Experimental Study and Fractal Analysis of Heterogeneity in Naturally Fractured Rocks

Capillary pressure curves of six low porosity and low permeability core samples from The Geysers geothermal field were measured using the mercury-intrusion approach to characterize the heterogeneity of rock. One high permeability Berea sandstone core sample was analyzed similarly, for comparison. The maximum pressure of mercury intruded into the rock was about 200 MPa to reach the extremely small pores. Experimental data showed that the capillary pressure curves of The Geysers rock are very different from that of the Berea sandstone. It was found that the frequently used capillary pressure models could not be used to represent the data from The Geysers rock samples. This might be because of the fractures in the rock. To this end, a fractal technique was proposed to model the features of the capillary pressure curves and to characterize the difference in heterogeneity between The Geysers rock and Berea sandstone. The results demonstrated that the rock from The Geysers geothermal field was fractal over a scaling range of about five orders of magnitude. The values of the fractal dimension of all the core samples (six from The Geysers and one Berea sandstone) calculated using the proposed approach were in the range from 2 to 3. The results showed that The Geysers rock with a high density of fractures had a greater fractal dimension than Berea sandstone which is almost without fractures. This shows that The Geysers rock has greater heterogeneity, as expected.     

Analysis of capillary interaction and oil recovery under ultrasonic waves

Although, the effects of ultrasonic irradiation on multiphase flow through porous media have been studied in the past few decades, the physics of the acoustic interaction between fluid and rock is not yet well understood. Various mechanisms may be responsible for enhancing the flow of oil through porous media in the presence of an acoustic field. Capillary related mechanisms are peristaltic transport due to mechanical deformation of the pore walls, reduction of capillary forces due to the destruction of surface films generated across pore boundaries, coalescence of oil drops due to Bjerknes forces, oscillation and excitation of capillary trapped oil drops, forces generated by cavitating bubbles, and sonocapillary effects. Insight into the physical principles governing the mobilization of oil by ultrasonic waves is vital for developing and implementing novel techniques of oil extraction. This paper aims at identifying and analyzing the influence of high-frequency, high-intensity ultrasonic radiation on capillary imbibition. Laboratory experiments were performed using cylindrical Berea sandstone and Indiana limestone samples with all sides (quasi-co-current imbibition), and only one side (counter-current imbibition) contacting with the aqueous phase. The oil saturated cores were placed in an ultrasonic bath, and brought into contact with the aqueous phase. The recovery rate due to capillary imbibition was monitored against time. Air–water, mineral oil–brine, mineral oil–surfactant solution and mineral oil-polymer solution experiments were run each exploring a separate physical process governing acoustic stimulation. Water–air imbibition tests isolate the effect of ultrasound on wettability, capillarity and density, while oil–brine imbibition experiments help outline the ultrasonic effect on viscosity and interfacial interaction between oil, rock and aqueous phase. We find that ultrasonic irradiation enhances capillary imbibition recovery of oil for various fluid pairs, and that such process is dependent on the interfacial tension and density of the fluids. Although more evidence is needed, some runs hint that wettability was not altered substantially under ultrasound. Preliminary analysis of the imbibition recoveries also suggests that ultrasound enhances surfactant solubility and reduce surfactant adsorption onto the rock matrix. Additionally, counter-current experiments involving kerosene and brine in epoxy coated Berea sandstone showed a dramatic decline in recovery. Therefore, the effectiveness of any ultrasonic application may strongly depend on the nature of interaction type, i.e., co- or counter-current flow. A modified form of an exponential model was employed to fit the recovery curves in an attempt to quantify the factors causing the incremental recovery by ultrasonic waves for different fluid pairs and rock types.     

