Phase Saturation Research Articles

A NOVEL ANALYTICAL MODEL OF THE EFFECTIVE THERMAL CONDUCTIVITY OF POROUS MATERIALS UNDER STRESS

With the increasing demand for energy, heat and mass transfer through porous media has been widely studied. To achieve accuracy in studying the behavior of heat transfer, a good knowledge of the effective thermal conductivity (ETC) of porous materials is needed. Because pore structure dominates the ETC of porous materials and effective stress leads to a change in pore structure, effective stress is one of the key influencing factors affecting ETC. In this study, considering the structure of surface roughness and pore size, based on fractal theory, a novel analytical solution at the pore scale for ETC of porous materials under stress conditions is proposed. Furthermore, in this model, capillaries in porous materials saturated with multiple phases have sinusoidal periodically constricted boundaries. The derived ETC model is validated against available experimental data. Moreover, the influences of the effective stress, initial effective porosity, roughness structure characterization, and wetting phase saturation on the ETC are analyzed. Compared with previous models, the rough surfaces of porous materials and the coupling of heat conduction and mechanics are taken into consideration to make the model more reasonable. As a result, this ETC model can better reveal the mechanism of heat conduction in porous media under stress conditions.

Подход к определению коэффициента теплообмена между породой и смесью флюидов при моделировании процессов неизотермической многофазной фильтрации

The paper presents an approach to calculation of the coefficient determining the rate of heat transfer between a fluid mixture in oil reservoir and a matrix-rock. This coefficient is necessary for further joint modeling of hydrodynamic and thermal processes that occur in the field reservoir during its development using, for example, thermal methods for enhanced oil recovery. To model the processes of a non-isothermal multiphase flow, an approach based on implicit pressure calculation using the finite element method and explicit calculation of phase saturations is used. The approach to determining the heat transfer coefficient is based on solving the thermal problem in an area corresponding to a channel of a porous medium and a part of the matrix-rock around it. In this case, a fluid mixture with a known temperature value, different from the initial temperature in the channel and matrix-rock, enters the channel at a given rate. A two-dimensional problem is solved in an axisymmetric formulation by the finite element method.Numerical experiments to determine the heat transfer coefficient were carried out on models for various values of the channel size, porosity, initial temperatures of the medium, temperature of the mixture entering the channel, thermal properties of the fluid mixture and rock. As a result of the study, it was found that the channel size and porosity have the most significant effect on the value of the heat transfer coefficient, since these characteristics determine the volume of the matrix-rock, which should “warm up / cool down” when the temperature of the fluid mixture in the channel changes. Also, the coefficient values obtained were quite large, since the heat exchange between the rock and the mixture in the channel occurs in minutes, which practically corresponds to instantaneous heat transfer when it comes to modeling field development processes, where time steps are days and months.

Stochastic inverse modeling of transient laboratory-scale three-dimensional two-phase core flooding scenarios

We develop a comprehensive and efficient workflow for a stochastic assessment of key parameters governing two-phase flow conditions associated with core-scale experiments. We rely on original and detailed datasets collected on a Berea sandstone sample. These capture the temporal evolution of pressure drop across the core and three-dimensional maps of phase saturations (determined via X-ray CT) in oil- and brine-displacement flooding scenarios characterized by diverse brine/oil viscosity contrasts. Such experiments are used as a test-bed for the proposed stochastic model calibration strategy. The latter is structured across three main steps: (i) a preliminary calibration, aimed at identifying a behavioral region of the model parameter space; (ii) a Global Sensitivity Analysis (GSA), geared towards identification of the relative importance of model parameters on observed model outputs and assessment of non-influential parameters to reduce dimensionality of the parameter space; and (iii) a stochastic inverse modeling procedure. The latter is based on a differential-evolution genetic algorithm to efficiently explore the reduced parameter space stemming from the GSA. It enables one to obtain a probabilistic description of the relevant model parameters through their frequency distributions conditional on the detailed type of information collected. Coupling GSA with a stochastic parameter estimation approach based on a genetic algorithm of the type we consider enables streamlining the procedure and effectively cope with the considerable computational efforts linked to the two-phase scenario considered. Results show a remarkable agreement with experimental data and imbue us with confidence on the potential of the approach to embed the type of rich datasets considered towards model parameter estimation fully including uncertainty.

