地震尺度下碳酸盐岩储层的岩石物理建模方法(英文)

碳酸盐岩油藏的强非均质性以及孔隙结构的复杂性,使得作为连接油藏参数与地震参数重要桥梁的岩石物理模型,以及作为油藏预测和定量表征最有效工具的流体替换成为岩石物理建模的难点与重点。在碳酸盐岩储层复杂孔隙结构与地震尺度下碳酸盐岩储层非均质性分析基础上,研究采用岩石网格化方法,将地震尺度下非均质碳酸盐岩储层岩石划分为具有独立岩石参数的均质岩石子体,根据岩石孔隙成因与结构特征采用不同岩石物理模型分步计算岩石子块干岩石弹性模量,并根据不同孔隙连通性进行流体替换,计算饱和不同流体岩石弹性模量。基于计算的岩石子块弹性模量,采用Hashin-Shtrikman-Walpole弹性边界计算理论方法实现地震尺度下碳酸盐岩储层弹性参数计算。通过对含有不同类型孔隙组合碳酸盐岩储层模型的弹性模量进行计算与分析,明确不同孔隙对岩石弹性参数的影响特征,模拟分析结果与实际资料认识一致。     

稠油热采时移地震监测研究与应用

我国具有丰富的稠油资源,但国内外针对陆相薄互层稠油油藏热采动态的时移地震监测研究还很少.通过分析火烧油层对储层的影响,结合已有的岩石物理测量结果,建立了薄互层油藏火烧油层模型,开展了地震正演模拟研究,并给出了应用实例.结果表明,稠油热采(注蒸汽、火烧油层、注热水)会引起储层岩石和孔隙流体弹性特性的显著改变,从而导致明显的地震属性差异;时移地震可以用来划分油层中高温区范围,跟踪高温前缘等.在陆相薄互层稠油田热采开发中,利用时移地震来监测油田开发的全过程是可行的.     

陆相薄互层稠油油藏热采时移地震监测研究

目前,针对陆相薄互层油藏实施时移地震监测尚没有明显的突破,加强时移地震方法、理论的研究和应用,对于我国时移地震监测技术的发展和应用具有积极的意义.根据油藏工程理论,在详细分析火烧油层对储层物性影响的基础上,结合已有的实验室岩石物理测量结果,重点就稠油热采过程中温度的剧烈变化对储层岩石和孔隙流体弹性特性的影响进行了较为详细的分析.并开展了薄互层油藏火烧油层地震正演模拟研究.结果表明,在稠油热采过程中,高温高压不仅会使得孔隙流体特性发生显著的改变,而且储层岩石本身弹性特性的变化也非常明显.即使是对于薄层或薄互层,两方面共同的变化将使得稠油热采前后储层弹性特性产生巨大的差异,进而引起显著的地震异常.因此,开展陆相薄互层稠油热采时移地震监测,不仅具有坚实的岩石物理基础,而且具有切实的可行性.     

When 4D seismic is not applicable: Alternative monitoring scenarios for the Arab-D reservoir in the Ghawar Field

Ghawar, the largest oilfield in the world, produces oil from the Upper Jurassic Arab‐D carbonate reservoir. The high rigidity of the limestone–dolomite reservoir rock matrix and the small contrast between the elastic properties of the pore fluids, i.e. oil and water, are responsible for the weak 4D seismic effect due to oil production. A feasibility study was recently completed to quantify the 4D seismic response of reservoir saturation changes as brine replaced oil. The study consisted of analysing reservoir rock physics, petro‐acoustic data and seismic modelling. A seismic model of flow simulation using fluid substitution concluded that time‐lapse surface seismic or conventional 4D seismic is unlikely to detect the floodfront within the repeatability of surface seismic measurements. Thus, an alternative approach to 4D seismic for reservoir fluid monitoring is proposed. Permanent seismic sensors could be installed in a borehole and on the surface for passive monitoring of microseismic activity from reservoir pore‐pressure perturbations. Reservoir production and injection operations create these pressure or stress perturbations. Reservoir heterogeneities affecting the fluid flow could be mapped by recording the distribution of epicentre locations of these microseisms or small earthquakes. The permanent borehole sensors could also record repeated offset vertical seismic profiling surveys using a surface source at a fixed location to ensure repeatability. The repeated vertical seismic profiling could image the change in reservoir properties with production.     

