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.

A New Empirical Method for Constructing Capillary Pressure Curves from Conventional Logs in Low-Permeability Sandstones

Pore structure reflected from capillary pressure curves plays an important role in low-permeability formation evaluation. It is a common way to construct capillary pressure curves by Nuclear Magnetic Resonance（NMR） log. However, the method＇s efficiency will be severely affected if there is no NMR log data or it cannot reflect pore structure well. Therefore, on the basis of J function and diagenetic facies classification, a new empirical model for constructing capillary pressure curves from conventional logs is proposed here as a solution to the problem. This model includes porosity and the relative value of natural gamma rays as independent variables and the saturation of mercury injection as a dependent variable. According to the 51 core experimental data sets of three diagenetic facies from the bottom of the Upper Triassic in the western Ordos Basin, China, the model＇s parameters in each diagenetic facies are calibrated. Both self-checking and extrapolation tests show a positive effect, which demonstrates the high reliability of the proposed capillary pressure curve construction model. Based on the constructed capillary pressure curves, NMR T_2 spectra under fully brine-saturated conditions are mapped by a piecewise power function. A field study is then presented. Agreement can be seen between the mapped NMR T_2 spectra and the MRIL-Plog data in the location of the major peak, right boundary, distribution characteristics and T_2 logarithmic mean value. In addition, the capillary pressure curve construction model proposed in this paper is not affected by special log data or formation condition. It is of great importance in evaluating pore structure, predicting oil production and identifying oil layers through NMR log data in low-permeability sandstones.

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.

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.

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.

Palaeogene Sandstones of the Manika Plateau in Kolwezi (DR Congo): Sedimentological and Geochemical Characterization, Provenance, Palaeoalteration and Tectonic Context

This work presents a study of the Paleogene sandstones of the Manika plateau in Kolwezi, DR Congo. These sandstones belong to the “Grès polymorphes” group, which together with the overlying “Sables ocre” makes up the Kalahari Supergroup. Sedimentological and geochemical analyses have enabled us to characterize these sandstones and determine their origin, the conditions of their formation and the tectonic context in which they were developed. The results show that the sandstones are quartz arenites with a high level of mineralogical, textural and chemical maturity. They are recycled sandstones, formed in an intracratonic sedimentary basin, in the context of a passive continental margin, after a long fluvial transport of sediments. These sandstones initially come from intense alteration of magmatic rocks with felsic composition, mainly tonalite-trondhjemite-granodiorite (TTG) complexes, in hot, humid palaeoclimatic conditions and oxidizing environments.

Statistical analysis of physico-mechanical parameters of sandstones occurring in orogenic settings

In northeastern Sicily(Italy),sandstone rock masses widely crop out as cover deposits over crystalline terrains belonging to the orogenic belt.Despite being part of the same geological formation,these sandstones are characterized by highly different features in terms of texture and physico-mechanical properties.This poses a scientific question on the possibility of tracing these rocks to a single statistical model,which could be representative of their main engineering geological properties.Therefore,it is worth investigating on the possible reasons of such differences,that should be searched either in the current geographical sandstone distribution or in the rock texture.For this study,sandstone samples were collected from different sites and were analyzed at both the hand and thin section scales.Three sandstone types were recognized,characterized by a different texture.Then,the laboratory characterization allowed estimating their main physico-mechanical and ultrasonic properties,such as porosity,density,mechanical strength,deformability,and ultrasonic velocities.The rock mechanical strength proved linked to the rock compactness and to the presence of lithic fragments,while pores and a pseudo-matrix between grains represent weakening features.Rock data were also statistically analyzed by grouping the specimens according to a geographical criterion,with respect to their sampling area,but no link was found between location and rock properties.Finally,with the aim of achieving mathematical laws that could be used to predict some rock properties from others,useful for practical purposes when dealing with such a high property variability,single and multiple regression analyses were carried out.Results show that the Uniaxial Compressive Strength,porosity,and P-wave velocity are the best predictors for a quick,indirect estimation of the main physico-mechanical parameters.The methodological approach developed for this research can be taken as reference to study other worldwide cases,involving rocks characterized by a wide range of physico-mechanical properties and covering large regional territories.

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.

