Effects Of Molecular Diffusion Research Articles

Reconstructing depleted fractured oil reservoirs into underground natural gas storages with the consideration of the effect of molecular diffusion and medium deformation on the dynamic performances

A model is constructed for the underground natural gas storages reconstructed from the depleted fractured oil reservoirs, in which the diffusion of molecules and the deformation of medium are taken into consideration. The model is solved by finite difference method and applied to the reconstruction from a depleted bottom water fractured oil reservoir into gas storages. The effect of molecular diffusion and medium deformation on the dynamic of the storage is analyzed and the optimal scheme for the reconstruction is selected from 12 given schemes. After the numerical simulation, we conclude that the diffusion of molecules and the deformation of medium have significant influence over the dynamic performances of the gas storages altered from the fractured oil reservoirs.

Modelling air injection in shale oil reservoirs: physical process and recovery mechanism

In this paper, reservoir simulation approach is conducted for qualitative analysis on EOR mechanisms of air injection in shale oil reservoirs. Effects of oxygen molecular diffusion, reaction enthalpy, activation energy, reaction scheme, and flowing well-bore pressure on the well performance of air injection are examined in detail. Results show that oxygen molecular diffusion has great effect on spontaneous ignition temperature, heat transfer and oil recovery, which should be considered in simulating air injection in shale oil reservoir for better understanding the real mechanisms. Reaction enthalpy and activation energy can significantly affect ignition temperature, but not on the production performance. High oil recovery can be favourably achieved when the crack reaction dominates, while the combustion reaction exhibits a negative effect on production performance. The development scheme with lower flowing well-bore pressure is more favourable for the air injection process. In-situ combustion and heat transfer cannot sustain due to the air low injectivity. More hydraulic fractures as well as an improved understanding of fracture and its distribution is helpful for enhancing air injectivity to better perform synergic recovery mechanisms of air injection in shale reservoirs. [Received: January 2, 2017; Accepted: June 25, 2018]

Modelling air injection in shale oil reservoirs: physical process and recovery mechanism

In this paper, reservoir simulation approach is conducted for qualitative analysis on EOR mechanisms of air injection in shale oil reservoirs. Effects of oxygen molecular diffusion, reaction enthalpy, activation energy, reaction scheme, and flowing well-bore pressure on the well performance of air injection are examined in detail. Results show that oxygen molecular diffusion has great effect on spontaneous ignition temperature, heat transfer and oil recovery, which should be considered in simulating air injection in shale oil reservoir for better understanding the real mechanisms. Reaction enthalpy and activation energy can significantly affect ignition temperature, but not on the production performance. High oil recovery can be favourably achieved when the crack reaction dominates, while the combustion reaction exhibits a negative effect on production performance. The development scheme with lower flowing well-bore pressure is more favourable for the air injection process. In-situ combustion and heat transfer cannot sustain due to the air low injectivity. More hydraulic fractures as well as an improved understanding of fracture and its distribution is helpful for enhancing air injectivity to better perform synergic recovery mechanisms of air injection in shale reservoirs. [Received: January 2, 2017; Accepted: June 25, 2018]

Recent Advances in Graphene Oxide Membranes for Gas Separation Applications.

Graphene oxide (GO) can dramatically enhance the gas separation performance of membrane technologies beyond the limits of conventional membrane materials in terms of both permeability and selectivity. Graphene oxide membranes can allow extremely high fluxes because of their ultimate thinness and unique layered structure. In addition, their high selectivity is due to the molecular sieving or diffusion effect resulting from their narrow pore size distribution or their unique surface chemistry. In the first part of this review, we briefly discuss different mechanisms of gas transport through membranes, with an emphasis on the proposed mechanisms for gas separation by GO membranes. In the second part, we review the methods for GO membrane preparation and characterization. In the third part, we provide a critical review of the literature on the application of different types of GO membranes for CO2, H2, and hydrocarbon separation. Finally, we provide recommendations for the development of high-performance GO membranes for gas separation applications.