Evaluation of Matrix-Fracture Transfer Functions for Counter-Current Capillary Imbibition

Different functions describing matrix-fracture transfer were tested for counter-current capillary imbibition interaction. The recovery curves obtained from capillary imbibition experiments were used to fit the transfer functions. The exponential coefficients yielding the best fit to the experimental data were obtained and correlated to the effective parameters such as viscosity, IFT, matrix length and diameter, matrix permeability and porosity, and wettability using multivariable regression analysis. In order to obtain the recovery curves, experiments were conducted on Berea sandstone and Indiana limestone samples. Cylindrical samples with different shape factors were obtained by cutting the plugs 1, 2.5, and 5 cm in diameter and 2.5, 5, and 10 cm in length. All sides were coated with epoxy except one end. More than fifty static imbibition experiments were carried out on vertically and horizontally situated samples where the imbibition took place upward and lateral directions, respectively. Brine–air, brine–kerosene, brine–mineral oil, and surfactant solution–mineral oil pairs were used as fluids. For many matrix shape factors (especially longer and small diameter ones), dividing the recovery curve into three parts were needed as the early, intermediate, and late times, which are typically distinguished by the time required for the imbibition front to reach the closed boundary at the end of the core. Correlations among the exponential coefficients and rock/fluid properties were developed. It was observed that different rock/fluid properties and transfer mechanisms (capillary imbibition and gravity drainage) govern the process for each part. Hence, the analyses done in this study were useful not only for developing explicit transfer functions but also identifying the physics of the counter-current imbibition recovery.     

冲击速度和轴向静载对红砂岩破碎及能耗的影响

地下岩体工程爆破开挖中,距爆源不同距离处岩体承受的地应力和动载荷大小不同,从动载荷的角度表征岩石动态破坏结果与工程实际更吻合。为研究动载荷和地应力大小对岩体破碎和能量耗散特性的影响,利用动静组合加载试验装置,分别设置7个冲击速度和轴向静应力等级,对红砂岩试件进行冲击试验。根据试件的破碎状况,分析不同静应力工况下冲击速度对岩石破坏模式和机理的影响。计算不同工况下的应力波能量值,研究冲击速度和轴向静应力对岩石能耗特性的影响。对破坏试件进行筛分试验,研究岩石破碎分形维数随冲击速度和轴向静应力的变化关系。结果表明,随着冲击速度的增大,试件的破坏程度逐渐加大。无轴压时岩石试件破坏后整体仍是一个圆柱体,属于张拉破坏;有轴压时岩石试件宏观破坏后呈沙漏状,属于拉剪破坏。岩石耗散能随冲击速度的升高呈二次函数关系递增;轴向静应力越高,递增幅度越小。随着冲击速度的升高,岩石分形维数由零逐渐增加;随着轴向静应力的升高,分形维数由零转为大于零的临界冲击速度先升高后降低。     

A New Method for Calculating Two-Phase Relative Permeability from Resistivity Data in Porous Media

Many resistivity data from laboratory measurements and well logging are available. Papers on the relationship between resistivity and relative permeability have been few. To this end, a new method was developed to infer two-phase relative permeability from the resistivity data in a consolidated porous medium. It was found that the wetting phase relative permeability is inversely proportional to the resistivity index of a porous medium. The proposed model was verified using the experimental data in different rocks (Berea, Boise sandstone, and limestone) at different temperatures up to 300°F. The results demonstrated that the oil and water relative permeabilities calculated from the experimental resistivity data by using the model proposed in this article were close to those calculated from the capillary pressure data in the rock samples with different porosities and permeabilities. The results demonstrated that the proposed approach to calculating two-phase relative permeability from resistivity data works satisfactorily in the cases studied.     

Modeling the elasto-acoustic hysteretic nonlinearity of dry Berea sandstone

By means of the dynamic acousto-elastic technique the instantaneous state of a material is probed by a high-frequency pulse while an external, low-frequency dynamic source modulates it in time. When it is applied to rocks, a remarkable variety of responses in the form of hysteresis of the material’s modulus defect is obtained. Among them, the response by Berea sandstone is perhaps the most investigated. Hysteresis of the modulus defect in dry Berea sandstone shows intriguing features which have not yet been interpreted in terms of specific mechanisms occurring at atomic or meso-scale. In the present communication, three rheological models providing simplified representations of realistic mechanisms are considered. They involve dislocations interacting with point defects, and microcracks with finite stiffness in compression. Constitutive relations linking macroscopic anelastic strain and stress are derived from them together with the modulus defect associated to each model. These relationships are employed to construct a composite model capable of reproducing several of the main features observed in the experimental data. The limitations of the present approach, the validity of its physical interpretation, and, possibly, of the current implementation of the dynamic acousto-elastic technique are also discussed.     

