Two-Dimensional Modeling of the NAPL Dissolution in Porous Media: Heterogeneities Effects on the Large Scale Permeabilities and Mass Exchange Coefficient

In this paper, we are interested by the dissolution of NAPL (Non-Aqueous Phase Liquid) contaminants in heterogeneous soils or aquifers. The volume averaging technique is applied to 2D systems with Darcy-scale heterogeneities. A large-scale model is derived from a Darcy-scale dissolution model in the case of small and large Damkholer numbers, i.e., for smooth or sharp dissolution fronts. The resulting models in both cases have the mathematical structure of a non-equilibrium dissolution model. It is shown how to calculate the resulting mass exchange and relative permeability terms from the Darcy-scale heterogeneities and other fluid properties. One of the important finding is that the obtained values have a very different behavior compared to the Darcy-scale usual correlations. The large scale correlations are also very different between the two limit cases. The resulting large-scale models are compared favorably to Darcy-scale direct simulations.

Homotopy analysis solution for micropolar fluid flow through porous channel with expanding or contracting walls of different permeabilities

The flow of a micropolar fluid through a porous channel with expanding or contracting walls of different permeabilities is investigated. Two cases are considered, in which opposing walls undergo either uniform or non-uniform motion. In the first case, the homotopy analysis method （HAM） is used＇to obtain the expressions for the velocity and micro-rotation fields. Graphs are sketched for some parameters. The results show that the expansion ratio and the different permeabilities have important effects on the dynamic characteristics of the fluid. Following Xu＇s model, in the second case which is more general, the wall expansion ratio varies with time. Under this assumption, the governing equations axe transformed into nonlinear partial differential equations that can also be solved analytically by the HAM. In the process, both algebraic and exponential models are considered to describe the evolution of α（t） from the initial state α0 to the final state al. As a result, the time-dependent solutions are found to approach the steady state very rapidly. The results show that the time-dependent variation of the wall expansion ratio can be ignored because of its limited effects.

Tracing in vivo of the vascular and cellular membranous permeabilities in the experimentally infected suckling mice with Chen

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Anisotropic dynamic permeability model for porous media

Based on the tortuous capillary network model,the relationship between anisotropic permeability and rock normal strain,namely the anisotropic dynamic permeability model(ADPM),was derived and established.The model was verified using pore-scale flow simulation.The uniaxial strain process was calculated and the main factors affecting permeability changes in different directions in the deformation process were analyzed.In the process of uniaxial strain during the exploitation of layered oil and gas reservoirs,the effect of effective surface porosity on the permeability in all directions is consistent.With the decrease of effective surface porosity,the sensitivity of permeability to strain increases.The sensitivity of the permeability perpendicular to the direction of compression to the strain decreases with the increase of the tortuosity,while the sensitivity of the permeability in the direction of compression to the strain increases with the increase of the tortuosity.For layered reservoirs with the same initial tortuosity in all directions,the tortuosity plays a decisive role in the relative relationship between the variations of permeability in all directions during pressure drop.When the tortuosity is less than 1.6,the decrease rate of horizontal permeability is higher than that of vertical permeability,while the opposite is true when the tortuosity is greater than 1.6.This phenomenon cannot be represented by traditional dynamic permeability model.After the verification by experimental data of pore-scale simulation,the new model has high fitting accuracy and can effectively characterize the effects of deformation in different directions on the permeability in all directions.

Hydromechanical characterization of gas transport amidst uncertainty for underground nuclear explosion detection

Given the challenge of definitively discriminating between chemical and nuclear explosions using seismic methods alone,surface detection of signature noble gas radioisotopes is considered a positive identification of underground nuclear explosions(UNEs).However,the migration of signature radionuclide gases between the nuclear cavity and surface is not well understood because complex processes are involved,including the generation of complex fracture networks,reactivation of natural fractures and faults,and thermo-hydro-mechanical-chemical(THMC)coupling of radionuclide gas transport in the subsurface.In this study,we provide an experimental investigation of hydro-mechanical(HM)coupling among gas flow,stress states,rock deformation,and rock damage using a unique multi-physics triaxial direct shear rock testing system.The testing system also features redundant gas pressure and flow rate measurements,well suited for parameter uncertainty quantification.Using porous tuff and tight granite samples that are relevant to historic UNE tests,we measured the Biot effective stress coefficient,rock matrix gas permeability,and fracture gas permeability at a range of pore pressure and stress conditions.The Biot effective stress coefficient varies from 0.69 to 1 for the tuff,whose porosity averages 35.3%±0.7%,while this coefficient varies from 0.51 to 0.78 for the tight granite(porosity<1%,perhaps an underestimate).Matrix gas permeability is strongly correlated to effective stress for the granite,but not for the porous tuff.Our experiments reveal the following key engineering implications on transport of radionuclide gases post a UNE event:(1)The porous tuff shows apparent fracture dilation or compression upon stress changes,which does not necessarily change the gas permeability;(2)The granite fracture permeability shows strong stress sensitivity and is positively related to shear displacement;and(3)Hydromechanical coupling among stress states,rock damage,and gas flow appears to be stronger in tight granite than in porous tuff.

