Fractal model of spontaneous imbibition in low-permeability reservoirs coupled with heterogeneity of pore seepage channels and threshold pressure

Spontaneous imbibition(SI)is an important mechanism for enhancing oil recovery in low-permeability reservoirs.Due to the strong heterogeneity,and the non-Darcy flow,the construction of SI model for lowpermeability reservoirs is extremely challenging.Commonly,traditional SI models based on single or averaged capillary tortuosity ignore the influence of heterogeneity of pore seepage channels and the threshold pressure(TP)on imbibition.Therefore,in this work,based on capillary model and fractal theory,a mathematical model of characterizing SI considering heterogeneity of pore seepage channels is established.On this basis,the threshold pressure was introduced to determine the pore radius at which the wetted phase can displace oil.The proposed new SI model was verified by imbibition experimental data.The study shows that for weakly heterogeneous cores with permeability of 0-1 m D,the traditional SI model can characterize the imbibition process relatively accurately,and the new imbibition model can increase the coefficient of determination by 1.05 times.However,traditional model has serious deviations in predicting the imbibition recovery for cores with permeability of 10-50 m D.The new SI model coupling with heterogeneity of pore seepage channels and threshold pressure effectively solves this problem,and the determination coefficient is increased from 0.344 to 0.922,which is increased by2.68 times.For low-permeability reservoirs,the production of the oil in transitional pores(0.01-0.1μm)and mesopores(0.1-1μm)significantly affects the imbibition recovery,as the research shows that when the heterogeneity of pore seepage channels is ignored,the oil recovery in transitional pores and mesopores decreases by 7.54%and 4.26%,respectively.Sensitivity analysis shows that increasing interfacial tension,decreasing contact angle,oil-water viscosity ratio and threshold pressure will increase imbibition recovery.In addition,there are critical values for the influence of these factors on the imbibition recovery,which provides theoretical support for surfactant optimization.

Performance and enhanced oil recovery efficiency of an acid-resistant polymer microspheres of anti-CO_(2) channeling in low-permeability reservoirs

CO_(2) flooding is a vital development method for enhanced oil recovery in low-permeability reservoirs,However,micro-fractures are developed in low-permeability reservoirs,which are essential oil flow channels but can also cause severe CO_(2) gas channeling problems.Therefore,anti-gas channeling is a necessary measure to improve the effect of CO_(2) flooding.The kind of anti-gas channeling refers to the plugging of fractures in the deep formation to prevent CO_(2) gas channeling,which is different from the wellbore leakage.Polymer microspheres have the characteristics of controllable deep plugging,which can achieve the profile control of low-permeability fractured reservoirs.In acidic environments with supercritical CO_(2),traditional polymer microspheres have poor expandability and plugging properties.Based on previous work,a systematic evaluation of the expansion performance,dispersion rheological properties,stability,deep migration,anti-CO_(2) channeling and enhanced oil recovery ability of a novel acid-resistant polymer microsphere(DCNPM-A)was carried out under CQ oilifield conditions(salinity of85,000 mg/L,80℃,pH=3).The results show that the DCNPM-A microsphere had a better expansion performance than the traditional microsphere,with a swelling rate of 13.5.The microsphere dispersion with a concentration of 0.1%-0.5%had the advantages of low viscosity,high dispersion and good injectability in the low permeability fractured core.In the acidic environment of supercritical CO_(2),DCNPM-A microspheres showed excellent stability and could maintain strength for over 60 d with less loss.In core experiments,DCNPM-A microspheres exhibited delayed swelling characteristics and could effectively plug deep formations.With a plugging rate of 95%,the subsequent enhanced oil recovery of CO_(2) flooding could reach 21.03%.The experimental results can provide a theoretical basis for anti-CO_(2)channeling and enhanced oil recovery in low-permeability fractured reservoirs.