Efficiency of diffusion controlled miscible displacement in fractured porous media

Experiments were performed to study the diffusion process between matrix and fracture while there is flow in fracture. 2-inch diameter and 6-inch length Berea sandstone and Indiana limestone samples were cut cylindrically. An artificial fracture spanning between injection and production ends was created and the sample was coated with heat-shrinkable teflon tube. A miscible solvent (heptane) was injected from one end of the core saturated with oil at a constant rate. The effects of (a) oil type (mineral oil and kerosene), (b) injection rates, (c) orientation of the core, (d) matrix wettability, (e) core type (a sandstone and a limestone), and (f) amount of water in matrix on the oil recovery performance were examined. The process efficiency in terms of the time required for the recovery as well as the amount of solvent injected was also investigated. It is expected that the experimental results will be useful in deriving the matrix–fracture transfer function by diffusion that is controlled by the flow rate, matrix and fluid properties.     

Effects of humidity and temperature on subcritical crack growth in sandstone

In order to ensure long-term stability of structures in a rock mass, the study of time-dependent fracturing is essential. The influences of the surrounding environmental conditions and rock fabric on subcritical crack growth in sedimentary rocks in air are yet to be clarified, while the nature of subcritical crack growth in igneous rocks has been studied well. In this study, the influences of temperature and relative humidity on subcritical crack growth in Berea sandstone, Shirahama sandstone and Kushiro sandstone were investigated in air. The load relaxation method of Double Torsion (DT) testing method was used to measure both crack velocity and stress intensity factor under a controlled temperature and relative humidity.Results show that the change of the crack velocity at a given stress intensity factor was unclear when the temperature increased under a constant relative humidity in air. On the other hand, we show that the crack velocity increased by several orders of magnitude when the relative humidity increased threefold or fourfold under a constant temperature at a given stress intensity factor. This increase is much larger than that expected from the conventional concept based on the theory of stress corrosion. It is therefore necessary to consider the additional mechanisms for subcritical crack growth in sandstone. The increase of the crack velocity was larger for sandstone which contained larger amount of clays. We conclude that subcritical crack growth in sandstone in air is affected remarkably by the relative humidity and the amount of clays in rock.     

A Hierarchical Sampling for Capturing Permeability Trend in Rock Physics

Among all properties of reservoir rocks, permeability is an important parameter which is typically measured from core samples in the laboratory. Due to limitations of core drilling all over a reservoir, simulation of rock porous media is demanded to explore more scenarios not seen in the available data. One of the most accurate methods is cross correlation based simulation (CCSIM) which recently has broadly applied in geoscience and porous media. The purpose of this study is producing realizations with the same permeability trend to a real sample. Berea sandstone sample is selected for this aim. Permeability results, extracted from smaller sub-samples of the original sample, showed that classic Kozeny–Carman permeability trend is not suitable for this sample. One reason can be due to lack of including geometrical and fractal properties of pore-space distribution in this equation. Thus, a general trend based on fractal dimensions of pore-space and tortuosity of the Berea sample is applied in this paper. Results show that direct 3D stochastic modeling of porous media preserves porous structure and fractal behavior of rock. On the other hand, using only 2D images for constructing the 3D pore structures does not reproduce the measured experimental permeability. For this aim, a hierarchical sampling is implemented in two and three steps using both 2D and 3D stochastic modeling. Results showed that two-step sampling is not suitable enough, while the utilized three-step sampling occurs to be show excellent performance by which different models of porous media with the same permeability trend as the Berea sandstone sample can be generated.     