Exoscopy of Detrital Zircons from Niamey Neoproterozoic Sandstones (Eastern Edge of the West African Craton, Southwestern Niger): Interpretation of Detrital Sediments Provenance

This study focuses on exoscopic analyses of detrital zircon grains of Archean and Paleoproterozoic age, contained in the sediments from the Niamey Neoproterozoic sandstones (Niamey region), with a view to confirming the sediments sources already proposed (Kénéma-Man domain for Archean-age zircons and Baoulé Mossi domain for Paleoproterozoic-age zircons). Exoscopic analysis reveals that Archean zircon grains are more corroded, with rounded to sub-rounded shapes, while Paleoproterozoic zircon grains are less corroded and mostly angular in shape. The strong corrosion of Archean zircon grains, implying long-distance transport, is consistent with the remoteness of the Kenema-Man domain which are the source these sediments. The fact that the Paleoproterozoic zircon grains show little or no wear implies a proximal source of sediments, corresponding to the Baoulé Mossi domain.

Permeability evolution mechanism and the optimum permeability determination of uranium leaching from low-permeability sandstone treated with low-frequency vibration

Low-frequency vibrations can effectively improve natural sandstone permeability,and higher vibration frequency is associated with larger permeability.However,the optimum permeability and permeability evolution mechanism for uranium leaching and the relationship between permeability and the change of chemical reactive rate affecting uranium leaching have not been determined.To solve the above problems,in this study,identical homogeneous sandstone samples were selected to simulate lowpermeability sandstone;a permeability evolution model considering the combined action of vibration stress,pore water pressure,water flow impact force,and chemical erosion was established;and vibration leaching experiments were performed to test the model accuracy.Both the permeability and chemical reactions were found to simultaneously restrict U6þleaching,and the vibration treatment increased the permeability,causing the U6þleaching reaction to no longer be diffusion-constrained but to be primarily controlled by the reaction rate.Changes of the model calculation parameters were further analyzed to determine the permeability evolution mechanism under the influence of vibration and chemical erosion,to prove the correctness of the mechanism according to the experimental results,and to develop a new method for determining the optimum permeability in uranium leaching.The uranium leaching was found to primarily follow a process consisting of(1)a permeability control stage,(2)achieving the optimum permeability,(3)a chemical reactive rate control stage,and(4)a channel flow stage.The resolution of these problems is of great significance for facilitating the application and promotion of lowfrequency vibration in the CO_(2)+O_(2) leaching process.

“Green Bank”Atop SandStones

The Pisha sandstone region in Jungar Banner once suffered the most severe water loss and soil erosion in the world.In just a couple of decades,the apple industry has become a major business for the local economy.

Estimation of unfrozen water content of saturated sandstones using nuclear magnetic resonance, mercury intrusion porosimetry, and ultrasonic tests

The unfrozenwater content(UWC)is a crucial parameter that affects the strength and thermal properties of rocks in relation to engineering construction and geological disasters in cold regions.In this study,three different methods were employed to test and estimate the UWC of saturated sandstones,including nuclear magnetic resonance(NMR),mercury intrusion porosimetry(MIP),and ultrasonic methods.The NMR method enabled the direct measurement of the UWC of sandstones using the free induction decay(FID).The MIP method was used to analyze the pore structures of sandstones,with the UWC subsequently calculated based on pore ice crystallization.Therefore,the MIP test constituted an indirect measurement method.Furthermore,a correlation was established between the P-wave velocity and the UWC of these sandstones based on the mixture theory,which could be employed to estimate the UWC as an empirical method.All methods demonstrated that the UWC initially exhibited a rapid decrease from 0C to5C and then generally became constant beyond20C.However,these test methods had different characteristics.The NMR method was used to directly and accurately calculate the UWC in the laboratory.However,the cost and complexity of NMR equipment have precluded its use in the field.The UWC can be effectively estimated by the MIP test,but the estimation accuracy is influenced by the ice crystallization process and the pore size distribution.The P-wave velocity has been demonstrated to be a straightforward and practical empirical parameter and was utilized to estimate the UWC based on the mixture theory.This method may be more suitable in the field.All methods confirmed the existence of a hysteresis phenomenon in the freezing-thawing process.The average hysteresis coefficient was approximately 0.538,thus validating the GibbseThomson equation.This study not only presents alternative methodologies for estimating the UWC of saturated sandstones but also contribute to our understanding of the freezing-thawing process of pore water.