Method of Distributions for Two‐Phase Flow in Heterogeneous Porous Media

AbstractMultiscale heterogeneity and insufficient characterization data for a specific subsurface formation of interest render predictions of multi‐phase fluid flow in geologic formations highly uncertain. Quantification of the uncertainty propagation from the geomodel to the fluid‐flow response is typically done within a probabilistic framework. This task is computationally demanding due to, for example, the slow convergence of Monte Carlo simulations (MCS), especially when computing the tails of a distribution that are necessary for risk assessment and decision‐making under uncertainty. The frozen streamlines method (FROST) accelerates probabilistic predictions of immiscible two‐phase fluid flow problems; however, FROST relies on MCS to compute the travel‐time distribution, which is then used to perform the transport (phase saturation) computations. To alleviate this computational bottleneck, we replace MCS with a deterministic equation for the cumulative distribution function (CDF) of travel time. The resulting CDF‐FROST approach yields the CDF of the saturation field without resorting to sampling‐based strategies. Our numerical experiments demonstrate the high accuracy of CDF‐FROST in computing the CDFs of both saturation and travel time. For the same accuracy, it is about 5 and 10 times faster than FROST and MCS, respectively.

Nucleation as a rate-determining step in catalytic gas generation reactions from liquid phase systems.

The observable reaction rate of heterogeneously catalyzed reactions is known to be limited either by the intrinsic kinetics of the catalytic transformation or by the rate of pore and/or film diffusion. Here, we show that in gas generation reactions from liquid reactants, the nucleation of gas bubbles in the catalyst pore structure represents an additional important rate-limiting step. This is highlighted for the example of catalytic hydrogen release from the liquid organic hydrogen carrier compound perhydro-dibenzyltoluene. A nucleation-inhibited catalytic system produces only dissolved hydrogen with fast saturation of the fluid phase around the active site, while bubble formation enhances mass transfer by more than a factor of 50 in an oscillating reaction regime. Nucleation can be efficiently triggered not only by temperature changes and catalyst surface modification but also by a mechanical stimulus. Our work sheds new light on performance-limiting factors in reactions that are of highest relevance for the future green hydrogen economy.

Performance of alcoholic solvents in the continuous countercurrent spent coffee grounds oil extraction

Ethanol and isopropanol, absolute (ET0, IPA0) and hydrated with 6 and 12 water mass% (ET6, IPA12), were evaluated as solvents in the oil extraction from spent coffee grounds (SCGO). Alcohols' performance evaluation was based on the SCGO partitioning between extract and raffinate phases and the extractor design. An SCGO concentration limit in systems containing ET indicates extract phase saturation. In this case, a Langmuir-type equation provided a satisfactory SCGO partitioning data mathematical description, while the IPA data presented a linear behavior. The increase in temperature from 60 to 80 °C did not affect SCGO partitioning when IPA0 was used as a solvent. ET6 required higher solvent proportions concerning SCG, leading to extractors with a higher number of theoretical stages. The minimum flow rates of ET6 were 1.9 times higher than those required by ET0 and IPA12 and up to 3.2 times higher than the IPA0 flow rate at 60 °C. At 80 °C, the SCGO extraction performance with ET0 and IPA0 was similar. A solvent-to-feed ratio of at least five must be used when an extractor with five theoretical stages operating at 80 °C is considered. In this case, extracts with about 5 mass% of SCGO are obtained.

Mathematical Model of the Process of Non-Equilibrium Hydrate Formation in a Porous Reservoir during Gas Injection

