Rock Stiffness Research Articles

From Static to Dynamic Stiffness of Shales: Frequency and Stress Dependence

The relation between static and dynamic stiffness in shales is important for many engineering applications. Dynamic stiffness, calculated from wave velocities, is often related to static stiffness through simple empirical correlations. The reason for this is that dynamic properties are often easier to obtain; however, it is the static properties that define the actual subsurface response to stress or pore pressure changes. Rocks are not elastic media, and stiffness depends on the stress state, stress change amplitude, loading rate, drainage conditions, fluid saturation, and scale. All these factors require consideration when static and dynamic stiffness properties are to be related. Two mechanisms that may have a strong effect on the stiffness of shales were studied in this experimental work: (1) a reduction of undrained static stiffness with an increase in stress amplitude and (2) a frequency dependence (or dispersion) of dynamic stiffness. Laboratory tests were performed on four fully brine-saturated undrained field shales from different overburden formations. Experiments were conducted using a low-frequency apparatus—a triaxial loading cell with the ability to measure dynamic stiffness at seismic frequencies (1–150 Hz) and ultrasonic velocities (500 kHz). Shale anisotropy was characterized by testing differently oriented core plugs. The results demonstrated that all the tested shales exhibited a dispersion of dynamic stiffness from seismic to ultrasonic frequencies. Young’s modulus dispersion for the tested shales ranged from nearly 30% to above 100%. Wave velocity dispersion was on the order of 10–20% for P-waves and 20–40% for S-waves. In static tests, the undrained rock stiffness gradually decreased with increasing stress amplitude. For one shale, the static undrained Young’s modulus was reduced by 50% when amplitude of the loading–unloading measurement cycle increased from 1 to 3 MPa. This finding is explained by non-elastic deformations that increase with the stress level. A method of zero-stress extrapolation of static stiffness was used to obtain the purely elastic response. The stiffness for the limit of zero stress change amplitude agreed well with the dynamic response at seismic frequency, providing a link between static and dynamic stiffness.

A simple effective medium approach for the bulk electrical and elastic properties of organic-rich shales

Shales are widespread in the Earth's crust, and organic-rich shales have become an important energy resource. Geophysical data are becoming increasingly important for characterizing shale reservoirs to find zones of good quality, typically characterized by high kerogen and low clay content. Away from well control, most geophysical characterization of shale reservoirs are based on the effects of kerogen on the elastic properties of the shale rock. However, both clay and kerogen act to reduce the stiffness of shale rocks, and their effects might be inseparable using seismic properties alone. A combination of the elastic and electrical properties of organic-rich shales might improve our ability to locate zones of good quality by decoupling the effects of kerogen and clay. Kerogen is considerably more resistive than clay and should, in theory, increase the bulk resistivity of the shale when present. The effects of shale composition on the joint elastic-electrical properties of shales can be explored using a combination of suitable well data and rock physics modeling. A comprehensive suite of well data could be used to observe trends, with a joint model aiding trend analysis. Effective medium models lend themselves well to estimating joint effective properties of a heterogeneous composite. This is because using the same approach for both the elastic and electrical properties would ensure an equivalent microstructure for both properties, as would be expected in practice. In this study, a joint effective medium model was calibrated and constrained using well data, achieving good correlation with elastic and electrical well log data from two wells. The results show that both kerogen and clay tend to reduce the stiffness of shales as expected, however; kerogen plays a significant role in increasing the bulk electrical resistivity of shales, whereas clay has the opposite effect. This joint elastic-electrical approach could potentially help discriminate kerogen-rich from clay-rich shales, in addition to constraining each individual property.

Emplacement and inflation of the Al-Halaq al Kabir lava flow field, central part of the Al Haruj Volcanic Province, Central Libya