Liquid injectivity in a SAG foam process:Effect of permeability

Foam is utilized in enhanced oil recovery and CO_(2) sequestration.Surfactant-alternating-gas(SAG)is a preferred approach for placing foam into reservoirs,due to it enhances gas injection and minimizes corrosion in facilities.Our previous studies with similar permeability cores show that during SAG injection,several banks occupy the area near the well where fluid exhibits distinct behaviour.However,underground reservoirs are heterogeneous,often layered.It is crucial to understand the effect of permeability on fluid behaviour and injectivity in a SAG process.In this work,coreflood experiments are conducted in cores with permeabilities ranging from 16 to 2300 mD.We observe the same sequence of banks in cores with different permeabilities.However,the speed at which banks propagate and their overall mobility can vary depending on permeability.At higher permeabilities,the gas-dissolution bank and the forced-imbibition bank progress more rapidly during liquid injection.The total mobilities of both banks decrease with permeability.By utilizing a bank-propagation model,we scale up our experimental findings and compare them to results obtained using the Peaceman equation.Our findings reveal that the liquid injectivity in a SAG foam process is misestimated by conventional simulators based on the Peaceman equation.The lower the formation permeability,the greater the error.

Pericytes protect rats and mice from sepsis-induced injuries by maintaining vascular reactivity and barrier function:implication of miRNAs and microvesicles

Background Vascular hyporeactivity and leakage are key pathophysiologic features that produce multi-organ damage upon sepsis.We hypothesized that pericytes,a group of pluripotent cells that maintain vascular integrity and tension,are protective against sepsis via regulating vascular reactivity and permeability.Methods We conducted a series of in vivo experiments using wild-type(WT),platelet-derived growth factor receptor-β(PDGFR-β)-Cre+mT/mG transgenic mice and Tie2-Cre+Cx43^(flox/flox)mice to examine the relative contribution of pericytes in sepsis,either induced by cecal ligation and puncture(CLP)or lipopolysaccharide(LPS)challenge.In a separate set of experiments with Sprague-Dawley(SD)rats,pericytes were depleted using CP-673451,a selective PDGFR-βinhibitor,at a dosage of 40 mg/(kg·d)for 7 consecutive days.Cultured pericytes,vascular endothelial cells(VECs)and vascular smooth muscle cells(VSMCs)were used for mechanistic investigations.The effects of pericytes and pericyte-derived microvesicles(PCMVs)and candidate miRNAs on vascular reactivity and barrier function were also examined.Results CLP and LPS induced severe injury/loss of pericytes,vascular hyporeactivity and leakage(P<0.05).Transplantation with exogenous pericytes protected vascular reactivity and barrier function via microvessel colonization(P<0.05).Cx43 knockout in either pericytes or VECs reduced pericyte colonization in microvessels(P<0.05).Additionally,PCMVs transferred miR-145 and miR-132 to VSMCs and VECs,respectively,exerting a protective effect on vascular reactivity and barrier function after sepsis(P<0.05).miR-145 primarily improved the contractile response of VSMCs by activating the sphingosine kinase 2(Sphk2)/sphingosine-1-phosphate receptor(S1PR)1/phosphorylation of myosin light chain 20 pathway,whereas miR-132 effectively improved the barrier function of VECs by activating the Sphk2/S1PR2/zonula occludens-1 and vascular endothelial-cadherin pathways.Conclusions Pericytes are protective against sepsis through regulating vascular reactivity and barrier function.Possible mechanisms include both direct colonization of microvasculature and secretion of PCMVs.

