the total gas transport. Decreased pressure and increased porosity enhance the sensitivity of gas transport efficiency to a pore size distribution. The relationship between apparent permeability and porosity based on different pore size distributions is also established for industrial application.

The complexity and heterogeneity of pore structure greatly affect gas-liquid accumulation and transport, and the fractal theory has been proven to be an effective approach for studying nanoscale reservoirs in shale, coal, and tight sandstones. However, researches on fractal characteristics and control mechanisms for the lacustrine tight carbonate have received little attention. Lacustrine tight carbonate samples from the Jurassic Da’anzhai Member in the Sichuan Basin in China were systematically investigated focusing on the fractal characteristics and control mechanisms of storage spaces, minerals, diagenesis, and paleoenvironments. The fractal dimensions can be separated into two different and valid parts including D1 (2.515–2.785, average 2.652) and D2 (2.424–2.562, average 2.485), and the correlation between them is negative rather than positive. The average pore diameters exhibit a positive correlation with D1 and a negative correlation with D2, and the storage space is positively correlated with D2 a...

Understanding and controlling the gas flow at the nanoscale has tremendous implications in the fields of separation science, catalytic reactions, and energy storage, conversion and extraction. However, the gas flow behavior at the nanoscale is significantly different from that occurring at larger scales. In this work, we focus on a real gas effect, stemming from a strong gas intermolecular interaction force at high pressure and an un-negligible gas molecule volume at the nanoscale, on gas flow through nanoporous shale. An analytical and unified model is developed and validated with the published results of the Lattice-Boltzmann equation and experiments. This unified model covers all gas flow mechanisms, including viscous flow, slip flow and transition flow, and captures the real gas effect, which enhances flow capacity through nanoporous shale. This unified model is a ready-to-use tool for fast and accurately modeling gas flow through nanopores, and provides a basic foundation for numerical simulation and production prediction in shale gas reservoirs.

Shale gas has become one of the primary energy resources during the past few years, and its impact has been profound in many countries. Hydraulic fracturing treatments are required for the development of shale gas reservoirs, and the consequent hydraulic fractures usually connect with the original small-scale natural fractures forming complex fracture networks in these reservoirs. Therefore, a model for numerical simulation, which is capable of accurately modeling naturally and hydraulically fractured reservoirs, is essential in optimization and management of such reservoirs. In this paper, we develop a comprehensive model that couples embedded discrete fractures, multiple interacting continua, and geomechanics to accurately simulate the fluid flow in shale gas reservoirs with multiscale fractures. Large-scale hydraulic fractures are described by an embedded discrete fracture method, while middle-scale and small-scale natural fractures are modeled by a multiple interacting continua method. Usually, the co...

The thin water film stabilized by disjoining pressure is non-negligible in tight formations which results in significant difference in multiphase flow behavior compared with that in conventional formations. In this work, a pore network model is proposed to simulate two phase flow in tight formations to highlight the contribution of thin water film on multiphase flow. The newly developed pore network model includes the influence of thin water film on fluid configuration, capillary entry pressure, fluid conductance and connectivity during multiphase flow in pore space. Our approach is first validated with the existing pore network model and then the influence of thin water film on two-phase flow is investigated extensively. The results show that the connate water saturation increases and its associated oil relative permeability decreases as the average pore radius decreases. It also suggests that in water-wet systems, the influence of thin water film on both oil and water phases becomes significant when the average pore radius is smaller than 100 nm. Existence of thin water film will increase the proportion of film water and corner water, resulting in an increasement in oil phase relative permeability and a slight decline of water phase relative permeability in tight porous media dominated by angular pores and throats; while in porous media dominated by circular shaped pores and throats, oil and water phase relative permeability are both enhanced due to better connectivity caused by thin water film; at the same time swelling of water film results in lower residue oil saturation and higher end point of water relative permeability. We also found higher water relative permeability when porous media has more irregular pores.

Nanoconfinement effects lead to the anomalous phase behavior of hydrocarbons in nanopores. Besides the capillary pressure, the critical properties’ shift and curvature-dependent effect are found to be wettability-dependent parameters. In this work, we propose novel methods to correlate the macroscopic contact angle to the critical properties’ shift and curvature-dependent effect with an in-depth analysis of the microscopic interactions, including molecule-wall interactions and intermolecular interactions at the liquid-vapor interface. Then, we extend the Peng-Robinson equation of state model to investigate the effects of wettability on the phase behavior and interfacial tension (IFT) of nanoconfined hydrocarbons. Our results show that the nanoconfinement effects are not only dependent on the pore size but also on the wettability of the pore wall. In nonhydrocarbon-wet nanopores, the nanoconfinement effects are limited, and the bubble point pressure (Pb) and IFT are close to the bulk values. In hydrocarbon-wet nanopores, with the pore radius smaller than 50 nm, the nanoconfinement effects become visible and they are further strengthened as the contact angle decreases. The calculated results suggest that under reservoir temperature for Eagle Ford reservoir with the pore size of 10 nm, the suppression of Pb and IFT with completely oil-wet cases are nearly six-fold and ten-fold higher than that of intermediate-wet cases.