Control and vibration analyses of a sandwich doubly curved micro-composite shell with honeycomb,truss,and corrugated cores based on the fourth-order shear deformation theory

Curved shells are increasingly utilized in applied engineering due to their shared characteristics with other sandwich structures,flexibility,and attractive appearance.However,the inability of controlling and regulating vibrations and destroying them afterward is a challenge to scientists.In this paper,the curve shell equations and a linear quadratic regulator are adopted for the state feedback design to manage the structure vibrations in state space forms.A five-layer sandwich doubly curved micro-composite shell,comprising two piezoelectric layers for the sensor and actuator,is modeled by the fourth-order shear deformation theory.The core(honeycomb,truss,and corrugated)is analyzed for the bearing of transverse shear forces.The results show that the honeycomb core has a greater effect on the vibrations.When the parameters related to the core and the weight percentage of graphene increase,the frequency increases.The uniform distribution of graphene platelets results in the lowest natural frequency while the natural frequency increases.Furthermore,without taking into account the piezoelectric layers,the third-order shear deformation theory(TSDT)and fourth-order shear deformation theory(FOSDT)align closely.However,when the piezoelectric layers are incorporated,these two theories diverge significantly,with the frequencies in the FOSDT being lower than those in the TSDT.

A Numerical Simulation Study of Temperature and Pressure Effects on the Breakthrough Pressure of CO_(2)in Unsaturated Low-permeability Rock Core

Gas breakthrough pressure is a key parameter to evaluate the sealing capacity of caprock,and it also plays important roles in safety and capacity of CO_(2)geological storage.Based on the published experimental results,we present numerical simulations on CO_(2)breakthrough pressure in unsaturated low-permeability rock under 9 multiple P-T conditions(which can keep CO_(2)in gaseous,liquid and supercritical states)and thus,a numerical method which can be used to accurately predict CO_(2)breakthrough pressure on rock-core scale is proposed.The simulation results show that CO_(2)breakthrough pressure and breakthrough time are exponential correlated with P-T conditions.Meanwhile,pressure has stronger effects on experimental results than that of temperature.Moreover,we performed sensitivity studies on the pore distribution indexλ(0.6,0.7,0.8,and 0.9)in van Genuchten-Muale model.Results show that with the increase ofλ,CO_(2)breakthrough pressure and breakthrough time both show decreasing trends.In other words,the larger the value ofλis,the better the permeability of the caprock is,and the worse the CO_(2)sealing capacity is.The numerical method established in this study can provide an important reference for the prediction of gas breakthrough pressure on rock-core scale and for related numerical studies.

Effect of external and internal cues on core muscle activation during the Sahrmann five-level core stability test

BACKGROUND Pain in the back or pelvis or fear of back pain may affect the timing or cocontraction of the core muscles.In both static and dynamic movements,the Sahrmann core stability test provides an assessment of core muscle activation and a person's ability to stabilize the lumbopelvic complex.Preparatory cues and images can be used to increase the activation of these muscles.To attain optimal movement patterns,it will be necessary to determine what cueing will give the most effective results for core stability.AIM To investigate the effects of external and internal cues on core muscle activation during the Sahrmann five-level core stability test.METHODS Total 68 participants(21.83±3.47 years)were randomly allocated to an external(n=35)or internal cue group(n=33).Participants performed the Sahrmann fivelevel core stability test without a cue as baseline and the five-level stability exercises with an internal or external cue.External cue group received a pressure biofeedback unit(PBU),and the internal cue group received an audio cue.A Delsys Trigno^(TM)surface electromyography unit was used for muscle activation from the rectus abdominis,external oblique,and transverse abdominis/internal oblique muscles.RESULTS Linear mixed effects model analysis showed that cueing had a significant effect on core muscle activation(P=0.001);however,there was no significant difference between cue types(internal or external)(P=0.130).CONCLUSION Both external and internal cueing have significant effects on core muscle activation during the Sahrmann five-level core stability test and the PBU does not create higher muscle activation than internal cueing.

Numerical simulation of rock electrical properties based on digital cores

In this paper, we obtained three dimensional digital cores using X-ray CT to describe the rock microstructure and applied the open morphology algorithm to simulate oil and formation water distribution in the pore space at different water saturations during the oil-displacing water flood process. The resistivity, formation factor, and resistivity index of rocks were calculated using the finite element method （FEM） and we studied the effect of rock wettability on electrical properties. The numerical simulation results indicate that the simulated formation factor and resistivity index of the water wet rock agrees well with experiments over the whole range of water saturation and extends the traditional resistivity experiment. The rock wettablilty has a large influence on the rock resistivity index. The resistivity and saturation exponent of oil wet rock are obviously larger than three of water wet rock.