Increasing the efficiency of natural gas storage in geological formations is possible by transferring gas from a free state to a gas hydrate state, since gas hydrates have a number of unique properties. For example, 1 m3 of methane hydrate contains 164 m3 of gas under normal conditions. It is possible to store a sufficiently large amount of gas in a small volume at a relatively low pressure. To study the regularities of the process of formation of underground gas hydrate gas storage, this article presents a mathematical model of the process of methane injection into a natural reservoir saturated with methane and water, accompanied by the formation of gas hydrate. Unlike previous works, the constructed mathematical model additionally takes into account a number of factors: the filtration flow of water, the real gas properties, the Joule–Thomson effects and adiabatic compression. The process of gas hydrate formation is considered as a non-equilibrium phase transition. Numerical solutions of the problem are constructed that describe the distributions of parameters (temperature, pressure, phase saturations) in a reservoir. Dependences are obtained that reveal the regularities of the process of non-equilibrium formation of gas hydrate in a natural reservoir during gas injection. The influence of gas injection pressure and temperature, as well as reservoir porosity and permeability, on the distributions of pressure, temperature, water saturation and hydrate saturation in the reservoir, as well as on the dynamics of changes in these parameters and the mass of gas hydrate formed in the reservoir over time, are analyzed.

Fluid-Fluid Interfacial Area and Its Impact on Relative Permeability: A Pore Network Modeling Study

SummaryRelative permeability (kr) is commonly modeled as an empirical function of phase saturation. Although current empirical models can provide a good match of one or two measured relative permeabilities using saturation alone, they are unable to predict relative permeabilities well when there is hysteresis or when physical properties such as wettability change. Further, current models often result in relative permeability discontinuities that can cause convergence and accuracy problems in simulation. To overcome these problems, recent research has modeled relative permeability as a state function of both saturation (S) and phase connectivity (X). Pore network modeling (PNM) data, however, show small differences in relative permeability for the same S-X value when approached from a different flow direction. This paper examines the impact of one additional Minkowski parameter (Mecke and Arns 2005), the fluid-fluid interfacial area, on relative permeability to identify if that satisfactorily explains this discrepancy.We calculate the total fluid-fluid interfacial areas (IA) during two-phase (oil/water) flow in porous media using PNM. The area is calculated from PNM simulations using the areas associated with corners and throats in pore elements of different shapes. The pore network is modeled after a Bentheimer sandstone, using square, triangular prism, and circular pore shapes. Simulations were conducted for numerous primary drainage (PD) and imbibition cycles at a constant contact angle of 0° for the wetting phase. Simultaneous measurements of capillary pressure, relative permeability, saturation, and phase connectivity are made for each displacement. The fluid-fluid IA is calculated from the PNM capillary pressure, the fluid location in the pore elements, and the pore element dimensional data.The results show that differences in the relative permeability at the same (S, X) point are explained well by differences in the fluid-fluid interfacial area (IA). That is, for a larger change in IA at these intersection points, the permeability difference is greater. That difference in relative permeability approaches zero as the difference in IA approaches zero. This confirms that relative permeability can be modeled better as a unique function of S, X, and IA. The results also show that an increase in IA restricts flow decreasing the nonwetting (oil) phase permeability. This decrease is caused by an increase in the throat area fraction compared to the corner area as the total area IA increases. The wetting phase relative permeability, however, shows the inverse trend in that its relative permeability is greater when IA becomes larger owing to a greater fraction of the total area associated with the corners. The area IA, however, impacts the nonwetting phase relative permeability more than the wetting phase relative permeability. Corner flow improves the wetting phase relative permeability because the wetting phase is continuous there. Finally, a sensitivity analysis shows that relative permeability is more sensitive to change in S than it is for IA for the case studied, implying that if only two parameters are used to model relative permeability, it is better to choose S and X.

Hydrodynamics of gas-liquid displacement in porous media: Fingering pattern evolution at the breakthrough moment and the stable state