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...

SummaryA model for gas transfer in nanopores is the basis for accurate numerical simulation, which has important implications for economic development of shale-gas reservoirs (SGRs). The gas-transfer mechanism in SGRs is significantly different from that of conventional gas reservoirs, which is mainly caused by the nanoscale phenomena and organic matter as a medium of gas sourcing and storage. The gas-transfer mechanism includes bulk-gas transfer and adsorption-gas surface diffusion in nanopores of SGRs, where the bulk-gas-transfer mechanism includes continuous flow, slip flow, and Knudsen diffusion. First, a model for bulk-gas transfer in nanopores was established, which was dependent on slip flow and Knudsen diffusion. The total gas flux in the bulk phase is not a simple sum of slip-flow flux and Knudsen-diffusion flux but a weighted sum on the basis of corresponding contributions. The weighted factors are primarily controlled by the mutual interaction between slip flow and Knudsen diffusion, which is determined by probabilities between gas molecules colliding with each other and colliding with nanopore surface in this newly proposed model. Second, a model for adsorbed-gas surface diffusion in nanopores was established, which was modeled after the Hwang and Kammermeyer (1966) model and considered the effect of gas coverage under a high-pressure condition. Finally, with the combination of these two models, a unified model for gas transport in nanopores of SGRs was established, and this model was validated through molecular simulation and experimental data. Results show that:Slip flow makes a great contribution to gas transfer under the condition of meso/macropores (pore radius greater than 2 nm) and high pressure. Knudsen diffusion makes an important contribution to gas transfer under the condition of macropores (pore radius greater than 50 nm) and less than 1 MPa in pressure, whereas it can be ignored in other cases. A surface-diffusion coefficient is comparable with a pore-diffusion coefficient, and gas transfer is always dominated by surface diffusion over all the ranges of pressure in micropores (pore radius ≤ 2 nm). Surface-diffusion contribution decreases with an increase in pore size, isosteric sorption heat, pressure, and temperature in SGRs.

The rock wettabilities and water contact angles describing interactions between CO2, CH4, brine and shale formations are of great significance to CO2 sequestration and enhanced gas recovery processes. However, water contact angles on the surfaces of shale organic matter in the atmospheres of CO2 and CH4 under reservoir conditions are not well-understood. In this study, we present an investigation of water/brine contact angles as functions of temperature, pressure, salinity, ion types, and gas contents by molecular dynamics simulations, and compare results with data from literature. It is found that temperature has profound effects on water contact angles below the critical temperature at an intermediate pressure. Meanwhile, water contact angles increase with pressure before reaching 180° at high pressure and the CO2-water-shale organic matter system turns from a neutrally-wet state to a CO2-wet state at the critical pressure of CO2. We also demonstrate that salinity and ion types have minor impacts on the brine contact angles in the CO2-brine-shale system. Only a slight increase in water contact angles is observed with increasing salinity, and an increase in brine contact angles caused by the divalent cations Mg2+ and Ca2+ is larger than that by the monovalent cations Na+ at the same salinity. Additionally, an increase in the CO2 fraction of gas mixtures can increase water contact angles at the same pressure and temperature. The surfaces of shale organic matter have a stronger affinity for CO2 than CH4, which contributes to a higher CO2 adsorption capacity and improves the displacement efficiency of CH4.