Computation of elastic properties of 3D digital cores from the Longmaxi shale

The dependence of elastic moduli of shales on the mineralogy and microstructure of shales is important for the prediction of sweet spots and shale gas production. Based on 3D digital images of the microstructure of Longmaxi black shale samples using X-ray CT, we built detailed 3D digital images of cores with porosity properties and mineral contents. Next, we used finite-element （FE） methods to derive the elastic properties of the samples. The FE method can accurately model the shale mineralogy. Particular attention is paid to the derived elastic properties and their dependence on porosity and kerogen. The elastic moduli generally decrease with increasing porosity and kerogen, and there is a critical porosity （0.75） and kerogen content （ca. ≤3%） over which the elastic moduli decrease rapidly and slowly, respectively. The derived elastic moduli of gas- and oil-saturated digital cores differ little probably because of the low porosity （4.5%） of the Longmaxi black shale. Clearly, the numerical experiments demonstrated the feasibility of combining microstructure images of shale samples with elastic moduli calculations to predict shale properties.

K-cores视角的区域产业结构的趋同演变与空间格局

本文分别从产业一体化、诸侯经济为特征的区域"均衡与非均衡增长"两种发展模式视角,以中国内地30个省域(西藏除外)2002-2007年中国地区42部门投入产出表为数据基础,构建多省域的产业网络模型,采用复杂网络分析技术上的K-cores网络解构方法,分析了我国省域产趋同演变及其空间格局与两者之间的关系。结果表明:区域产业一体化视野下存在着省域产业趋同演化的空间差异性,东部地区的长三角、京津唐经济圈,中部地区的长江中游经济圈和西部成渝经济区超越了早期的产业趋同实现了不同程度的产业互补与错位发展,其他区域一体化演变效果表现并不突出;而强调本省域的局部经济利益最大化的诸侯经济发展模式,使得众多不临接省域在产业战略布局上,形成了与国家产业宏观调控政策实施效果相协调一致的产业结构趋同现象。

Extracting and evaluating method of web dense cores

This paper focuses on some key problems in web community discovery and link analysis.Based on the topic-oriented technology,the characteristics of a bipartite graph are studied.An Х bipartite core set is introduced to more clearly define extracting ways.By scanning the topic subgraph to construct Х bipartite graph and then prune the graph with i and j ,an Х bipartite core set,which is also the minimum element of a community,can be found.Finally,a hierarchical clustering algorithm is applied to many Х bipartite core sets and the dendrogram of the community inner construction is obtained.The correctness of the constructing and pruning method is proved and the algorithm is designed.The typical datasets in the experiment are prepared according to the way in HITS（hyperlink-induced topic search）.Ten topics and four search engines are chosen and the returned results are integrated.The modularity,which is a measure of the strength of the community structure in the social network,is used to validate the efficiency of the proposed method.The experimental results show that the proposed algorithm is effective and efficient.

3D characterization of porosity and minerals of low-permeability uranium-bearing sandstone based on multi-resolution image fusion

In the process of in situ leaching of uranium,the microstructure controls and influences the flow distribution,percolation characteristics,and reaction mechanism of lixivium in the pores of reservoir rocks and directly affects the leaching of useful components.In this study,the pore throat,pore size distribution,and mineral composition of low-permeability uranium-bearing sandstone were quantitatively analyzed by high pressure mercury injection,nuclear magnetic resonance,X-ray diffraction,and wavelength-dispersive X-ray fluorescence.The distribution characteristics of pores and minerals in the samples were qualitatively analyzed using energy-dispersive scanning electron microscopy and multi-resolution CT images.Image registration with the landmarks algorithm provided by FEI Avizo was used to accurately match the CT images with different resolutions.The multi-scale and multi-mineral digital core model of low-permeability uranium-bearing sandstone is reconstructed through pore segmentation and mineral segmentation of fusion core scanning images.The results show that the pore structure of low-permeability uranium-bearing sandstone is complex and has multi-scale and multi-crossing characteristics.The intergranular pores determine the main seepage channel in the pore space,and the secondary pores have poor connectivity with other pores.Pyrite and coffinite are isolated from the connected pores and surrounded by a large number of clay minerals and ankerite cements,which increases the difficulty of uranium leaching.Clays and a large amount of ankerite cement are filled in the primary and secondary pores and pore throats of the low-permeability uraniumbearing sandstone,which significantly reduces the porosity of the movable fluid and results in low overall permeability of the cores.The multi-scale and multi-mineral digital core proposed in this study provides a basis for characterizing macroscopic and microscopic pore-throat structures and mineral distributions of low-permeability uranium-bearing sandstone and can better understand the seepage characteristics.