Experimental investigation on the contribution of gas molecular diffusion to gas mass flux in micro-nano pores

ABSTRACTThe mass transfer from the matrix to the fracture face is driven by both concentration and pressure differences. In this work, high-temperature high-pressure (HPHT) systems for diffusion experiments with only concentration differences were used to determine the diffusion coefficient, and flow experiments with only pressure differences were also conducted; and the magnitude of gas molecular diffusion and its contribution to production were analyzed in this study. The results show as follows: (1) Gas flow from the matrix to the fracture system is driven by the combined effect of gas molecular diffusion and seepage. The pore structure characteristics of the reservoir and the contribution of the diffusion to the yield can vary greatly. (2) In tight reservoirs with an average permeability of 0.3067 mD, the contribution of gas molecular diffusion to the total gas mass flux is only 0.08%, while in shale reservoirs, the average permeability is 0.0015 mD; the contribution of diffusion to the total gas mass flux could be as large as 1%. (3) The contribution of molecular diffusion to gas production is closely related to the pore sizes of the porous medium. The smaller the pore sizes are, the greater the contribution of molecular diffusion to gas production.

Heat and Mass Transfer of Free Convection Flow Over a Vertical Plate with Chemical Reaction Under Wall–Slip Effect

This research work deals with the influence of heat and mass transfer on the natural convection flow over an infinite vertical plate with constant concentration and ramped wall temperature under the influence of slip boundary condition. The effects of chemical molecular diffusivity along with chemical and heat transfer processes have been studied. Solutions for the fluid velocity, temperature and concentration are achieved in closed forms by applying Laplace transform technique. The influence of embedded physical parameters on the flow characteristics has been analyzed graphically.

Simulation Study of CO2 Huff-n-Puff in Tight Oil Reservoirs Considering Molecular Diffusion and Adsorption

CO2 injection has great potentials to improve the oil production for the fractured tight oil reservoirs. However, Current works mainly focus on its operation processes; full examination of CO2 molecular diffusion and adsorption was still limited in the petroleum industry. To fill this gap, we proposed an efficient method to accurately and comprehensively evaluate the efficiency of CO2-EOR process. We first calculated the confined fluid properties with the nanopore effects. Subsequently, a reservoir simulation model was built based on the experiment test of the Eagle Ford core sample. History matching was performed for the model validation. After that, we examined the effects of adsorption and molecular diffusion on the multi-well production with CO2 injection. Results illustrate that in the CO2-EOR process, the molecular diffusion has a positive impact on the oil production, while adsorption negatively impacts the well production, indicating that the mechanisms should be reasonably incorporated in the simulation analysis. Additionally, simulation results show that the mechanisms of molecular diffusion and adsorption make great contributions to the capacity of CO2 storage in tight formations. This study provides a strong basis to reasonably forecast the long-term production during CO2 Huff-n-Puff process.

Mild Ammonia Synthesis over Ba-Promoted Ru/MPC Catalysts: Effects of the Ba/Ru Ratio and the Mesoporous Structure

A series of novel mesoporous carbon-supported, Ba-promoted, Ru catalysts with Ba/Ru ratios of 0.1–1.6 and a Ru loading of 10 wt% (denoted as 0.1–1.6Ba-10Ru/MPC) were prepared via stepwise impregnation of Ru and Ba precursors on the mesoporous carbon materials. The catalysts were applied to mild ammonia synthesis and compared to reference materials, including an analog of the prepared catalyst with a Ba/Ru ratio of 1.6 and a Ru loading of 10 wt% (denoted as 1.6Ba-10Ru/AC). Characterization by X-ray diffraction (XRD), nitrogen physisorption, and electronic microscopy revealed that the 0.1–1.6Ba-10Ru/MPC catalysts contained Ru particles (approximately 2 nm) that were well-dispersed on the mesoporous structure and nanostructured Ba(NO3)2 species. These species decomposed into amorphous BaOx species, acting as a promoter on the metallic Ru particles forming catalytically active sites for ammonia synthesis. All the 0.1–1.6Ba-10Ru/MPC catalysts showed a synergistic effect of the active Ba and Ru species, which were stabilized in the mesoporous carbon framework with fast molecular diffusion and could effectively catalyze mild ammonia synthesis (280–450 °C and 0.99 MPa) even under intermittently variable conditions, particularly for those with Ba/Ru ratios of >0.5. In contrast, the 1.6Ba-10Ru/AC analog showed poor activity and stability for ammonia synthesis due to the sintering of Ba and Ru particles on the outer surface of the microporous carbon framework, resulting in low molecular diffusion and weak synergistic effect of the catalytically active sites.