A boom in the production of shale gas has recently impacted the world’s energy supply. The hydraulic fracturing technology has been widely used in the development of shale gas reservoirs. Models for accurate reservoir simulation are essential for their economic production. In this paper, a model for shale gas reservoir production is proposed to account for slip flow, Knudsen diffusion, surface diffusion, gas adsorption/desorption, stress dependence of a pore structure, a non-ideal gas effect, and a flow mechanism difference between organic and inorganic content in the shale matrix. This model is implemented in our in-house simulator with a coupled MINC-EDFM approach to study and predict shale gas production behavior. Comprehensive sensitivity studies are performed to analyze the importance of different parameters in shale gas production. These parameters are divided into two categories. The first category includes reservoir data, such as shale matrix porosity, a nanopore radius, an organic/inorganic volume ratio, hydraulic fracture half-length, and fracture spacing. The second category includes parameters relevant to flow mechanisms, such as a non-ideal gas effect, stress dependence, presence of an adsorbed layer as well as a selection of a flow mechanism model. It is found that parameters related to hydraulic fractures impact calculated gas production more than reservoir matrix data. Among the fracturing parameters, hydraulic fracture half-length has a stronger effect than fracture spacing, and among matrix properties, porosity has a larger impact than a nanopore radius or the assumed organic/inorganic content ratio. These results help to optimize a shale gas reservoir production design. In addition, in a synthetic case assuming a 1 nm pore radius, the presence of an adsorbed gas layer has a more tremendous effect compared to the non-ideal gas and stress dependence phenomena. Moreover, the developed simulator with the multiple transport mechanisms can be used to accurately predict shale gas reservoir production. The findings of this study help a better understanding of shale gas flow and can be used to enhance the production of shale gas reservoirs.

Although the exploration and development of tight gas have made great progress, the quantified study on gas migration and accumulation in sweet spots of tight gas reservoir is still limited. In this work, a computer program is developed to conveniently describe the different shape of sweet spots and the fractures in tight reservoir. Then, gas migration and accumulation processes are simulated, and the numerical simulation results are visualized and quantified. Based on the simulation results, the mechanism of gas migration and accumulation in sweet spots is revealed. The results indicate that the migration and accumulation of gas are two relatively independent processes. The gas migration process is determined by the permeability of rocks. The critical condition of gas accumulation in sweet spots is mostly determined by the capillary pressure difference between sweet spots and surrounding rock. The two migration patterns are clearly observed during the numerical simulations. When surrounding rock has seepage capacity for gas, the migration pattern tends to be piston-like displacement; when surrounding rock is impermeable for gas, the gas can only migrate into sweet spots through connected fractures. As a result, the migration pattern for this situation tends to be fingering displacement.

Initial water content and subsequent fracturing fluid injection lead to gas-water flow in shale nanopores, especially the water-wet pores. But there is few research and experiment to introduce relative permeability curves governing multiphase transport behaviors in shale nanopores. With the consideration of water true slippage and gas slippage, an analytical model illustrating gas-water relative permeability curve in fractal-like tree pore structures has been constructed, aiming to explain gas-water two phase flow behaviors and further evaluate the effects of pore size distributions and water films on gas-water transport. Sensitivity analysis verifies that smaller pore radius, more branching levels and less branching number tend to increase the gas relative flow capacity. Also, ignoring the existence of high-viscosity water molecules has been discovered to reduce water flow resistance. But if the high-viscosity water film loses its mobility, water relative permeability drops slightly. In contrast, mobile bulk water molecules are mainly conducive to increase the gas molecules relative movements. Besides, the analysis of pore size distribution confirms that the fractal-like tree network possesses a more significant gas dominancy compared with log-normal pore network.

A void volume, which is measured by helium expansion tests and used in the calculation of methane adsorption amounts, is always overestimated due to helium adsorption. In this study, by comparing void volumes of carbon nanopores determined under different temperatures and pressures using GCMC (Grand Canonical Monte Carlo) simulation, suitable experimental conditions for helium expansion tests are obtained. Five volumes, including one apparent volume Vapp, three referred volumes Vref and one physical volume Vphy, are recognized. The apparent volume Vapp corresponds to the volume directly determined under traditional experimental conditions, while three referred volumes are determined at 500 K with different pressure ranges (low, moderate, high). The physical volume is calculated by multiplying a pore width and a surface area. Besides, a volume determined by using a helium probe is named an accessible volume Vacc and used as a criterion for a determined volume through mass balance. It is found that use of a void volume determined under traditional experimental conditions or a physical volume leads to negative adsorption amounts at high pressures. Considering an economic effect and measurement accuracy, determining a void volume by helium expansion tests within a moderate pressure range at 500 K is suggested. Excess isotherms of methane calculated by the suggested volume are more appropriate and of great physical meanings for further investigation of adsorption mechanisms.