Characteristics of non-Darcy flow in low-permeability reservoirs

Well testing is recognized as an effective means of accurately obtaining the formation parameters of low-permeability reservoirs and effectively analyzing the deliverability.Well test models must comply with the particular characteristics of flow in low-permeability reservoirs in order to obtain reasonable well test interpretation.At present,non-Darcy flow in low-permeability reservoirs is attracting much attention.In this study,displacement tests were conducted on typical cores taken from low-permeability reservoirs.Two dimensionless variables were introduced to analyze the collected experimental data.The results of the dimensionless analysis show whether non-Darcy flow happens or not depends on the properties of fluid and porous media and the pressure differential.The combination of the above three parameters was named as dimensionless criteria coefficient（DCC）.When the value of the DCC was lower than a critical Reynolds number（CRN）,the flow could not be well described by Darcy＇s law（so-called non-Darcy flow）,when the DCC was higher than CRN,the flow obeyed Darcy＇s law.Finally,this paper establishes a transient mathematical model considering Darcy flow and non-Darcy flow in low-permeability reservoirs,and proposes a methodology to solve the model.The solution technique,which is based on the Boltzmann transformation,is well suited for solving the flow model of low-permeability reservoirs.Based on the typical curves analysis,it was found that the pressure and its derivative curves were determined by such parameters as non-Darcy flow index and the flow characteristics.The results can be used for well test analysis of low-permeability reservoirs.

Heavy metal pollution in tidal zones of Bohai Bay using the dated sediment cores

Three sediment cores were collected in November 2003 from Dagu estuary to Qikou estuary. The main polluted heavy metals in the sediment of tidal zones for the Bohai Bay have been found by analyzing the relationship among the contents of heavy metals, the contents of geochemical elements （Fe, AI and Mn） and the size of grain. The dominating contaminative elements in tidal sediments of Bohai Bay are Pb, Zn and Cd. Their contents are higher than the corresponding upper limit of environmental background values and they have very faint correlation with the corresponding contents of geochemical elements and the size of grain, indicating the anthropogenic enrichment. Especially, the preliminary study on the pollution sources and the history of heavy metals in the Dagu estuary has been done using the dated results. The contamination by Zn and Cd also started in the middle 1950s, while the contamination by Pb appeared in the early 1940s. The pollution by Zn and Cd mainly originate from sewage discharge, while the pollution by Pb has many sources, like atmosphere deposition and industrial discharRe.

Non-Darcy flow in oil accumulation (oil displacing water) and relative permeability and oil saturation characteristics of low-permeability sandstones

Hydrocarbon resources in low-permeability sandstones are very abundant and are extensively distributed. Low-permeability reservoirs show several unique characteristics, including lack of a definite trap boundary or caprock, limited buoyancy effect, complex oil-gas-water distribution, without obvious oil-gas-water interfaces, and relatively low oil （gas） saturation. Based on the simulation experiments of oil accumulation in low-permeability sandstone （oil displacing water）, we study the migration and accumulation characteristics of non-Darcy oil flow, and discuss the values and influencing factors of relative permeability which is a key parameter characterizing oil migration and accumulation in low-permeability sandstone. The results indicate that： 1） Oil migration （oil displacing water） in low- permeability sandstone shows non-Darcy percolation characteristics, and there is a threshold pressure gradient during oil migration and accumulation, which has a good negative correlation with permeability and apparent fluidity; 2） With decrease of permeability and apparent fluidity and increase of fluid viscosity, the percolation curve is closer to the pressure gradient axis and the threshold pressure gradient increases. When the apparent fluidity is more than 1.0, the percolation curve shows modified Darcy flow characteristics, while when the apparent fluidity up＂ non-Darcy percolation curve; 3） Oil-water is less than 1.0, the percolation curve is a ＂concave- two-phase relative permeability is affected by core permeability, fluid viscosity, apparent fluidity, and injection drive force; 4） The oil saturation of low- permeability sandstone reservoirs is mostly within 35%-60%, and the oil saturation also has a good positive correlation with the permeability and apparent fluidity.