Permeability damage micro-mechanisms and stimulation of low-permeability sandstone reservoirs: A case study from Jiyang Depression, Bohai Bay Basin, China

According to the characteristics of"structural elements"(framework grain,interstitial material and pore throat structure)of low-permeability sandstone reservoir,the"step by step dissolution and separation"acidification and acid fracturing technology has been developed and tested in field.There are three main mechanisms affecting permeability of low-permeability sandstone reservoir:(1)The mud fillings between the framework grains block the seepage channels.(2)In the process of burial,the products from crystallization caused by changes in salinity and solubility and uneven migration and variation of the syn-sedimentary formation water occupy the pores and throat between grains.(3)Under the action of gradual increase of overburden pressure,the framework grains of the rock is compacted tighter,making the seepage channels turn narrower.The"step by step dissolution and separation"acidification(acid fracturing)technology uses sustained release acid as main acidizing fluid,supramolecular solvent instead of hydrochloric acid to dissolve carbonate,and a composite system of ammonium hydrogen fluoride,fluoroboric acid,and fluorophosphoric acid to dissolve silicate,and dissolving and implementing step by step,finally reaching the goal of increasing porosity and permeability.By using the technology,the main blocking interstitial material can be dissolved effectively and the dissolution residual can be removed from the rock frame,thus expanding the effective drainage radius and increasing production and injection of single well.This technology has been proved effective by field test.

Laboratory study of fluid viscosity induced ultrasonic velocity dispersion in reservoir sandstones

Ultrasonic velocities of a set of saturated sandstone samples were measured at simulated in-situ pressures in the laboratory.The samples were obtained from the W formation of the WXS Depression and covered low to nearly high porosity and permeability ranges.The brine and four different density oils were used as pore fluids,which provided a good chance to investigate fluid viscosity-induced velocity dispersion.The analysis of experimental observations of velocity dispersion indicates that（1）the Biot model can explain most of the small discrepancy（about 2–3%）between ultrasonic measurements and zero frequency Gassmann predictions for high porosity and permeability samples saturated by all the fluids used in this experiment and is also valid for medium porosity and permeability samples saturated with low viscosity fluids（less than approximately 3 mP·S）and（2）the squirt flow mechanism dominates the low to medium porosity and permeability samples when fluid viscosity increases and produces large velocity dispersions as high as about 8%. The microfracture aspect ratios were also estimated for the reservoir sandstones and applied to calculate the characteristic frequency of the squirt flow model,above which the Gassmann’ s assumptions are violated and the measured high frequency velocities cannot be directly used for Gassmann’s fluid replacement at the exploration seismic frequency band for W formation sandstones.

A generalized viscoelastic Biot/squirt model for clay-bearing sandstones in a wide range of permeabilities

To simultaneously take into account the Biot-flow mechanism, the squirt-flow mechanism, and the frame-viscoelasticity mechanism, a generalized viscoelastic BISQ （Biot/squirt） model is developed for wave propagation in clay-bearing sandstones based on Dvorkin＇s elastic BISQ model. The present model is extended to a wide range of permeabilities （k 〉 0.05 mD） by introducing a dimensionless correction factor for viscoelastic parameters, defined as a function of the permeability and the clay content. We describe the frame＇s stress-strain relationship of the clay-bearing sandstones by the differential constitutive equations of generalized viscoelasticity and then derive the viscoelastic-wave dynamic equations. With the assumption of a plane-wave solution, we finally yield the phase velocities and the attenuation coefficients by solving the dynamic wave equations in the frequency and wave number domain. The comparison of numerical results and experimental data shows that the generalized viscoelastic BISQ model is applicable for modeling the wave propagation in most of the sandstones mainly bearing kaolinite clay.