断层内破碎岩石渗透性的实验研究

断层破碎带岩石的渗透性是影响地下工程中由渗流失稳而引发灾害事故的重要影响因素之一。利用一种专门的破碎岩石压实渗透仪,在MTS815.02岩石力学伺服试验系统上测试了取自断层内的破碎灰岩、破碎砂岩、破碎泥岩的渗透系数,得到并分析了轴向压力、岩样粒径、水流速度与渗透系数的关系曲线。研究表明:破碎岩石渗透系数与其压实状态密切相关,随着轴压的增加,渗透系数都相应降低;在相同的轴向压力状态下,岩样粒径越小,其渗透系数也越小,因此,挤压程度和充填程度都较低的小断层导水性好,容易导致突水;破碎岩石的渗透系数随着水流速度的增大呈减小趋势,但水流速度对破碎岩石渗透系数的影响程度有限;在相同的压力、粒径情况下,破碎泥岩的渗透系数比破碎灰岩、破碎砂岩的要小1～2个量级,说明当断层上下盘为坚硬岩石时,断层带渗透性好、易导水。研究结果可为采动过程中评价断层的导水性提供参考。     

Wettability Alteration to Intermediate Gas-Wetting in Porous Media at Elevated Temperatures

Wettability alteration to intermediate gas-wetting in porous media by treatment with FC-759, a fluorochemical polymer has been studied experimentally. Berea sandstone was used as the main rock sample in our work, and its wettability before and after chemical treatment was studied at various temperatures from 25 to 93°C. We also studied recovery performance for both gas/oil and oil/water systems for Berea sandstone before and after wettability alteration by chemical treatment. Our experiment shows that chemical treatment with FC-759 can result in: (1) wettability alteration from strong liquid-wetting to stable intermediate gas-wetting at room temperature and at elevated temperatures; (2) neutral wetting for gas, oil, and water phases in two-phase flow; (3) significant increase in oil mobility for gas/oil system; and (4) improved recovery behavior for both gas/oil and oil/water systems. This work reveals a potential for field application for improved gas-well deliverability and well injectivity by altering the rock wettability around wellbore in gas condensate reservoirs from strong liquid-wetting to intermediate gas-wetting.     

花岗岩动静态压剪复合加载实验研究

岩石为天然含有微裂纹微孔洞等缺陷的复杂介质,其在复杂应力状态,尤其是在压剪应力状态下的性能研究,对工程应用有着十分重要的意义。本文利用双斜面垫块改进现有装置对花岗岩进行了动静态下的压剪复合加载实验,其中静态实验基于MTS材料试验机,动态实验基于分离式Hopkinson压杆（以下简称SHPB）,由此得到不同压剪载荷联合作用下花岗岩的静态和动态力学性能。通过改变倾斜端面的角度就能够得到岩石在不同压剪加载路径下的力学性能,由此可以得到岩石的静动态破坏面。结果表明:花岗岩的破坏强度具有明显的加载速率效应。本研究为探讨岩石在复杂应力状态下的力学性能提供了新的方法。     

大理岩和砂岩动态本构的实验研究

探讨了在Ｈｏｐｋｉｎｓｏｎ压杆装置上进行岩石长杆冲击实验。用多组埋入式聚偏四氟乙烯薄膜应力计，进行了波衰减的测量，获得了大理岩、砂岩在干燥、饱水、饱油情况下的衰减系数。对实测波形运用拉格朗日分析和路径线方法获取了大理岩、砂岩动态本构关系。     

强角闪石化橄榄二辉岩的动态拉伸强度实验研究

对强角闪石化橄榄二辉岩的动态拉伸断裂强度进行了实验研究。设计了能在样品中产生持续时间大约为1.5 s拉伸应力脉冲的平板冲击回收实验。通过对回收样品的宏观和微观观察,确定了样品出现拉伸破坏开始阶段以及破坏裂纹的扩展阶段,进而确定了该岩石样品的动态拉伸强度约为265.6~315.3 MPa。同时,基于线弹性近似,导出了在一维应变条件下样品内拉伸应力和作用时间的估算公式。     

Fractal Prediction Model of Spontaneous Imbibition Rate

By utilizing fractal dimension as one of the parameters to characterize rocks, a mathematical model was derived to predict the production rate by spontaneous imbibition. This fractal production model predicts a power law relationship between spontaneous imbibition rate and time. Fractal dimension can be estimated from the fractal production model using the experimental data of spontaneous imbibition in porous media. The experimental data of recovery in gas-water-rock and oil–water–rock systems were used to test the fractal production model. The rocks (Berea sandstone, chalk, and The Geysers graywacke) in which the spontaneous water imbibition experiments were conducted had different permeabilities ranging from 0.5 to over 1000 md. The results demonstrate that the fractal production model can match the experimental data satisfactorily in the cases studied. The fractal dimension data inferred from the model match were approximately equal to the values of fractal dimension measured using a different technique (mercury-intrusion capillary pressure) in Berea sandstone.     