Integrating gravimetric and interferometric synthetic aperture radar data for enhancing reservoir history matching of carbonate gas and volatile oil reservoirs

Reservoir history matching is assuming a critical role in understanding reservoir characteristics, tracking water fronts, and forecasting production. While production data have been incorporated for matching reservoir production levels and estimating critical reservoir parameters, the sparse spatial nature of this dataset limits the efficiency of the history matching process. Recently, gravimetry techniques have significantly advanced to the point of providing measurement accuracy in the microgal range and consequently can be used for the tracking of gas displacement caused by water influx. While gravity measurements provide information on subsurface density changes, i.e., the composition of the reservoir, these data do only yield marginal information about temporal displacements of oil and inflowing water. We propose to complement gravimetric data with interferometric synthetic aperture radar surface deformation data to exploit the strong pressure deformation relationship for enhancing fluid flow direction forecasts. We have developed an ensemble Kalman‐filter‐based history matching framework for gas, gas condensate, and volatile oil reservoirs, which synergizes time‐lapse gravity and interferometric synthetic aperture radar data for improved reservoir management and reservoir forecasts. Based on a dual state–parameter estimation algorithm separating the estimation of static reservoir parameters from the dynamic reservoir parameters, our numerical experiments demonstrate that history matching gravity measurements allow monitoring the density changes caused by oil–gas phase transition and water influx to determine the saturation levels, whereas the interferometric synthetic aperture radar measurements help to improve the forecasts of hydrocarbon production and water displacement directions. The reservoir estimates resulting from the dual filtering scheme are on average 20%–40% better than those from the joint estimation scheme, but require about a 30% increase in computational cost.     

Monitoring viscosity changes from time‐lapse seismic attenuation: case study from a heavy oil reservoir

Heating heavy oil reservoirs is a common method for reducing the high viscosity of heavy oil and thus increasing the recovery factor. Monitoring of these viscosity changes in the reservoir is essential for delineating the heated region and controlling production. In this study, we present an approach for estimating viscosity changes in a heavy oil reservoir. The approach consists of three steps: measuring seismic wave attenuation between reflections from above and below the reservoir, constructing time‐lapse Q and Q^?1 factor maps, and interpreting these maps using Kelvin–Voigt and Maxwell viscoelastic models. We use a 4D relative spectrum method to measure changes in attenuation. The method is tested with synthetic seismic data that are noise free and data with additive Gaussian noise to show the robustness and the accuracy of the estimates of the Q‐factor. The results of the application of the method to a field data set exhibit alignment of high attenuation zones along the steam‐injection wells, and indicate that temperature dependent viscosity changes in the heavy oil reservoir can be explained by the Kelvin–Voigt model.     

An approach to combined rock physics and seismic modelling of fluid substitution effects

The aim of seismic reservoir monitoring is to map the spatial and temporal distributions and contact interfaces of various hydrocarbon fluids and water within a reservoir rock. During the production of hydrocarbons, the fluids produced are generally displaced by an injection fluid. We discuss possible seismic effects which may occur when the pore volume contains two or more fluids. In particular, we investigate the effect of immiscible pore fluids, i.e. when the pore fluids occupy different parts of the pore volume. The modelling of seismic velocities is performed using a differential effective‐medium theory in which the various pore fluids are allowed to occupy the pore space in different ways. The P‐wave velocity is seen to depend strongly on the bulk modulus of the pore fluids in the most compliant (low aspect ratio) pores. Various scenarios of the microscopic fluid distribution across a gas–oil contact (GOC) zone have been designed, and the corresponding seismic properties modelled. Such GOC transition zones generally give diffuse reflection regions instead of the typical distinct GOC interface. Hence, such transition zones generally should be modelled by finite‐difference or finite‐element techniques. We have combined rock physics modelling and seismic modelling to simulate the seismic responses of some gas–oil zones, applying various fluid‐distribution models. The seismic responses may vary both in the reflection time, amplitude and phase characteristics. Our results indicate that when performing a reservoir monitoring experiment, erroneous conclusions about a GOC movement may be drawn if the microscopic fluid‐distribution effects are neglected.     