Origin of Tafoni in the Late Cretaceous Aeolian Sandstones,Danxiashan UNESCO Global Geopark,South China

Tafoni occur generally in granular rocks around the world, but their origin remains controversial. In this study,the roles of lithology, micro–climate, and organism in tafoni development are investigated in the Danxiashan UNESCO Global Geopark of South China. The Jinshiyan Temple and Luyitang sites along the Jinjiang River are chosen to conduct tafoni morphometry, bedrock petrography, and micro–climate analyses. The research methods used in this study include field observations and measurements, Voronoi diagrams, polarizing microscopic and scanning electron microscopic(SEM)image analysis, and meteorological detection. The tafoni are mostly 2–10 cm in length and elliptical in shape. The Late Cretaceous Jinshiyan sandstones are characterized by a grain–to–grain contact fabric and moderate sorting with a high proportion of soluble grains and cements. The Voronoi diagrams developed through the Arc GIS software are largely consistent with the tafoni openings. Moreover, owing to exposure to solar insolation, the external temperature values are higher than the internal ones, while the external relative humidity values are lower than the internal ones. Therefore, the permeable Jinshiyan sandstones are fundamental for tafoni development, while the abundant moisture from the Jinjiang River and frequent rains is favorable for salt weathering in tandem with biological activities. At last, a five–stage development model is proposed for the tafoni progression in the study area.

The effective pressure law for permeability of clay-rich sandstones

To study the relative sensitivity of permeability to pore pressure Pp and confining pressure Pc for clay-rich rocks, permeability measurements were performed on samples of four clay-rich sandstones. A new method （hereafter denoted the ＂slide method＂） was developed and used for analyzing the permeability data obtained. The effective pressure coefficients for permeability nk were calculated. The values of nk were found to be greater than 1.0 and insensitive to changes in pressure. These results confirmed observations previously made on clay-rich rocks. Also, the coefficients nk obtained had different characteristics for different samples because of differences in the types of clay they contained. The effective pressure law （σeff=Pc-nkPp） determined using the slide method gave better results about k（oefr） than classic Terzaghi＇s law （σeff=Pc-nkPp）.

Architectural Units and Groundwater Resource Quantity Evaluation of Cretaceous Sandstones in the Ordos Basin,China

Sandstone is a common lithology in a number of groundwater reservoirs. Studying the skeleton sandstone architectural units, therefore, lays the basis for characterizing aquifer systems, groundwater quality, and resource evaluation. This comprehensive analysis of Cretaceous aquiferous sandstones in the Ordos basin, China, shows that there exists a basin-scale skeleton sandstone in the Luohe Formation which contains 11 isolated barrier beds, 12 small skeleton sandstone bodies in Huanhe Formation, and 3 in the Luohandong Formation. The spatial structure and superimposed relationship as well as the medium properties of these skeleton sandstones and isolated barrier beds can be shown by 3D visualization models. Simultaneously, resource quantity can be evaluated with the 3D inquiry functions. The comparison between property models and structural models indicates that the salinity of groundwater of the Luohe Formation has a close connection with the locations of isolated barrier beds that contain abundant gypsum. Through quantitative calculation, groundwater resource of the Cretaceous Luohe and Luohandong formations is estimated to be 1.6×10-（12） m-3, and the total groundwater resource of the Cretaceous system in the Ordos basin is more than 2×10-（12） m-3.

Tectonic Setting and Nature of the Provenance of Sedimentary Rocks in Lanping Mesozoic-Cenozoic Basin: Evidence from Geochemistry of Sandstones

The geochemical composition of sandstones in the sedimentary basin is controlled mainly by the tectonic setting of the provenance, and it is therefore possible to reveal the tectonic setting of the provenance and the nature of source rocks in terms of the geochemical composition of sandstones. The major elements, rare\|earth elements and trace elements of the Mesozoic\|Cenozoic sandstones in the Lanping Basin are studied in this paper, revealing that the tectonic settings of the provenance for Mesozoic\|Cenozoic sedimentary rocks in the Lanping Basin belong to a passive continental margin and a continental island arc. Combined with the data on sedimentary facies and palaeogeography, it is referred that the eastern part of the basin is located mainly at the tectonic setting of the passive continental margin before Mesozoic, whereas the western part may be represented by a continental island arc. This is compatible with the regional geology data. The protoliths of sedimentary rocks should be derived from the upper continental crust, and are composed mainly of felsic rocks, mixed with some andesitic rocks and old sediment components. Therefore, the Lanping Mesozoic\|Cenozoic Basin is a typical continental\|type basin. This provides strong geochemical evidence for the evolution of the paleo\|Tethys and the basin\|range transition.

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.