Quercetin Alleviates Lipopolysaccharide-Induced Cardiac Inflammation via Inhibiting Autophagy and Programmed Cell Death

Objective The aim of this study is to explore the potential modulatory role of quercetin against Endotoxin or lipopolysaccharide(LPS)induced septic cardiac dysfunction.Methods Specific pathogen-free chicken embryos(n=120)were allocated untreated control,phosphate buffer solution(PBS)vehicle,PBS with ethanol vehicle,LPS(500 ng/egg),LPS with quercetin treatment(10,20,or 40 nmol/egg,respectively),Quercetin groups(10,20,or 40 nmol/egg).Fifteenday-old embryonated eggs were inoculated with abovementioned solutions via the allantoic cavity.At embryonic day 19,the hearts of the embryos were collected for histopathological examination,RNA extraction,real-time polymerase chain reaction,immunohistochemical investigations,and Western blotting.Results They demonstrated that the heart presented inflammatory responses after LPS induction.The LPS-induced higher mRNA expressions of inflammation-related factors(TLR4,TNFα,MYD88,NF-κB1,IFNγ,IL-1β,IL-8,IL-6,IL-10,p38,MMP3,and MMP9)were blocked by quercetin with three dosages.Quercetin significantly decreased immunopositivity to TLR4 and MMP9 in the treatment group when compared with the LPS group.Quercetin significantly decreased protein expressions of TLR4,IFNγ,MMP3,and MMP9 when compared with the LPS group.Quercetin treatment prevented LPS-induced increase in the mRNA expression of Claudin 1 and ZO-1,and significantly decreased protein expression of claudin 1 when compared with the LPS group.Quercetin significantly downregulated autophagyrelated gene expressions(PPARα,SGLT1,APOA4,AMPKα1,AMPKα2,ATG5,ATG7,Beclin-1,and LC3B)and programmed cell death(Fas,Bcl-2,CASP1,CASP12,CASP3,and RIPK1)after LPS induction.Quercetin significantly decreased immunopositivity to APOA4,AMPKα2,and LC3-II/LC3-I in the treatment group when compared with the LPS group.Quercetin significantly decreased protein expressions of AMPKα1,LC3-I,and LC3-II.Quercetin significantly decreased the protein expression to CASP1 and CASP3 by immunohistochemical investigation or Western blotting in treatment group when compared with LPS group.Conclusion Quercetin alleviates cardiac inflammation induced by LPS through modulating autophagy,programmed cell death,and myocardiocytes permeability.

Experimental investigation on the permeability of gap-graded soil due to horizontal suffusion considering boundary effect

The boundary condition is a crucial factor affecting the permeability variation due to suffusion.An experimental investigation on the permeability of gap-graded soil due to horizontal suffusion considering the boundary effect is conducted,where the hydraulic head difference(DH)varies,and the boundary includes non-loss and soil-loss conditions.Soil samples are filled into seven soil storerooms connected in turn.After evaluation,the variation in content of fine sand(ΔR_(f))and the hydraulic conductivity of soils in each storeroom(C_(i))are analyzed.In the non-loss test,the soil sample filling area is divided into runoff,transited,and accumulated areas according to the negative or positive ΔR_(f) values.ΔR_(f) increases from negative to positive along the seepage path,and Ci decreases from runoff area to transited area and then rebounds in accumulated area.In the soil-loss test,all soil sample filling areas belong to the runoff area,where the gentle-loss,strengthened-loss,and alleviated-loss parts are further divided.ΔR_(f) decreases from the gentle-loss part to the strengthened-loss part and then rebounds in the alleviated-loss part,and C_(i) increases and then decreases along the seepage path.The relationship between ΔR_(f) and Ci is different with the boundary condition.Ci exponentially decreases with ΔR_(f) in the non-loss test and increases with ΔR_(f) generally in the soil-loss test.