Creation of Triple Hierarchical Micro-Meso-Macroporous N-doped Carbon Shells with Hollow Cores Toward the Electrocatalytic Oxygen Reduction Reaction

A series of triple hierarchical micro-mesomacroporous N-doped carbon shells with hollow cores have been successfully prepared via etching N-doped hollow carbon spheres with CO_2 at high temperatures.The surface areas, total pore volumes and microporepercentages of the CO_2-activated samples evidently increase with increasing activation temperature from 800 to950 °C, while the N contents show a contrary trend from7.6 to 3.8 at%. The pyridinic and graphitic nitrogen groups are dominant among various N-containing groups in the samples. The 950 °C-activated sample(CANHCS-950) has the largest surface area(2072 m^2 g^(-1)), pore volume(1.96 cm^3 g^(-1)), hierarchical micro-mesopore distributions(1.2, 2.6 and 6.2 nm), hollow macropore cores(*91 nm)and highest relative content of pyridinic and graphitic N groups. This triple micro-meso-macropore system could synergistically enhance the activity because macropores could store up the reactant, mesopores could reduce the transport resistance of the reactants to the active sites, and micropores could be in favor of the accumulation of ions.Therefore, the CANHCS-950 with optimized structure shows the optimal and comparable oxygen reduction reaction(ORR) activity but superior methanol tolerance and long-term durability to commercial Pt/C with a 4 e--dominant transfer pathway in alkaline media. These excellent properties in combination with good stability and recyclability make CANHCSs among the most promising metal-free ORR electrocatalysts reported so far in practical applications.

Infiltration characteristics of non-aqueous phase liquids in undisturbed loessal soil cores

The widespread contamination of soils and aquifers by non-aqueous phase liquids （NAPL）, such as crude oil, poses serious environmental and health hazards globally. Understanding the infiltration characteristics of NAPL in soil is crucial in mitigating or remediating soil contamination. The infiltration characteristics of crude and diesel oils into undisturbed loessal soil cores, collected in polymethyl methacrylate cylindrical columns, were investigated under a constant fluid head （3 era） of either crude oil or diesel oil. The infiltration rate of both crude and diesel oils decreased exponentially as wetting depth increased with time. Soil core size and bulk density both had significant effects on NAPL infiltration through the undisturbed soil cores; a smaller core size or a greater bulk density could reduce oil penetration to depth. Compacting soil in areas susceptible to oil spills may be an effective stratage to reduce contamination. The infiltration of NAPL into soil cores was spatially anisotropic and heterogeneous, thus recording the data at four points on the soil core is a good stratage to improve the accuracy of experimental results. Our results revealed that crude and diesel oils, rather than their components, have a practical value for remediation of contaminated loessal soils.

Stress dependent permeability and porosity of low-permeability rock

The seepage property of low-permeability rock is of significant importance for the design and safety analysis of underground cavities. By using a self-developed test system, both permeability and porosity of granite from an underground oil storage depot were measured. In order to study the influence of rock types on permeability, a tight sandstone was selected as a contrast. The experimental results suggested that the porosity of this granite is less than 5% and permeability is low to 10–20 m^2 within the range of effective stress. During the loading process, both exponential relationship and power law can be utilized to describe the relationship between effective stress and permeability. However, power law matches the experimental data better during the unloading condition. The stress dependent porosity of granite during loading process can be described via an exponential relationship while the match between the model and experimental data can be improved by a power law in unloading paths. The correlation of permeability and porosity can be described in a power law form. Besides, granite shows great different evolution rules in permeability and porosity from sandstone. It is inferred that this difference can be attributed to the preparing of samples and different movements of microstructures subjected to effective stress.