Gas-liquid displacement in porous media widely exists in many terrestrial/extraterrestrial subsurface resource extraction and utilization applications. The typical fingering displacement during gas invading has been well identified through extensive research efforts. Yet, the evolution of fingering structures after invading breakthrough is rarely reported. Herein, through a joint approach of experimental flow imaging and digital image processing, we investigated the gas-liquid fingering displacement in a porous-patterned microfluidic chip from the breakthrough moment until reaching the steady state. With a wide range of capillary number Ca and viscosity ratio M, we visualized the evolution of finger morphologies in different flow regimes including capillary fingering (CF), viscous fingering (VF), and crossover zone (CZ). Interestingly, we found that finger structures of CF regime remain the same after the breakthrough, whereas fingers of VF regime keep expanding until almost all the pore space is invaded and eventually reaches to steady state. Followed with experimental observations, a comparative quantification of fingering patterns was also conducted in terms of invasion velocity, phase saturation and fractal dimension. A dramatic increase of gas saturation, from 0.15 to 0.60 at the case of Log10Ca=-5.17 and Log10M=-2.78, is obtained in the VF regime when the steady state is reached, so is the fractal dimension (from 0.14 to 0.16, even higher than one of CF). The underlying mechanism of such fingering expansion in VF is further revealed from the time evolution of fingering after breakthrough. A previously unobserved fingering cycle, consisting of new finger forming, cap invading, breakthrough and finger vanishing, keeps repeating until the saturation reaches the maximum. We believe that these findings are of significance in evaluating extraction effectiveness, economic benefits and storage safety for subsurface applications.

An efficient and physically consistent numerical method for the Maxwell–Stefan–Darcy model of two‐phase flow in porous media

AbstractNumerical modeling of two‐phase flow in porous media has extensive applications in subsurface flow and petroleum industry. A comprehensive Maxwell–Stefan–Darcy (MSD) two‐phase flow model has been developed recently, which takes into consideration the friction between two phases by a thermodynamically consistent way. In this article, we for the first time propose an efficient energy stable numerical method for the MSD model, which can preserve multiple important physical properties of the model. First, the proposed scheme can preserve the original energy dissipation law. This is achieved through a newly‐developed energy factorization approach that leads to linear semi‐implicit discrete chemical potentials. Second, the scheme preserves the famous Onsager's reciprocal principle and the local mass conservation law for both phases by introducing different upwind strategies for two phase saturations and applying the cell‐centered finite volume method to the original formulation of the model. Third, by introducing two auxiliary phase velocities, the scheme has ability to guarantee the positivity of both saturations under proper conditions. Another distinct feature of the scheme is that the resulting discrete system is totally linear, well‐posed and unbiased for each phase. Numerical results are also provided to show the excellent performance of the proposed scheme.

Counter-current imbibition and non-linear diffusion in fractured porous media: Analysis of early- and late-time regimes and application to inter-porosity flux

The displacement of non-aqueous phase liquid (NAPL) in permeable porous rock by water saturating the surrounding fractures is studied. In many situations of practical interest, capillarity is the dominant driving force. Using the global pressure concept, it is shown that the water saturation is driven by a generic non-linear diffusion equation governing the matrix block counter-current spontaneous imbibition. In addition, in most cases, the saturation-dependent diffusion coefficient vanishes at the saturation end points, that renders the driving equation highly singular.In this paper, two exact asymptotic solutions valid for short and long times are presented, under the assumption that the conductivity vanishes as a power-law of both phase saturations at the extreme values of the fluid saturation.Focusing on the late-time domain, the asymptotic solution is derived using an Ansatz that is written under the form of a power-law time decay of the NAPL saturation. In the spatial domain, this solution is an eigenvector of the non-linear diffusion operator driving the saturation, for a problem with Dirichlet boundary conditions. If the diffusion coefficient varies as a power law of the NAPL saturation, the spatial variations of the solution are given analytically for a one-dimensional porous medium corresponding to parallel fracture planes. The analytical solution is in very good agreement with results of numerical simulations involving various realistic sets of input transport parameters.Generalization to the case of two- or three-dimensional matrix blocks of arbitrary shape is proposed using a similar Ansatz, solution of a non-linear eigenvalue problem. A fast converging algorithm based on a fixed-point sequence starting from a suitable first guess was developed. Comparisons with full-time simulations for several typical block geometries show an excellent agreement.These results permit to set-up an analytical formulation generalizing linear single-phase representation of matrix-to-fracture exchange term. It accounts for the non-linearity of the local flow equations using the power-law dependence of the conductivity for low NAPL saturation. The corresponding exponent can be predicted from the input conductivity parameters. Similar findings are also presented and validated numerically for two- or three-dimensional matrix blocks. That original approach paves the way to research leading to a more faithful description of matrix-to-fracture exchanges when considering a realistic fractured medium composed of a population of matrix blocks of various size and shapes.