Insights into in-situ imbibition behavior of fracturing fluid in propped shale fractures based on nuclear magnetic resonance:A case study from Longmaxi Formation shale,Sichuan Basin,China

Shale gas is an important component of unconventional oil and gas resources.Studying the imbibition behavior is helpful to optimize flowback parameters and enhance gas recovery.Recent imbibition studies have focused on shale matrix,and the pressure conditions discussed were mostly atmospheric.The initial imbibition behavior begins from propped fractures to matrix,but there are few studies working on explaining the imbibition behavior in propped fractures or the phenomenon of many shale wells exhibit higher productivity after a“soaking”period.Therefore,propped fracture samples were designed for imbibition and migration experiments.In order to accurately study the mechanism and main influencing factors of fracturing fluid imbibition and migration in propped and unpropped shale fractures under high temperature and high pressure,a series of experiments based on nuclear magnetic resonance(NMR)were carried out.Results showed that NMR T_(2) spectra of all samples exhibited a bimodal distribution.The final imbibition volume of fracturing fluid was positively related to pressure and fracture width.The imbibition effect of fracturing fluid was more evident in matrix pores under high pressure.In the migration during soaking stage,the fracturing fluid gradually migrated from large pores to small pores and gradually displaced the shale gas from the matrix,thus allowing the water blocking in propped fractures to self-unlock to some extent.Gas permeability decreased in the imbibition stage,while it recovered in the migration stage to some extent.

Effect of Modification Treatment on Chloride Ions Permeability and Microstructure of Recycled Brick-mixed Aggregate Concrete

The modification methods of pozzolan slurry combined with sodium silicate and silicon-based additive were respectively adopted to treat recycled coarse brick-mixed aggregate(RCBA)in this study.The compressive strength and chloride permeability resistance of recycled aggregate concrete(RAC)before and after modification treatment were tested,and the microstructure of RAC was analyzed by mercury intrusion porosimetry(MIP)and scanning electron microscopy(SEM).The results show that the physical properties of RCBA strengthened by modification treatment are improved,and the compressive strength and chloride permeability resistance of treated RAC are also significantly improved.The modification treatment optimizes the pore size distribution of RAC,which increases the number of gel pores and transition pores,and decreases the number of capillary pores and macro pores.The surface fractal dimension shows a significant correlation with chloride diffusion coefficient,indicating that the variation of chloride permeability of treated RAC is consistent with the microstructure evolution.

Impact of effective stress on permeability for carbonate fractured-vuggy rocks

To gain insight into the flow mechanisms and stress sensitivity for fractured-vuggy reservoirs,several core models with different structural characteristics were designed and fabricated to investigate the impact of effective stress on permeability for carbonate fractured-vuggy rocks(CFVR).It shows that the permeability performance curves under different pore and confining pressures(i.e.altered stress conditions)for the fractured core models and the vuggy core models have similar change patterns.The ranges of permeability variation are significantly wider at high pore pressures,indicating that permeability reduction is the most significant during the early stage of development for fractured-vuggy reservoirs.Since each obtained effective stress coefficient for permeability(ESCP)varies with the changes in confining pressure and pore pressure,the effective stresses for permeability of four representative CFVR show obvious nonlinear characteristics,and the variation ranges of ESCP are all between 0 and 1.Meanwhile,a comprehensive ESCP mathematical model considering triple media,including matrix pores,fractures,and dissolved vugs,was proposed.It is proved theoretically that the ESCP of CFVR generally varies between 0 and 1.Additionally,the regression results showed that the power model ranked highest among the four empirical models mainly applied in stress sensitivity characterization,followed by the logarithmic model,exponential model,and binomial model.The concept of“permeability decline rate”was introduced to better evaluate the stress sensitivity performance for CFVR,in which the one-fracture rock is the strongest,followed by the fracture-vug rock and two-horizontalfracture rock;the through-hole rock is the weakest.In general,this study provides a theoretical basis to guide the design of development and adjustment programs for carbonate fractured-vuggy reservoirs.

High Permeability in Broadband of Co-sputtered [Fe-Fe_(20)Ni_(80)/Cr]_(n) Multilayer Films

To achieve high microwave permeability in wide-band for the micron-thick magnetic films,[Fe-Fe_(20)Ni_(80)/Cr]_(n) multilayer structure was proposed by co-sputtering Fe and FeNi to form the magnetic layers and Cr to form the interlayers.The multilayer structure contributes to the high permeability by reducing the coercivity and diminishing out-of-plane magnetization.The maximum imaginary permeability of[Fe-Fe_(20)Ni_(80)/Cr]_(n) multilayer film reaches a large value of 800 at 0.52 GHz even though its overall thickness exceeds 1μm.Besides,the magnetic resonance frequency of the multilayer film can be modulated from 0.52 to 1.35 GHz by adjusting the sputtering power of Fe from 0 to 86 W,and its bandwidth for μ’’>200(Δf) is as large as 2.0 GHz.The desirable broad Δf of magnetic permeability,which can be well fitted by the Landau-Lifshitz-Gilbert equations,is due to dual magnetic resonances originated from double magnetic phases of Fe and FeNi that are of different saturation magnetization.The micron-thick multilayer films with high permeability in extended waveband are promising candidate for electromagnetic noise suppression application.