Unlike conventional gas reservoirs, gas flow in shale reservoirs is a complex and multiscale flow process which has special flow mechanisms. Shale gas reservoirs contain a large fraction of nano pores, which leads to an apparent permeability that is dependent on pore pressure, fluid type, and pore structure. Study of gas flow in nano pores is essential for accurate numerical simulation of shale gas reservoirs. However, no comprehensive study has been conducted pertaining to the gas flow in nano pores. In this paper, experiments for nitrogen flow through nano membranes (with pore throat size: 20 nm, 55 nm, and 100 nm) have been done and analyzed. Obvious discrepancy between apparent permeability and intrinsic permeability has been observed; and the relationship between this discrepancy and pore throat diameter (PTD) has been analyzed. Then, based on the advection-diffusion model, a new mathematical model has been constructed to characterize gas flow in nano pores. A new apparent permeability expression has been derived based on advection and Knudsen diffusion. A comprehensive coefficient for characterizing the flow process was proposed. Simulation results were verified against the experimental data for gas flow through nano membranes and published data. By changing the comprehensive coefficient, we found the best candidate for the case of argon with a membrane PTD of 235 nm. We verified the model using experimental data with different gases (oxygen, argon) and different PTDs (235 nm, 220 nm). The comparison shows that the new model matches the experimental data very closely. Additionally, we compared our results with experimental data, the Knudsen/Hagen–Poiseuille analytical solution, and existing models available in the literature. Results show that the model proposed in this study yielded a more reliable solution. Shale gas simulations, in which gas flowing in nano pores plays a critical role, can be made more accurate and reliable based on the results of this work.

In this paper, physical experiments and numerical simulations were applied to systematically investigate the non-Newtonian flow characteristics of heavy oil in porous media. Rheological experiments were carried out to determine the rheology of heavy oil. Threshold pressure gradient (TPG) measurement experiments performed by a new micro-flow method and flow experiments were conducted to study the effect of viscosity, permeability and mobility on the flow characteristics of heavy oil. An in-house developed novel simulator considering the non-Newtonian flow was designed based on the experimental investigations. The results from the physical experiments indicated that heavy oil was a Bingham fluid with non-Newtonian flow characteristics, and its viscosity-temperature relationship conformed to the Arrhenius equation. Its viscosity decreased with an increase in temperature and a decrease in asphaltene content. The TPG measurement experiments was impacted by the flow rate, and its critical flow rate was 0.003 mL/min. The TPG decreased as the viscosity decreased or the permeability increased and had a power-law relationship with mobility. In addition, the critical viscosity had a range of 42–54 mPa∙s, above which the TPG existed for a given permeability. The validation of the designed simulator was positive and acceptable when compared to the simulation results run in ECLIPSE V2013.1 and Computer Modelling Group (CMG) V2012 software as well as when compared to the results obtained during physical experiments. The difference between 0.0005 and 0.0750 MPa/m in the TPG showed a decrease of 11.55% in the oil recovery based on the simulation results, which demonstrated the largely adverse impact the TPG had on heavy oil production.

Condensate liquids retrograde below the dew point pressure and diminish gas relative permeability and thus reduce the deliverability of gas condensate wells. The deliverability varies due to the changes of gas effective permeability and other parameters; however, the present deliverability testing methods were not applicable to gas condensate wells because those methods were all based on the assumption that the formation properties such as permeability and fluid properties were constant. A new testing method for gas condensate wells is proposed in this work, by which the variable coefficient deliverability equation can be obtained. Case study shows that the variable coefficient deliverability equation obtained from the proposed deliverability testing method can represent changes of formation properties and fluid properties, thus the deliverability of gas condensate wells can be accurately evaluated and predicted by this testing method.

Gas-assisted gravity drainage (GAGD), solving the problem of low volume sweep coefficient for continuous gas injection (CGI) or water-alternating-gas injection (WAG) and increasing the ultimate recovery to a great extent, is a latest method for enhancing oil recovery. However, no effective predicting methods of oil recovery for GAGD exists. The oil recovery is determined by a set of parameters, such as heterogeneity of the formation, wettability, oil and gas density, oil and gas viscosity, viscous force, capillary force, gravity, gas injection rate, and other controllable parameters. Based on the research of producing mechanism of GAGD and dimensional analysis method, the authors analyzed four dimensionless varies, capillary number, bond number, gravity number, and gravity drainage number, and evaluated its influence on oil recovery. Considering the effect of wettability, viscosity ratio, and the difference between oil density and gas density, gravity number and gravity drainage number are modified. Relat...

In abnormal pressure gas reservoirs, a traditional binomial deliverability equation is insufficient to accurately describe the gas filtration theory, but only the trinomial deliverability equation considering non-Darcy flow effect and ripple effect can be reasonable to some extent. When gas reservoirs are characterized by low porosity and permeability, strong heterogeneity, and high water saturation, gas flow, similar to liquid flow, is featured in significant threshold pressure gradient effect. Therefore, a threshold pressure gradient is added to the trinomial deliverability equation, and it is derived that the pressure drop caused by the pressure gradient is a variable related to production but not a constant. Consequently, a novel deliverability equation of abnormal pressure gas reservoirs considering variable threshold pressure drop has been established, providing theoretical guidance for determining reasonable gas production in abnormal pressure gas reservoirs.