Numerous of lava rise plateaus and tumuli developed in the medial and distal portions of the Al-Halaq al Kabir lava flow field during the last (Holocene) eruption in the central part of the Al Haruj Volcanic Province (AHVP). These inflation structures provide important data on the lava-emplacement mechanism in this part of the Al Haruj region where the widespread occurrence of tumuli and lava rise plateaus are good indicators of the mode of emplacement. We report the results of detailed measurements of the maximum and minimum diameters in plan-view of 551 lava-rise plateaus and 289 tumuli from the distal part of the Al-Halaq al Kabir lava field using ArcGIS and field observations. Tumuli and lava rise plateaus may be divided into subpopulations according to abrupt changes in the scaling exponents on log-log plots of their frequency versus diameter. Using the estimated stiffness (Young's modulus) of the basaltic rocks in the study area of 10–34 GPa, numerical and analytical results show that theoretical maximum tensile stresses in the inflated upper (solidified) crustal layers of the developing tumuli and lava rises at tens of mega-pascals (MPa). This theoretical stress is orders of magnitude higher than typical in-situ tensile strengths of rocks (0.5–9 MPa) and thus high enough to rupture the crustal layers of the lava rises and tumuli. The high tensile stresses are generated during crustal doming driven by a magmatic overpressure of only about 1 MPa. Our results partly explain the abundance of tension fractures at the surface of the Al-Halaq al Kabir lava flow field. Tumuli observed in the area are remarkably similar in morphology and aspect (height/width) ratios to the flow-lobe tumuli in Holocene lava flow fields in Iceland, suggesting an analogous mechanics of formation. There appears to be a coincidence between the age of an initial volcanism in the AHVP (7.9–5.3 Ma) and a local fauna and flora disappearance in the As-Sahabi area, NE Sirt Basin, during Messinian-Zanclean time (7–5 to 5 Ma). We speculate that the volcanism may have had a local negative environmental impact and contributed to the reported decline in the fauna and flora in the area.

Coupled Motion Characteristics of Offshore Wind Turbines during the Integrated Transportation Process

The offshore wind turbine (OWT) supported by bucket foundations can be installed in the integrated transportation process by a dedicated vessel. During the integrated transportation process, the wind turbine is considered as a coupling system with the transport ship, which is easily influenced by waves and storms. In view of the motion response and influential factors, the heave and rock stiffness of the entire floating system was proposed, and then the analytical dynamic motion model of the coupling system was established based on the movement mechanism of the traditional floating body in the wave in this paper. Subsequently, the rationality of the proposed motion model was verified based on the field observation data, with the maximum deviation of the motion responses less than 14%. Further, the influence on the heave and pitch motion of the coupling system considering different factors (vessel speed, wave height, wind speed and wave angle) and the factor sensitivity were discussed by the novel analytical model. It is explained that the heave and pitch motion responses rise with the increase of the wave height and wave angle. Simultaneously, the responses decrease as the vessel speed increases considering sailing along the waves. On the contrary, the responses show an obvious increasing trend with the increase of vessel speed in the case of the top wave sailing. In addition, it is also illustrated that the wave height has the greatest influence on the heave and pitch motion responses, followed by the vessel speed. The wave angle has the lowest sensitivity when the heave and pitch motion are far away from its harmonic resonance region.

Evolution of Local Mine Stiffness with Mining Process: Insight from Physical and Numerical Modeling

It is well known that local mine stiffness (LMS) plays a role in the violent failure of a pillar prone to strainburst. Very limited laboratory experiments have been carried out to simulate bursts caused by a gradual decrease in the local mine stiffness resulting from excavation. In this study, an experimental study is performed aiming to provide insight into the coal burst caused by a decrease in the LMS. Coal bursts were produced using a physical model in which excavation was performed stage by stage to produce a gradual decrease in the LMS. A numerical study was then carried out to study the evolution of the LMS with excavations. The effect of pillar strength, immediate roof stiffness, and excavation sequence was examined using the numerical model. The result suggests that the LMS at a given condition depends on a combination of various factors including pillar strength, pillar stiffness, host rock stiffness, etc. The interaction between these factors may play a key role in the LMS. It is also found that mining and excavation at the far field (e.g., mining at the adjacent panel) may not cause a great decrease in the LMS and thus is less likely to produce coal bursts at distant coal pillar. Great concern should be paid when mining and excavation activities are carried out at the current panel.

The role of thermal stress in near wellbore instabilities and its implications: a case study from the HTHP well, offshore East India

Drilling through a narrow pore pressure-fracture pressure window, especially under HTHP (high temperature-high pressure) conditions, is one of the most challenging and costly operations in the oil and gas industry. In this case study, drilling results and thermal stress modelling emphasized the role of thermal stress in several borehole failures encountered at shallow depths and severe formation breakdown incidents at deeper depths. The thermal stress from cooling effects delayed the shear failure conditions by reducing the maximum tangential stress of the formation around the wellbore, but induced formation breakdown as the minimum tangential stress exceeded the tensile strength of the formation. The result from this study shows both the rock stiffness (Young’s Modulus, Poisson Ratio) and differential temperatures (ΔT) have a critical control on thermal stress-related instabilities. Thermal stress-based wellbore stability modelling shows that temperature fluctuations in the dynamic drilling environment can induce a stress change at the rate of 300-500 psi/10°C. Our study results show that the range of thermal stress magnitudes in stiff rocks can vary between 300-4000 psi for a ΔT range of 20-60°C.