An analytical transient coal permeability model:Sorption non-equilibrium index-based swelling switch

Long-term permeability experiments have indicated that sorption-induced swelling can switch from internal to bulk depending on the evolutive sorption status.However,this sorption swelling switch mechanism has not been considered in current analytical permeability models.This study introduces a normalized sorption non-equilibrium index(SNEI)to characterize the sorption status,quantify the dynamical variations of matrix swelling accumulation and internal swelling partition,and formulate the sorption swelling switch model.The incorporation of this index into the extended total effective stress concept leads to an analytical transient coal permeability model.Model results show that the sorption swelling switch itself results in the permeability switch under stress-constrained conditions,while the confined bulk swelling suppresses the permeability recovery to the continuous reduction under displacement-constrained conditions.Model verifications show that current experimental observations correspond to the early stages of the transient process,and they could be extended to the whole process with these models.This study demonstrates the importance of the sorption swelling switch in determining permeability evolution using simple boundary conditions.It provides new insights into experimentally revealing the sorption swelling switch in the future,and underscores the requirement of a rigorous model for complex coupled processes in large-scale coal seams.

Effect of particle composition and consolidation degree on the wave-induced liquefaction of soil beds

The wave-induced liquefaction of seabed is responsible for causing damage to marine structures.Particle composition and consolidation degree are the key factors affecting the pore water pressure response and liquefaction behavior of the seabed under wave action.The present study conducted wave flume experiments on silt and silty fine sand beds with varying particle compositions.Furthermore,a comprehensive analysis of the differences and underlying reasons for liquefaction behavior in two different types of soil was conducted from both macroscopic and microscopic perspectives.The experimental results indicate that the silt bed necessitates a lower wave load intensity to attain the liquefaction state in comparison to the silty fine sand bed.Additionally,the duration and development depth of liquefaction are greater in the silt bed.The dissimilarity in liquefaction behavior between the two types of soil can be attributed to the variation in their permeability and plastic deformation capacity.The permeability coefficient and compression modulus of silt are lower than those of silty fine sand.Consequently,silt is more prone to the accumulation of pore pressure and subsequent liquefaction under external loading.Prior research has demonstrated that silt beds with varying consolidation degrees exhibit distinct initial failure modes.Specifically,a dense bed undergoes shear failure,whereas a loose bed experiences initial liquefaction failure.This study utilized discrete element simulation to examine the microscopic mechanisms that underlie this phenomenon.

An Investigation into the Compressive Strength,Permeability and Microstructure of Quartzite-Rock-Sand Mortar

River sand is an essential component used as a fine aggregate in mortar and concrete.Due to unrestrained exploitation,river sand resources are gradually being exhausted.This requires alternative solutions.This study deals with the properties of cement mortar containing different levels of manufactured sand(MS)based on quartzite,used to replace river sand.The river sand was replaced at 20%,40%,60%and 80%with MS(by weight or volume).The mechanical properties,transfer properties,and microstructure were examined and compared to a control group to study the impact of the replacement level.The results indicate that the compressive strength can be improved by increasing such a level.The strength was improved by 35.1%and 45.5%over that of the control mortar at replacement levels of 60%and 80%,respectively.Although there was a weak link between porosity and gas permeability in the mortars with manufactured sand,the gas permeability decreased with growing the replacement level.The microstructure of the MS mortar was denser,and the cement paste had fewer microcracks with increasing the replacement level.