岩石对冲击波的非线性动态响应

对干燥、饱水、饱泵油大理岩和饱和砂岩进行了SHPB冲击压缩实验,得到了干燥岩石和饱和岩石的应力波衰减规律。在应力波传播过程中,其幅值有较大的衰减,干燥岩石的衰减最大,且孔隙度越大衰减越大,饱和岩石还存在较强的波弥散效应。在小于岩石屈服强度时,多次冲击加载下获得随冲击加载次数的增加,加载模量增大,残余应变减小的压实效应。这一结果可用于大型地震工程和防护工程的设计和建造。     

三峡工程基岩爆破振动特性的试验研究

以三峡工程坝基岩体开挖爆破为背景 ,在弱风化花岗岩底板内进行了 6次现场爆破试验 ,测量出距爆源不等距离处的 36组地震波形。通过频域与统计分析发现 ,岩石质点振动主频率与药量、距离成反比关系 ;地震波作用时间与爆破药量成正比关系 ,而与距离成反比关系。应用神经网络理论建立的基于爆破地震效应先验知识的网络模型 (PKFN)能很好地描述爆破地震波的衰减规律 ,其计算平均相对误差仅为 3 .5 %。用地震层析成象方法 (CT)较准确地测定出了岩体爆破松裂区边界 ,并结合PKFN模型得到了三峡工程坝基岩体的临界质点振动速度范围 13 .816 .6cm/s。     

A Criterion for Non-Darcy Flow in Porous Media

Non-Darcy behavior is important for describing fluid flow in porous media in situations where high velocity occurs. A criterion to identify the beginning of non-Darcy flow is needed. Two types of criteria, the Reynolds number and the Forchheimer number, have been used in the past for identifying the beginning of non-Darcy flow. Because each of these criteria has different versions of definitions, consistent results cannot be achieved. Based on a review of previous work, the Forchheimer number is revised and recommended here as a criterion for identifying non-Darcy flow in porous media. Physically, this revised Forchheimer number has the advantage of clear meaning and wide applicability. It equals the ratio of pressure drop caused by liquid–solid interactions to that by viscous resistance. It is directly related to the non-Darcy effect. Forchheimer numbers are experimentally determined for nitrogen flow in Dakota sandstone, Indiana limestone and Berea sandstone at flowrates varying four orders of magnitude. These results indicate that superficial velocity in the rocks increases non-linearly with the Forchheimer number. The critical Forchheimer number for non-Darcy flow is expressed in terms of the critical non-Darcy effect. Considering a 10% non-Darcy effect, the critical Forchheimer number would be 0.11.     

Direct Observation of Trapped Gas Bubbles by Capillarity in Sandy Porous Media

We investigated the mechanism of residual gas trapping at a microscopic level. We imaged trapped air bubbles in a Berea sandstone chip after spontaneous imbibition at atmospheric pressure. The pore structure and trapped bubbles were observed by microfocused X-ray computed tomography. Distributions of trapped bubbles in Berea and Tako sandstone were imaged in coreflooding at a capillary number of 1.0 × 10⁻⁶. Trapped bubbles are of two types, those occupying the center of the pore with a pore-scale size and others having a pore-network scale size. In low-porosity media such as sandstone, connected bubbles contribute greatly to trapped gas saturation. Effects of capillary number and injected water volume were investigated using a packed bed of glass beads 600μm in diameter, which had high porosity (38%). The trapped N₂ bubbles are stable against the water flow rate corresponding to a capillary number of 1.0 × 10⁻⁴.