A simple permeability model for shale gas and key insights on relative importance of various transport mechanisms

Gas transport mechanism in a shale nanopore is investigated by considering convective flow, gas diffusion, and surface diffusion. A common practice in modeling shale gas permeability is to use Knudsen diffusion coefficient when calculating diffusive flux, but the use of Knudsen diffusion coefficient would be incorrect if the shale gas flow regime is lying either in the transition diffusion or Fick’s diffusion, in which case the diffusion coefficient must correspond to that regime. This study proposes an apparent permeability model of shale based on a unified diffusion coefficient that transforms its value per the flow regime, including the effect of molecular diffusion, viscous flow, and surface diffusion of adsorbed gas through linear superposition. The proposed model is verified by comparing against other models for shale gas permeability. Results of sensitivity analysis indicate that permeability of gas due to diffusive transport is independent of pressure and pore size when pressure is larger than 6.895 MPa, but is dominant at lower pressures and increases with pore size. For pore diameters larger than 100 nm, the permeability due to surface diffusion is independent of pressure or pore size, indicating negligible gas transport due to surface diffusion in relatively larger pores (>100 nm) at any pressure, but it is dominant in small pore sizes when pressure is below 10 MPa. Permeability of gas (with or without surface diffusion) increases with the decrease of pressure when the pore diameters are smaller than 100 nm, whereas for pore diameters larger than 300 nm it is not affected by pressure, but increases with the increase of pore size, indicating that Darcy’s law is applicable in pores with the diameters larger than 300 nm.

Compositional Simulation of CO2 Huff ’n’ Puff in Eagle Ford Tight Oil Reservoirs With CO2 Molecular Diffusion, Nanopore Confinement, and Complex Natural Fractures

Summary Although numerous studies proved the potential of carbon dioxide (CO2) huff ’n’ puff, relatively few models exist to comprehensively and efficiently simulate CO2 huff ’n’ puff in a way that considers the effects of molecular diffusion, nanopore confinement, and complex fractures for CO2. The objective of this study was to introduce a numerical compositional model with an embedded-discrete-fracture-model (EDFM) method to simulate this process in an actual Eagle Ford tight oil well. Through nonneighboring connections (NNCs), the EDFM method can properly and efficiently handle any complex fracture geometries. We built a 3D reservoir model with six fluid pseudocomponents. We performed history-matching with measured flow rates and bottomhole pressure (BHP). Good agreements between field data, EDFM, and local grid refinement (LGR) were achieved. However, the EDFM method performed faster than the LGR method. After that, we evaluated the CO2-enhanced-oil-recovery (EOR) effectiveness for molecular diffusion and nanopore confinement effects. The traditional phase equilibrium calculation was modified to calculate the critical fluid properties with nanopore confinement. The simulation results showed that the CO2 EOR with larger diffusion coefficients performed better than the primary production. In addition, both effects were favorable for the CO2 huff ’n’ puff effectiveness. The relative increase of cumulative oil production after 20 years was approximately 12% for this well. Furthermore, when considering complex natural fractures, the relative increase of cumulative oil production was approximately 8%. This study provided critical insights into a better understanding of the impacts of CO2 molecular diffusion, nanopore confinement, and complex natural fractures on well performance during the CO2-EOR process in tight oil reservoirs.