Existence of a Weak Solutionto the Two-Dimensional Filtration Problem in a Thin Poroelastic Layer

The paper considers a mathematical model of the joint motion of two immiscible incompressible fluids in a poroelastic medium. This model is a generalization of the classical Musket-Leverett model, in which porosity is considered to be a given function of the spatial coordinate. The model under study is based on the mass conservation equations for liquids and the porous skeleton, Darcy's law for liquids, which takes into account the movement of the porous skeleton, the Laplace formula for capillary pressure, the Maxwell-type rheological equation for porosity, and the "system as a whole" equilibrium condition. In the thin layer approximation, the original problem is reduced to the successive determination of the porosity of the solid skeleton and its velocity. Then an elliptic-parabolic system is derived for the “reduced pressure” and saturation of the wetting phase. Its solution is understood in a generalized sense due to the degeneration on the solution of the equations of the system. The proof of the existence theorem is carried out in four stages: regularization of the problem, proof of the physical maximum principle for saturation, construction of Galerkin approximations, passage to the limit in regularization parameters based on the method of compensated compactness.

Seepage Characteristics of Mixed-Wettability Porous Media on the Phase-Field Model.

Clarifying the microscale gas–water flow behaviors in a mixed wettability reservoir is of great importance for underground engineering. A numerical model of mixed wettability based on circular particles was constructed using the MATLAB stochastic distribution program, and the gas–water flow was simulated based on the phase-field method. The Navier–Stokes equations were solved by the finite element method. The work analyzed the effects of the content of heterogeneous wetting particles, wettability, and inversed wettability of the matrix on the flow path and pressure distribution of the mixed wettability model. Besides, the two-phase flow behaviors were evaluated in microscale mixed-wettability porous media. The simulation results revealed that (i) the residual saturation of the gas phase showed a positive correlation with the hydrophobic particle content, and closed gases only existed in isolated pore channels with small content. Isolated closed gases gradually connected as the content increased. (ii) The residual gas content in the corner and tail end increased as the hydrophobicity of particles increased in hydrophilic matrices. Hydrophobic matrices showed a negative correlation, with the greatest pressure drop due to capillary resistance and step changes in the neutral-hydrophobic transition zone. (iii) Water-phase breakthrough time and gas-phase residual saturation showed a negative correlation change. The more space occupied by the gas phase, the faster the water-phase breakthrough. Moreover, the saturation no longer changes after the breakthrough. The work provides a guideline for determining the dominant flow path of phase displacements and the distribution of residual phases.

Sensitivity Analysis of Fluid–Fluid Interfacial Area, Phase Saturation and Phase Connectivity on Relative Permeability Estimation Using Machine Learning Algorithms

Recent studies have shown that relative permeability can be modeled as a state function which is independent of flow direction and dependent upon phase saturation (S), phase connectivity (X), and fluid–fluid interfacial area (A). This study evaluates the impact of each of the three state parameters (S, X, and A) in the estimation of relative permeability. The relative importance of the three state parameters in four separate quadrants of S-X-A space was evaluated using a machine learning algorithm (out-of-bag predictor importance method). The results show that relative permeability is sensitive to all the three parameters, S, X, and A, with varying magnitudes in each of the four quadrants at a constant value of wettability. We observe that the wetting-phase relative permeability is most sensitive to saturation, while the non-wetting phase is most sensitive to phase connectivity. Although the least important, fluid–fluid interfacial area is still important to make the relative permeability a more exact state function.

Determination of kinetic parameters of the hardening phases in Al–Mg–Si alloy using DSC analysis and its photo-electrochemical protection

Differential scanning calorimetric (DSC) is a good tool for investigating the phases transformation, since it permits the determination of the kinetic parameters such as activation energy and reaction order. The hardening phase precipitation in the Al–Mg–Si alloy was investigated by using DSC and isothermal and non-isothermal calculation models. All specimens were treated up to 550 °C with heating rates (ν) of 5, 10, 20 and 30 °C/min. The shift from the temperature peak to a higher for high heating rate indicates that the precipitation reactions are thermally activated. The results showed that the activation energy and the reaction orders, obtained from both methods are similar. The decreased activation energy is attributed to the saturation of the previous phase, which acts as precursor for the metastable phases. The pre-exponential factor (ko) calculated by the isothermal calculation method is equal to 8.36 × 107 s−1. On the other hand, the corrosion resistance of the alloy is significantly enhanced by photoelectrochemical cathodic protection. This was achieved by short-circuiting the alloy to n-CdS under visible irradiation where the corrosion current decreases by 88%.