A novel nano-grade organosilicon polymer:Improving airtightness of compressed air energy storage in hard rock formations

Enhancing cavern sealing is crucial for improving the efficiency of compressed air energy storage(CAES)in hard rock formations.This study introduced a novel approach using a nano-grade organosilicon polymer(NOSP)as a sealant,coupled with an air seepage evaluation model that incorporates Knudsen diffusion.Moreover,the initial coating application methods were outlined,and the advantages of using NOSP compared to other sealing materials,particularly regarding cost and construction techniques,were also examined and discussed.Experimental results indicated a significant reduction in permeability of rock specimens coated with a 7–10μm thick NOSP layer.Specifically,under a 0.5 MPa pulse pressure,the permeability decreased to less than 1 n D,and under a 4 MPa pulse pressure,it ranged between4.5×10^(-6)–5.5×10^(-6)m D,marking a 75%–80%decrease in granite permeability.The sealing efficacy of NOSP surpasses concrete and is comparable to rubber materials.The optimal viscosity for application lies between 95 and 105 KU,and the coating thickness should ideally range from 7 to 10μm,applied to substrates with less than 3%porosity.This study provides new insights into air transport and sealing mechanisms at the pore level,proposing NOSP as a cost-effective and simplified solution for CAES applications.

Experimental study on workability and permeability of sandy soils conditioned with thickened foam

Water spewing and muck plugging often occur during earth pressure balance(EPB)shield machines tunnelling in water-rich sandy strata,even though the conventional foam has been employed to condition sandy soils.In this study,a novel thickened foaming agent suitable for EPB shield tunnelling in water-rich sandy strata is developed.In contrast to conventional foam-conditioned sands,the thickened foam-conditioned sand has a low permeability due to the consistent filling of soil pores with the thickened foam,and the initial permeability coefficient decreases by approximately two orders of magnitude.It also exhibits a suitable workability,which is attributed to the enhanced capability of the thickened foam to condition sandy soils.In addition,the effect of concentration on the stability of the foam is explained by the Gibbs-Marangoni effect,and conditioning mechanisms for the thickened foam on sands are discussed from the evolution of foam bubbles.

A novel profile modification HPF-Co gel satisfied with fractured low permeability reservoirs in high temperature and high salinity

Conformance control and water plugging are a widely used EOR method in mature oilfields.However,majority of conformance control and water plugging agents are unavoidable dehydrated situation in high-temperature and high-salinity low permeability reservoirs.Consequently,a novel conformance control system HPF-Co gel,based on high-temperature stabilizer(CoCl_(2)·H_(2)O,CCH)is developed.The HPF-Co bulk gel has better performances with high temperature(120℃)and high salinity(1×10^(5)mg/L).According to Sydansk coding system,the gel strength of HPF-Co with CCH is increased to code G.The dehydration rate of HPF-Co gel is 32.0%after aging for 150 d at 120℃,showing excellent thermal stability.The rheological properties of HPF gel and HPF-Co gel are also studied.The results show that the storage modulus(G′)of HPF-Co gel is always greater than that of HPF gel.The effect of CCH on the microstructure of the gel is studied.The results show that the HPF-Co gel with CCH has a denser gel network,and the diameter of the three-dimensional network skeleton is 1.5-3.5μm.After 90 d of aging,HPF-Co gel still has a good three-dimensional structure.Infrared spectroscopy results show that CCH forms coordination bonds with N and O atoms in the gel amide group,which can suppress the vibration of cross-linked sites and improve the stability at high temperature.Fractured core plugging test determines the optimized polymer gel injection strategy and injection velocity with HPF-Co bulk gel system,plugging rate exceeding 98%.Moreover,the results of subsequent waterflooding recovery can be improved by 17%.

Optimization of Gas-Flooding Fracturing Development in Ultra-Low Permeability Reservoirs

Ultra-low permeability reservoirs are characterized by small pore throats and poor physical properties, which areat the root of well-known problems related to injection and production. In this study, a gas injection floodingapproach is analyzed in the framework of numerical simulations. In particular, the sequence and timing of fracturechanneling and the related impact on production are considered for horizontal wells with different fracturemorphologies. Useful data and information are provided about the regulation of gas channeling and possible strategiesto delay gas channeling and optimize the gas injection volume and fracture parameters. It is shown that inorder to mitigate gas channeling and ensure high production, fracture length on the sides can be controlled andlonger fractures can be created in the middle by which full gas flooding is obtained at the fracture location in themiddle of the horizontal well. A Differential Evolution (DE) algorithm is provided by which the gas injectionvolume and the fracture parameters of gas injection flooding can be optimized. It is shown that an improvedoil recovery factor as high as 6% can be obtained.