A comprehensive model for the prediction of fluid compositional gradient in two-dimensional porous media

Compositional gradient can be described as changes in the composition of components both vertically and horizontally in a hydrocarbon reservoir. In the present work, two-dimensional compositional gradient in multi-component gas and oil mixtures is modeled. A thermodynamic model is developed based on molecular diffusion coefficients in mass diffusive flux. A combination of Sigmund and Bird correlations is considered to estimate molecular diffusion coefficients for gas mixtures. Implementing this comprehensive developed model on a gas condensate sample shows interesting differences not only in trends of component compositions but also in gradient magnitude. A real set of data from a supergiant gas condensate field is used to validate the model. It is perceived that the developed model reduces relative absolute errors to about 50%. In the next step, a comprehensive study was conducted to understand the cross effects of molecular diffusion and natural convection in gas condensate and volatile oil samples. Gas and oil samples are selected to investigate if natural convection has the same effects in different samples. It is observed that increase in natural convection causes to reduce horizontal and vertical composition gradients. This effect is more significant in gas reservoir, as methane composition varies by more than 5.2 mol% diagonally in gas condensate sample, whereas this value is about 0.45 mol% in volatile oil sample. Lower density and higher bulk velocity in gas sample cause more disturbances in flow streams of gas mixture. Evaluation of the developed model shows that the model is reliable for reservoir studies and management programs.

Study of CO2 molecular diffusion effect on the production of fractured reservoirs: The role of matrix porosity, and a new model for predicting the oil swelling factor

The study of carbon dioxide injection into fractured reservoirs is of great importance, because carbon dioxide is the most effective greenhouse gas in the global warming phenomenon; moreover, being the residual oil in the matrix of fractured reservoirs is significant, with the injection of carbon dioxide into the fractured reservoirs, various mechanisms are involved which reduce the amount of residual oil, among which, the most important are: gravity drainage, molecular diffusion, oil swelling, viscosity reduction, evaporation and extraction. In the present study, we have two goals. The first one is the extension of previous studies of CO2 molecular diffusion effects on single block modeling of fractured reservoirs considering three porosities, 11%, 26% and 44%. For the porosity effect study, it is observed that, at a higher porosity, the viscosity decreases later, and the duration of viscosity reduction as well as increase in viscosity, or oil swelling and oil evaporation mechanism, is longer. Also, the higher the porosity of the matrix, the greater the effect of the molecular diffusion on the oil recovery. The second goal is to present a new model which calculates the oil swelling factor. In this regard, Fick’s second law is applied to a constant pressure diffusion cell considering the corresponding initial and boundary conditions. Then, taking into account the works by Kendall Marra et al. (1988), swelling model, by modifying the gridding and initial conditions, a new moving boundary swelling factor numerical model is presented. The model results are compared with measured experimental swelling factor data, which show good compatibility.

Effects of aqueous solubility and molecular diffusion on CO2-enhanced hydrocarbon recovery and storage from liquid-rich shale reservoirs

ABSTRACTThis study investigates the effects of aqueous solubility and aqueous molecular diffusion of gaseous components (CO2 and CH4) on the CO2 huff and puff process in the liquid-rich shale reservoirs. In a gas-condensate reservoir, the effects negligibly enhance the hydrocarbon production, but increase the CO2 storage with 4.4% by solubility trapping. In a shale oil reservoir, they increase the production and CO2 storage up to 5% and 14% by more CO2 imbibition and contacting between CO2 and oil. This study clarifies the importance of aqueous solubility and aqueous-phase molecular diffusion of CO2 huff and puff in shale reservoirs.

Cyclic CH4 Injection for Enhanced Oil Recovery in the Eagle Ford Shale Reservoirs

Gas injection is one of the most effective enhanced oil recovery methods for the unconventional reservoirs. Recently, CH4 has been widely used; however, few studies exist to accurately evaluate the cyclic CH4 injection considering molecular diffusion and nanopore effects. Additionally, the effects of operation parameters are still not systematically understood. Therefore, the objective of this work is to build an efficient numerical model to investigate the impacts of molecular diffusion, capillary pressure, and operation parameters. The confined phase behavior was incorporated in the model considering the critical property shifts and capillary pressure. Subsequently, we built a field-scale simulation model of the Eagle Ford shale reservoir. The fluid properties under different pore sizes were evaluated. Finally, a series of studies were conducted to examine the contributions of each key parameter on the well production. Results of sensitivity analysis indicate that the effect of confinement and molecular diffusion significantly influence CH4 injection effectiveness, followed by matrix permeability, injection rate, injection time, and number of cycles. Primary depletion period and soaking time are less noticeable for the well performance in the selected case. Considering the effect of confinement and molecular diffusion leads to the increase in the well performance during the CH4 injection process. This work, for the first time, evaluates the nanopore effects and molecular diffusion on the CH4 injection. It provides an efficient numerical method to predict the well production in the EOR process. Additionally, it presents useful insights into the prediction of cyclic CH4 injection effectiveness and helps operators to optimize the EOR process in the shale reservoirs.