Formation mechanisms of heavy oils in the Liaohe Western Depression,Bohai Gulf Basin

The Liaohe Oilfield in the Liaohe Western Depression of the Bohai Gulf Basin is the third-largest oil producing province and the largest heavy oil producing oilfield in China. A total of 65 oil samples,35 rock samples and 36 reservoir sandstone samples were collected and analyzed utilizing conventional geochemical and biogeochemical approaches to unravel the mechanisms of the formation of the heavy oils. Investigation of the oils with the lowest maturity compared with the oils in the Gaosheng and Niuxintuo oilfields indicates no apparent relation between the maturity and physical properties of the heavy oils. It is suggested that the heavy oil with primary origin is not likely the main mechanism re-sponsible for the majority of the heavy oils in the Liaohe Western Slope. The absence and/or depletion of n-alkanes etc.,with relatively low molecular weight and the occurrence of 25-norhopane series in the heavy oils as well as the relatively high acidity of the oils all suggest that the majority of the heavy oils once experienced secondary alteration. The fingerprints of the total scanning fluorescence (TSF) of the inner adsorbed hydrocarbons on the reservoir grains and the included hydrocarbons in fluid inclusions are similar to that of the normal oils in the area but are different from the outer adsorbed and reser-voired free oils at present,further indicating that most of the heavy oils are secondary in origin. Analyses of bacteria (microbes) in 7 oil samples indicate that anaerobic and hyperthermophilic Ar-chaeoglobus sp. are the dominant microbes relevant to oil biodegradation,which coincides with the shallow commercial gas reservoirs containing anaerobic bacteria derived gas in the Gaosheng and Leijia teotonic belts. The biodegradation most likely occurs at the water/oil interface,where the forma-tion water is essential for microbe removal and nutrient transportation. We think that biodegradation,water washing and oxidization are interrelated and are the main mechanisms for the formation of the heavy oils. Biodegradation was the predominant process with water washing being a prerequisite,and oxidization acting as a metabolic manifestation. This study provides unique approaches for further investigation of the formation mechanisms of heavy oils in general,and may provide some important insight for the exploration of shallow biogas in the area.     

基于叠前反演的流体敏感属性实验研究及应用

提取叠前地震振幅信息的叠前反演技术已成为储层预测的重要手段,其能获得各种岩石弹性参数,丰富储层预测方法.因目标储层的差异性,优选并建立有利的流体敏感参数对储层流体检测尤为重要.本文基于岩石物理实验, 测量并分析了岩石弹性参数随流体饱和度的变化特征, 进一步根据岩石物理理论建立组合流体敏感参数, 达到对油气检测的最佳敏感效果.定义了流体敏感量,定量分析岩石弹性参数的流体敏感性.最后本文在X区块进行了叠前地震反演的应用, 结果表明通过岩石物理实验分析并建立获得的流体敏感参数能明显的提高储层的识别能力.     

有效压力与饱和度变化的气藏多波时移地震AVO响应

天然气在开发过程中,储层有效压力和含气饱和度均会发生变化,研究有效压力和含气饱和度的变化对地震响应特征的影响,在基于时移地震的剩余气分布预测研究中具有重要意义。天然气和石油的声学性质有着明显的差异,油藏时移地震的研究成果不能直接应用于气藏,因此需要开展气藏的时移地震研究。利用Shapiro模型表征干岩石弹性模量随有效压力的变化,借助Batzle-Wang方程描述流体速度随压力的变化关系,联合Gassmann理论进行流体替代,表征饱和流体岩石速度随含气饱和度的变化,建立了饱和流体岩石速度随有效压力和饱和度变化的岩石物理模型。基于该模型,对不同含气饱和度和不同有效压力下的气藏储层模型进行了多波时移地震叠前振幅变化（AVO）模拟。结果表明多波时移地震AVO技术可以有效地区分有效压力变化和含气饱和度变化,为进一步开展气藏多波时移地震流体监测提供了理论参考依据。      

Monitoring fluid substitution in rock samples from noise correlation

An alternative laboratory technique to measure the elastic constants of solid samples, based on the analysis of the cross‐correlation spectra of the vibratory response of randomly excited short solid cylinders, has been recently proposed. The aim of this paper is to check the ability of the technique called passive ultrasonic interferometry to monitor fluid substitution in different rock samples. Velocity variations due to fluid substitution are easily measured if the wave attenuation in the fluid‐saturated rock is not too large (typically in rocks with few cracks or microfractures). The experimental results are in agreement with the predictions of Biot–Gassmann poroelastic theory. The effect of substituting water with a stiffer saturating fluid, such as ethylene glycol, is to increase the overall bulk modulus of the rock, without any substantial effect on shear modulus. Furthermore, the experimental results compare well with those obtained independently with conventional pulse‐transmission technique using ultrasonic transducers. However, the measured pulse‐transmission bulk moduli are slightly larger than the corresponding measured ultrasonic interferometry moduli, with the deviation increasing with increasing fluid viscosity. This can be explained by dispersion due to wave‐induced flow of the viscous fluid since pulse‐transmission experiments involve higher frequencies than ultrasonic interferometry experiments.     