A Comprehensive Evaluation Method for Low-permeability Reservoirs

According to the geological characteristics and their influential factors of the low-permeability reservoirs, a comprehensive method for evaluation of low-permeability reservoirs is put forward. The method takes a matrix system as the basis, a fracture system as the focus and a stress field system as the restricted factor. It can objectively reflect not only the storage capability and seepage capability of low-permeability reservoirs, but also the effect on development as well. At the same time, it can predict the seepage characteristics at different development stages and provide a reasonable geological basis for the development of low-permeability reservoirs.

Permeability and heterogeneity adaptability of surfactant-alternating-gas foam for recovering oil from low-permeability reservoirs

As the traditional polymer stabilizer is eliminated to improve the injectability of foam in lowpermeability reservoirs,the stability,plugging capacity,conformance control and oil recovery performance of the surfactant-alternating-gas(SAG)foam become significantly important for determining its adaptability to permeability and heterogeneity,which were focused and experimentally researched in this paper.Results show that the SAG bubbles are highly stable in micron-sized channels and porous media(than in the conventional unconstrained graduated cylinder),making it possible to use in enhanced oil recovery(EOR).Such bubbles formed in porous media could be passively adjusted to match their diameter with the size of the pore.This endows the SAG foam with underlying excellent injectability and deep migration capacity.Permeability adaptability results indicate a reduced plugging capacity,but,increased incremental oil recovery by the SAG foam with decreased permeability.This makes it a good candidate for EOR over a wide range of permeability,however,parallel core floods demonstrate that there is a limiting heterogeneity for SAG application,which is determined to be a permeability contrast of 12.0(for a reservoir containing oil of 9.9 m Pa s).Beyond this limit,the foam would become ineffective.

The Relationship between Fractures and Tectonic Stress Field in the Extra Low-Permeability Sandstone Reservoir at the South of Western Sichuan Depression

The formation and distribution of fractures are controlled by paleotectonic stress field, and their preservative status and effects on development are dominated by the modern stress field. Since Triassic, it has experienced four tectonic movements and developed four sets of tectonic fractures in the extra low-permeability sandstone reservoir at the south of western Sichuan depression. The strikes of fractures are in the S-N, NE-SW, E-W, and NW-SE directions respectively. At the end of Triassic, under the horizontal compression tectonic stress field, for which the maximum principal stress direction was NW.SE, the fractures were well developed near the S-N faults and at the end of NE-SW faults, because of their stress concentration. At the end of Cretaceous, in the horizontal compression stress fields of the NE-SW direction, the stress was obviously lower near the NE-SW faults, thus, fractures mainly developed near the S-N faults. At the end of Neogene-Early Pleistocene, under the horizontal compression tectonic stress fields of E-W direction, stress concentrated near the NE-SW faults and fractures developed at these places, especially at the end of the NE-SE faults, the cross positions of NE-SW, and S-N faults. Therefore, fractures developed mostly near S-N faults and NE-SW faults. At the cross positions of the above two sets of faults, the degree of development of the fractures was the highest. Under the modern stress field of the NW-SE direction, the NW-SE fractures were mainly the seepage ones with tensional state, the best connectivity, the widest aperture, the highest permeability, and the minimum opening pressure.

FORMATION OF NECROTIC CORES IN THE GROWTH OF TUMORS: ANALYTIC RESULTS

In this article, the author studies the mechanism of formation of necrotic cores in the growth of tumors by using rigorous analysis of a mathematical model. The model modifies a corresponding tumor growth model proposed by Byrne and Chaplain in 1996, in the case where no inhibitors exist. The modification is made such that both necrotic tumors and nonnecrotic tumors can be considered in a joint way. It is proved that if the nutrient supply is below a threshold value, then there is not dormant tumor, and all evolutionary tumors will finally vanish. If instead the nutrient supply is above this threshold value then there is a unique dormant tumor which can either be necrotic or nonnecrotic, depending on the level of the nutrient supply and the level of dead-cell dissolution rate, and all evolutionary tumors will converge to this dormant tumor. It is also proved that, in the se.cond case, if the dormant tumor is necrotic then an evolutionary tumor will form a necrotic core at a finite time, and if the dormant tumor is nonnecrotic then an evolutionary tumor will also be nonnecrotic from a finite time.