Reynolds-number power-law scaling of differential molecular diffusion in turbulent nonpremixed combustion

A statistical analysis is conducted to provide support to a theoretical power-law scaling of the effect of differential molecular diffusion with respect to the Reynolds number in turbulent non-premixed combustion by using previously published direct number simulation data.

The Stability Criterion Model and Stability Analysis of Waxy Crude Oil Pipeline Transportation System Based on Excess Entropy Production

Based on the theory of non-equilibrium thermodynamics, considering the dynamic effect of molecular diffusion and the change in thermodynamic parameters caused by wax precipitation, the phenomenological relations of different thermodynamic “force” and “flow” interactions were derived. The corresponding thermodynamic model of a waxy crude oil pipeline transportation system was built, and then, the excess entropy production expression was proposed. Furthermore, the stability criterion model of the pipeline transportation system was established on the basis of Lyapounov stability theory. Taking the oil pipeline in Daqing oilfield as an example, based on the four parameters of out-station temperature, out-station pressure, flow rate and water content, the stable and unstable regions of the system were divided, and the formation mechanisms of the two different regions were analyzed. The experimental loop device of wax deposition rate was designed, and then, the wax deposition rate under the four parameters was measured. The results showed that the stable region of the wax deposition rate fluctuation was basically in accordance with the stability region analyzed by the criterion model established in this paper, which proved that the stability criterion model was feasible for analyzing the stability of the waxy crude oil pipeline transportation process.

Effect of Thermal Radiation, Chemical Reaction and Viscous Dissipation on MHD Flow

This study examines the effect of thermal radiation, chemical reaction and viscous dissipation on a magnetohydro- dynamic flow in between a pair of infinite vertical Couette channel walls. The momentum equation accounts the effects of both the thermal and the concentration buoyancy forces of the flow. The energy equation addresses the effects of the thermal radiation and viscous dissipation of the flow. Also, the concentration equation includes the effects of molecular diffusivity and chemical reaction parameters. The gray colored fluid considered in this study is a non-scattering medium and has the property of absorbing and emitting radiation. The Roseland approximation is used to describe the radiative heat flux in the energy equation. The velocity of flow transforms kinetic energy into heat energy. The increment of the velocity due to internal energy results in heating up of the fluid and consequently it causes increment of the thermal buoyancy force. The Eckert number being the ratio of the kinetic energy of the flow to the temperature difference of the channel walls is directly proportional to the thermal energy dissipation. It can be observed that increasing the Eckert number results in increasing velocity. A uniform magnetic field is applied perpendicular to the channel walls. The temperature of the moving wall is high enough due to the presence of thermal radiation. The solution of the governing equations is obtained using regular perturbation techniques. These techniques help to convert partial differential equations to a set of ordinary differential equations in dimensionless form and thus they are solved analytically. The following results are obtained: from the simulation study it is observed that the flow pattern of the fluid is affected due to the influence of the thermal radiation, the chemical reaction and viscous dissipation. The increment in the Hartmann number results in the increment of the Lorentz force but a decrement in velocity of the flow. An increment in the radiative parameter results in a decrement in temperature. An increment in the Prandtl number results in a decrement in thermal diffusivity. An increment in both the chemical reaction parameter and molecular diffusivity results in a decrement in concentration.