Research on seismic fluid identification driven by rock physics

Seismic fluid identification works as an effective approach to characterize the fluid feature and distribution of the reservoir underground with seismic data. Rock physics which builds bridge between the elastic parameters and reservoir parameters sets the foundation of seismic fluid identification, which is also a hot topic on the study of quantitative characterization of oil/gas reservoirs. Study on seismic fluid identification driven by rock physics has proved to be rewarding in recognizing the fluid feature and distributed regularity of the oil/gas reservoirs. This paper summarizes the key scientific problems immersed in seismic fluid identification, and emphatically reviews the main progress of seismic fluid identification driven by rock physics domestic and overseas, as well as discusses the opportunities, challenges and future research direction related to seismic fluid identification. Theoretical study and practical application indicate that we should incorporate rock physics, numerical simulation, seismic data processing and seismic inversion together to enhance the precision of seismic fluid identification.     

Controlled‐source electromagnetic monitoring of reservoir oil saturation using a novel borehole‐to‐surface configuration

To advance and optimize secondary and tertiary oil recovery techniques, it is essential to know the areal propagation and distribution of the injected fluids in the subsurface. We investigate the applicability of controlled‐source electromagnetic methods to monitor fluid movements in a German oilfield (Bockstedt, onshore Northwest Germany) as injected brines (highly saline formation water) have much lower electrical resistivity than the oil within the reservoir. The main focus of this study is on controlled‐source electromagnetic simulations to test the sensitivity of various source–receiver configurations. The background model for the simulations is based on two‐dimensional inversion of magnetotelluric data gathered across the oil field and calibrated with resistivity logs. Three‐dimensional modelling results suggest that controlled‐source electromagnetic methods are sensitive to resistivity changes at reservoir depths, but the effect is difficult to resolve with surface measurements only. Resolution increases significantly if sensors or transmitters can be placed in observation wells closer to the reservoir. In particular, observation of the vertical electric field component in shallow boreholes and/or use of source configurations consisting of combinations of vertical and horizontal dipoles are promising. Preliminary results from a borehole‐to‐surface controlled‐source electromagnetic field survey carried out in spring 2014 are in good agreement with the modelling studies.     

The effect of orthorhombic anisotropy and its implication for oil recovery and reservoir exploitation

Results of an experimental study of shear‐ and compressional‐wave propagation in an orthorhombically anisotropic medium are presented. The experiments were performed on a physical model consisting of two sets of fractures. The first set consisted of orientated rubber inclusions simulating weak material‐filled cracks. The second set consisted of a system of closely spaced parallel fractures simulated by thin plates of epoxy resin, superimposed orthogonally on the first set. Three cases of fracture orientations within the model were identified and studied. Case 1 is analogous to a jointed fracture reservoir with one vertical set of fluid‐filled cracks or fractures and one non‐filled horizontal set. This case is referred to as JFV. Case 2 is analogous to a double fracture reservoir with one horizontal set of fluid‐filled fractures or cracks and one non‐filled vertical set. This is referred to as DFH. Case 3 is analogous to a double fracture reservoir with two vertical sets of fractures or cracks, with only one fluid‐filled. Case 3 is referred to as DFV. A pulse transmission method was performed on all three modelled cases along the three principal axes. A directional variation in the compressional‐ and shear‐wave velocities, as well as distinct shear‐wave splitting, was observed. The elastic constants for each case were determined and differences between them were noted and compared with the controlled results of both layered (transverse isotropy, TI) and vertically fractured (azimuthally anisotropic models, VF) media. The differences in elastic moduli and velocities indicate the potential of recognizing the different fracture orientations and suggest an approach to designing a method of drilling to further enhance oil recovery and reservoir exploitation.     