Stress concentration in shape memory alloy sheets with circular cavities: Effects of transformation, saturation, and plasticity

The analysis of stress concentration in geometrically heterogeneous smart structures is of great importance. In this study, by utilizing a recent constitutive model which considered both transformation and plasticity of shape memory alloys (SMAs), the stress concentration factor (SCF) in plates with circular cavities is investigated and the effect of phase transformation, saturation, and plasticity which may occur locally is studied. The results show that the conversion of the austenitic phase to the martensite leads to a reduction in SCF. After saturation of phase transformation at the stress concentration point, the SCF increases until the entire sheet enters the martensite phase. In the example under study, the SCF reaches 5.8 which is greatly higher than the elastic SCF. By entering the plastic region locally, the SCF reduces. Also, the modeling of sheets with more than one cavity has been done. It is concluded that extra hole, as a stress relief method, has a stronger effect on decreasing maximum stress concentration of shape memory alloys (considering transformation and plasticity) compared to purely elastic stress concentration studies.

Generic saturation-induced phase error correction for structured light 3D shape measurement.

Intensity saturation is a challenging problem in structured light 3D shape measurement. Most of the existing methods achieve high dynamic range (HDR) measurement by sacrificing measurement speed, making them limited in high-speed dynamic applications. This Letter proposes a generic efficient saturation-induced phase error correction method for HDR measurement without increasing any fringe patterns. We first theoretically analyze the saturated signal model and deduce the periodic characteristic of saturation-induced phase error. Based on this, we specially design a saturation-induced phase error correction method by joint Fourier analysis and Hilbert transform. Furthermore, the relationship among phase error, saturation degree, and number of phase-shifting steps is established by numerical simulation. Since the proposed method requires no extra captured images or complicated intensity calibration, it is extremely convenient in implementation and is applicable to performing high-speed 3D shape measurements. Simulations and experiments verify the feasibility of the proposed method.

Retaining an Upper Bound for the Capillary Retention of Two-Phase Flow in Porous Media

At the sub-meter scale, capillary retention occurs when two immiscible phases flow across two heterogeneous media. It happens in the upstream medium, and the phase retained depends on the heterogeneity order and the system wettability. This phenomenon has a major impact on the oil recovery and hence requires comprehension. The analysis of the spatial variation in the phase saturation along the flowing domain is well established. However, the literature lacks the general characteristics of capillary retention caused by such variation at various flowing conditions. The continuum model for the flow of two immiscible phases in porous media at steady-state conditions is examined. The analysis is limited to the medium with a single discontinuity in rock properties. In this examination, the characteristics of the capillary retention upstream of the discontinuity are the primary consideration. Three retention regions related to the flow regime are identified: two plateaus and a transition zone occurring, in general, at intermediate capillary number. The width and location of the transition depend on the fractional flow. The crucial finding is related to the identification of an upper bound for the capillary retention and its dependency on the capillary variable ratio and the form of the Leverett J-curve. Two J-models are investigated, and it is shown that, for a given capillary variable ratio, the upper bound depends on the level of flatness of the J-curve at intermediate saturations. Potential implications of the current analysis to reservoir characterization are also discussed.Article HighlightsThree retention regions related to the ow regime are identified: two plateaus and a transition zone occurring at intermediate capillary numbers. The width and position of the transition depend on the fractional flow.An upper bound for the capillary retention is derived and its dependency on the heterogeneity ratio and the form of the Leverett-J curve is discussed..Potential implication to reservoir characterization: In the case of steeper Leverett-J curves with low to moderate random heterogeneity ratios, the upper bound is minimal regardless of the various lithologies and their congurations. In such conditions, the upper bound can be used to assert the insignicance of the eld-scale capillary retention.