Quality Measures of Mixing in Turbulent Flow and Effects of Molecular Diffusivity

Results from numerical simulations of the mixing of two puffs of scalars released in a turbulent flow channel are used to introduce a measure of mixing quality, and to investigate the effectiveness of turbulent mixing as a function of the location of the puff release and the molecular diffusivity of the puffs. The puffs are released from instantaneous line sources in the flow field with Schmidt numbers that range from 0.7 to 2400. The line sources are located at different distances from the channel wall, starting from the wall itself, the viscous wall layer, the logarithmic layer, and the channel center. The mixing effectiveness is quantified by following the trajectories of individual particles with a Lagrangian approach and carefully counting the number of particles from both puffs that arrive at different locations in the flow field as a function of time. A new measure, the mixing quality index Ø, is defined as the product of the normalized fraction of particles from the two puffs at a flow location. The mixing quality index can take values from 0, corresponding to no mixing, to 0.25, corresponding to full mixing. The mixing quality in the flow is found to depend on the Schmidt number of the puffs when the two puffs are released in the viscous wall region, while the Schmidt number is not important for the mixing of puffs released outside the logarithmic region.

Effect of molecular weight and diffusivity on the adsorption of PEO-PPO-PEO block copolymers at PTFE-water and oil-water interfaces

The diffusion and adsorption behaviors of a few PEO-PPO-PEO type triblock copolymers, namely, Pluronics® L62, L64, F68, F87, and F88 at solid-liquid and liquid-liquid interfaces is investigated using water penetration through packed PTFE powder, dynamic surface tension (DST), interfacial tension (IFT), dynamic light scattering (DLS), and contact angle measurements. The water penetration and DST data reveal that the diffusivity of these block copolymers to the interface decreases with increase in the PEO molecular weight of the polymer and is governed by adsorption of surfactant molecules at the interface through PPO blocks. The DST and IFT results reveal faster diffusion to the interface for low molecular L62 and L64. The adsorption behaviors at isopropyl myristate (IPM)-water and PTFE-water interfaces are in good agreement, where lower molecular weight and lower PEO content favor the faster diffusion kinetics. The size of the formed emulsion droplets in presence of different surfactant molecules is measured using DLS, which shows bigger emulsion droplet size for high molecular weight and PEO containing polymer F88. Thus, it was found that surfactant having lower DST will result in higher wettability, lower contact angle, and lower interfacial tension.

Investigation of Cyclic $$\text {CO}_{2}$$ CO 2 Injection Process with Nanopore Confinement and Complex Fracturing Geometry in Tight Oil Reservoirs

Carbon dioxide is one of the capable processes in improving oil recovery from low-permeable oil reservoirs. However, the evaluation of cyclic $$\text {CO}_{2}$$ injection process with nanopore confinement effect in tight reservoirs is deficient in the oil industry. The nanopores confinement plays a significant role in low-permeable formations, creating a high capillary pressure which substantially influences fluid phase behavior and fluid flow in tight reservoirs. In order to consider the effect of nanopore confinement in unconventional reservoirs, the conventional methods need to be modified. Thus, we evolve an effective model for cyclic $$\text {CO}_{2}$$ injection process considering the effect of complex fracture geometry with nanopore confinement on the production from tight formations. Firstly, the reservoir fluid properties with nanopore confinement are estimated. Secondly, the minimum miscibility pressure is measured and verified with experimental data. Lastly, the well performance of cyclic $$\text {CO}_{2}$$ injection process in unconventional tight reservoirs is evaluated based on few parameters such as $$\text {CO}_{2}$$ diffusivity and matrix permeability. The results show that the combined effect of capillary pressure and $$\text {CO}_{2}$$ dispersion has significantly influenced the oil production efficiency from tight oil reservoirs. The oil recovery factor of cyclic $$\text {CO}_{2}$$ injection process at five years boosts from 14.67% as primary recovery to 22.54% due to $$\text {CO}_{2}$$ molecular diffusion effect with overall 7.87% incremental recovery. Moreover, the incremental oil recovery of cyclic $$\text {CO}_{2}$$ injection process is increased further by 1.7% while taking into consideration the combine effect of capillary pressure and $$\text {CO}_{2}$$ diffusion on the oil recovery. This study provides an appropriate method for predicting the production of cyclic $$\text {CO}_{2}$$ injection process with a complex fracture geometry, considering the capillary pressure and $$\text {CO}_{2}$$ diffusion on well performance of tight oil reservoirs.