Crude-oil hydrocarbon composition characteristics and oil viscosity prediction in the northern Songliao Basin

Crude oil hydrocarbon composition characteristics and oil viscosity prediction are important bases in petroleum exploration.A total of 54 oil/heavy-oil samples and 17 oil sands were analyzed and quantified using both comprehensive 2D gas chromatography(GC×GC)and comprehensive 2D gas chromatography/time-of-flight mass spectrometry(GC×GC/TOFMS).The results show that crude oil in the West slope is mainly heavy oil and its hydrocarbon composition is characterized overall by paraffinsmono-aromaticsnaphthenesnon-hydrocarbonsdi-aromaticstri-aromaticstetra-aromatics.Aromatics are most abundant and non-hydrocarbons are least abundant,whilst content differences among paraffins,naphthenes,aromatics,and non-hydrocarbons are less than 15%.There are two types of heavy oil,secondary type and mixing type.Biodegradation is the main formation mechanism of heavy oil.Biodegradation levels cover light biodegradation,moderate biodegradation,and severe biodegradation.With increasing biodegradation,paraffin content decreases while contents of aromatics and nonhydrocarbons increase.In contrast,naphthene content increases first and then decreases with increasing biodegradation.In severe biodegradation stage,naphthenes decrease more quickly than aromatics and non-hydrocarbons.This provides a new method for studying oil/heavy-oil biodegradation mechanism and biodegradation resistance of different hydrocarbons at different biodegradation stages.In the Longhupao-Daan terrace and Qijia-Gulong depression,most crude oil is conventional oil.Its composition is dominated by paraffins with the lowest content of aromatics.In some casual oil wells from the Longhupao-Daan terrace,crude oil from Saertu oil reservoirs is moderately biodegraded whereas crude oil from Putaohua oil reservoir is lightly biodegraded.Chemical parameters using saturate hydrocarbons and aromatics are usually not suitable for determining organic type and thermal maturity of biodegraded oil,especially of moderately or severely biodegraded oil,whilst Ts/(Ts+Tm)ratio can be used to determine thermal maturity of both conventional crude oil and heavy oil.     

Brittleness characteristics of tight oil siltstones

Rock brittleness directly affects reservoir fracturing and its evaluation is essential for establishing fracturing conditions prior to reservoir reforming. Dynamic and static brittleness data were collected from siltstones of the Qingshankou Formation in Songliao Basin. The brittle–plastic transition was investigated based on the stress–strain relation. The results suggest that the brittleness indices calculated by static elastic parameters are negatively correlated with the stress drop coefficient and the brittleness index B₂, defined as the average of the normalized Young’s modulus and Poisson’s ratio, is strongly correlated with the stress drop. The brittleness index B₂, Young’s modulus, and Poisson’s ratio correlate with the brittle minerals content; that is, quartz, carbonates, and pyrite. We also investigated the correlation between pore fluid and porosity and dynamic brittle characteristic based on index B₂. Pore fluid increases the plasticity of rock and reduces brittleness; moreover, with increasing porosity, rock brittleness decreases. The gas-saturated siltstone brittleness index is higher than that in oil- or water-saturated siltstone; the difference in the brittleness indices of oil- and water-saturated siltstone is very small. By comparing the rock mechanics and ultrasonic experiments, we find that the brittleness index obtained from the rock mechanics experiments is smaller than that obtained from the ultrasonic experiments; nevertheless, both decrease with increasing porosity as well as their differences. Ultrasonic waves propagate through the rock specimens without affecting them, whereas rock mechanics experiments are destructive and induce microcracking and porosity increases; consequently, the brittleness of low-porosity rocks is affected by the formation of internal microcrack systems.     

DHI evaluation by combining rock physics simulation and statistical techniques for fluid identification of Cambrian-to-Cretaceous clastic reservoirs in Pakistan

The use of seismic direct hydrocarbon indicators is very common in exploration and reservoir development to minimise exploration risk and to optimise the location of production wells. DHIs can be enhanced using AVO methods to calculate seismic attributes that approximate relative elastic properties. In this study, we analyse the sensitivity to pore fluid changes of a range of elastic properties by combining rock physics studies and statistical techniques and determine which provide the best basis for DHIs. Gassmann fluid substitution is applied to the well log data and various elastic properties are evaluated by measuring the degree of separation that they achieve between gas sands and wet sands. The method has been applied successfully to well log data from proven reservoirs in three different siliciclastic environments of Cambrian, Jurassic, and Cretaceous ages. We have quantified the sensitivity of various elastic properties such as acoustic and extended elastic (EEI) impedances, elastic moduli (K _sat and K _sat–μ), lambda–mu–rho method (λρ and μρ), P-to-S-wave velocity ratio (V _P/V _S), and Poisson’s ratio (σ) at fully gas/water saturation scenarios. The results are strongly dependent on the local geological settings and our modeling demonstrates that for Cambrian and Cretaceous reservoirs, K _sat–μ, EEI, V _P/V _S, and σ are more sensitive to pore fluids (gas/water). For the Jurassic reservoir, the sensitivity of all elastic and seismic properties to pore fluid reduces due to high overburden pressure and the resultant low porosity. Fluid indicators are evaluated using two metrics: a fluid indicator coefficient based on a Gaussian model and an overlap coefficient which makes no assumptions about a distribution model. This study will provide a potential way to identify gas sand zones in future exploration.     