Permeability Models of Hydrate-Bearing Sediments: A Comprehensive Review with Focus on Normalized Permeability

Natural gas hydrates (NGHs) are regarded as a new energy resource with great potential and wide application prospects due to their tremendous reserves and low CO2 emission. Permeability, which governs the fluid flow and transport through hydrate-bearing sediments (HBSs), directly affects the fluid production from hydrate deposits. Therefore, permeability models play a significant role in the prediction and optimization of gas production from NGH reservoirs via numerical simulators. To quantitatively analyze and predict the long-term gas production performance of hydrate deposits under distinct hydrate phase behavior and saturation, it is essential to well-establish the permeability model, which can accurately capture the characteristics of permeability change during production. Recently, a wide variety of permeability models for single-phase fluid flowing sediment have been established. They typically consider the influences of hydrate saturation, hydrate pore habits, sediment pore structure, and other related factors on the hydraulic properties of hydrate sediments. However, the choice of permeability prediction models leads to substantially different predictions of gas production in numerical modeling. In this work, the most available and widely used permeability models proposed by researchers worldwide were firstly reviewed in detail. We divide them into four categories, namely the classical permeability models, reservoir simulator used models, modified permeability models, and novel permeability models, based on their theoretical basis and derivation method. In addition, the advantages and limitations of each model were discussed with suggestions provided. Finally, the challenges existing in the current research were discussed and the potential future investigation directions were proposed. This review can provide insightful guidance for understanding the modeling of fluid flow in HBSs and can be useful for developing more advanced models for accurately predicting the permeability change during hydrate resources exploitation.

Neutron Response Modeling to Track Lean Gas Plume in Recycled Gas Cap Reservoir in Concurrent Gas Cap-Oil Rim Development: A Step Forward

Summary Gas cap pressure maintenance while developing the associated oil rim is a critical aspect for optimum recovery. Preventing gas cap pressure dropping below dewpoint by injecting lean gas is essential for concurrent gas cap-oil rim development. Reservoir heterogeneity aggravates lean gas override causing preferential movement of lean gas plume. Thus, it is important to track lean gas plume while recycling and understanding the breakthrough potential of lean gas. This paper demonstrates a new workflow to track lean gas plume by estimating phase saturations with a case study from one of the giant oil and gas fields, Onshore, Abu Dhabi. Pulsed neutron capture (PNC) tools are used for reservoir monitoring and surveillance. However, sigma log evaluation is insufficient to derive individual hydrocarbon phase saturations to monitor lean gas plume. Neutron response modeling (NRM) is devised to differentiate between lean and rich gas. NRM is a probabilistic solver with input of mineral and fluid phase parameters into tool response functions in petrophysical evaluation. To distinguish with discrete neutron fluid response between lean and rich gas, pressure/volume/temperature (PVT) data are utilized to derive hydrogen index, capture cross section, thermal decay length, and neutron macro parameters, such as neutron slowing down length and migration length. Neutron response is investigated for lean and rich gas with sensitivity of invasion effects on neutron log by calibrating to core porosity. The response for each phase under thermal neutron and capture modes with corresponding raw neutron log statistics is reviewed in both openhole and casedhole environments in known lean/rich gas intervals. Thirty-five wells spread across gas cap and oil leg with quality neutron log data are modeled and individual phase saturations are estimated. The target reservoir is under development with over three decades of lean gas injection to support oil production. NRM results and phase saturations are validated with recent formation sampling, which enhanced the confidence in the overall workflow. Later, the results are verified to be in excellent agreement with lean gas injection and production history of the target reservoir. The identified movement of lean gas highlights nonuniform geology and gravity segregation of injected lean gas into upper members of the target reservoir. The results also emphasized the need for better injection support to lower members of the target reservoir where gas cap development is ongoing. The solution presented is unique, particularly for lean gas injection projects by utilizing PVT for NRM based on neutron transport mechanism in pore fluids. Existing workflows require a special nuclear modeling platform with computationally expensive processing on data sets acquired using advanced logging technology. In spite of these prerequisites, existing workflows are not able to distinguish lean gas over rich gas. This paper effectively demonstrates NRM workflow distinguishing lean gas plume from rich gas using neutron logs and reveals compelling reservoir management insights. The sensitivity studies and practicality of this workflow highlight the fundamental importance of neutron logs in mature fields.