Episodic fluid movements in superimposed basin:Combined evidence from outcrop and fluid inclusions of the Majiang ancient oil reservoir,Guizhou Province

Combined evidence from the outcrop and the fluid inclusion assemblage (FIA) analysis indicates that there exist two episodes of fluid flow controlled by the tectonic activity. The first episode was recorded mainly in the reservoir rock of the Honghuayuan Formation,representing the fluid flow of hydrocarbon charging. The second episode occurred mainly along the fault systems,representing the fluid move-ment when the ancient oil reservoir was destroyed. The host mineral morphology,homogeneous tem-perature,and salinity of the FIAs record an episodic fluid movement. Characters of high homogenous temperature,low salinity and a quick temperature variation of the first episode fluid flow may indicate an early-stage fluid eruption,and correspondingly,fine-grained calcite was formed. Temperature of the erupted fluid tended to decrease during its mixing with the upper formation fluid and finally had the same temperature as the upper formation. From then on,the temperature was rather steady and fa-vored the growth of the coarse calcite. Due to this character of the temperature variation of the episodic fluid flow,we can use the homogenous temperature of the FIA of the coarse calcite to date the forma-tion and the destruction time of the Majiang ancient oil reservoir. Episodic fluid flow was known for its inhomogeneous trapping,which resulted in the failure of dating according to the burial history. But taking a close look at its temperature variation,we think that the latest stage of fluid flow,characterized by steady state temperature and grow of the coarser crystals,can be used for dating. It will be of great value if this method is proved to be effective. The formation and the destruction time of the Majiang ancient oil reservoir were dated to be in the Indosinian Period and the late Yanshan-early Hymalayan Period respectively. This conclusion is in great discrepancy with the common accepted idea that the Majiang ancient oil reservoir was formed and destroyed during the Caledonian tectonic movement. Even so,this paper further discussed its reliability from the view of the source rock evolution and also the local tectonic evolution.     

A triple porosity scheme for fluid/solid substitution: theory and experiment

Quantifying the effects of pore-filling materials on elastic properties of porous rocks is of considerable interest in geophysical practice. For rocks saturated with fluids, the Gassmann equation is proved effective in estimating the exact change in seismic velocity or rock moduli upon the changes in properties of pore infill. For solid substance or viscoelastic materials, however, the Gassmann theory is not applicable as the rigidity of the pore fill (either elastic or viscoelastic) prevents pressure communication in the pore space, which is a key assumption of the Gassmann equation. In this paper, we explored the elastic properties of a sandstone sample saturated with fluid and solid substance under different confining pressures. This sandstone sample is saturated with octadecane, which is a hydrocarbon with a melting point of 28°C, making it convenient to use in the lab in both solid and fluid forms. Ultrasonically measured velocities of the dry rock exhibit strong pressure dependency, which is largely reduced for the filling of solid octadecane. Predictions by the Gassmann theory for the elastic moduli of the sandstone saturated with liquid octadecane are consistent with ultrasonic measurements, but underestimate the elastic moduli of the sandstone saturated with solid octadecane. Our analysis shows that the difference between the elastic moduli of the dry and solid-octadecane-saturated sandstone is controlled by the squirt flow between stiff, compliant, and the so-called intermediate pores (with an aspect ratio larger than that of compliant pore but much less than that of stiff pores). Therefore, we developed a triple porosity model to quantify the combined squirt flow effects of compliant and intermediate pores saturated with solid or viscoelastic infill. Full saturation of remaining stiff pores with solid or viscoelastic materials is then considered by the lower embedded bound theory. The proposed model gave a reasonable fit to the ultrasonic measurements of the elastic moduli of the sandstone saturated with liquid or solid octadecane. Comparison of the predictions by the new model to other solid substitution schemes implied that accounting for the combined effects of compliant and intermediate pores is necessary to explain the solid squirt effects.