A Numerical Study to Assist Assessment of the Stability of Shallow Coal Mine Goafs

Coal mine goafs are distributed widely across many parts of the world and their stability is a major cause for concern, particularly when designing new infrastructure. To reduce risk, the coal mine goafs are often stabilized using cement grout and such operations can be very expensive and difficult to verify. This paper uses the finite element method to examine the relative influence of a number of key factors controlling the stability and surface deformations of shallow, horizontal coal mine goafs overlain by sedimentary rock. Representative ranges in the stiffness and strength characteristics of coal and rock are examined and each material is assumed to satisfy the Hoek–Brown failure criterion. The analyses show that, for a typical maximum coal extraction rate of 40%, the critical goaf span varies linearly with the depth of the coal seam (for the maximum depth investigated of 45 m) and increases with the competency of the overlying rock. A relationship combining the rock quality and the ratio of the critical goaf span to the depth of the coal seam is proposed to enable assessment of abandoned coal mines with marginal stability. This relationship is shown to be consistent with observations made in two coal mining case histories.

Grain assemblages and diagenesis in the Vaca Muerta Formation (Jurassic-Cretaceous), Neuquén Basin, Argentina

Mudrocks of the Vaca Muerta Formation (Tithonian-early Valanginian; Neuquén Basin, Argentina) contain grain assemblages of mixed extrabasinal and intrabasinal derivation. Mudrocks that contained, at deposition, relatively more abundant carbonate and siliceous biogenic debris display cementation by calcite and quartz that occluded pores and enhanced rock stiffness, perhaps acting to retard further pore loss by compaction. Another notable diagenetic feature in this mudrock succession is grain replacement that includes carbonate replacement of biosilica and feldspar and replacement of calcitic and aragonitic skeletal debris by calcite, dolomite, quartz, albite, chlorite, and pyrite. Organic matter is present as both detrital and diagenetic components that can in some cases be discriminated petrographically. The extensive chemical reorganization of Vaca Muerta mudrocks in diagenesis can be attributed to the high reactivity of the primary grain assemblage. Petrographic evidence suggests a chemical system in which silicate, carbonate, and organic matter components mutually participate in a complex set of reactions in which silicates provide acid buffering that controls the precipitation of carbonate. Despite the prominent role of chemical diagenesis in the post-depositional history of the Vaca Muerta, compaction is the major cause of porosity decline in these mudrocks.While the relatively small size of the sample set in this study (19 samples) does not permit lithologic heterogeneity to be assessed in the context of basin-scale stratigraphy, the observed variety of mudstones suggests that a stratigraphically representative sample set would need to be much larger than the one used here.

Dilatancy as a measure of fracturing development in the process of rock damage

Abstract Dilatancy understood as inelastic volume changes of rock under conditions of differential stress not only foreshadows brittle rock failure [1, 2, 3], preceding such phenomena as earthquakes or mining-induced rockbursts, but also defines the kinematics of rock deformation [4, 5]. This article shows that there is a quantitative relationship between the dilatancy occurring at different levels of rock load and the development of fracturing that accompanies the process of rock degradation. Based on the mechanical laboratory test results of Wustenzelleer fine-grained sandstone, the article presents analyses of plastic volume changes in rock samples and a certain measure of fracture development accompanying the process of their degradation. Thanks to the characteristics obtained through mechanical tests with unloading, the inelastic volumetric strain of the samples was established, and the scalar damage variable (CDM - continuum damage mechanics approach) was determined at various load levels. These results demonstrated the relationship between dilatancy and rock stiffness changes describing the development of fracturing. Three load intervals were determined, in which the nature of the analysed phenomena, i.e. dilatancy and damage describing the development of cracks, undergoes significant changes. The highest intensity of both phenomena was obtained in the post-critical load range, between the ultimate strength limit and the residual strength of the samples, in which rock samples undergo the process of degradation the most. Obtained dependencies allow the correlation to be taken into account in damage mechanics models describing the variable stiffness of rocks in the loading process.

Computation of effective elastic properties of clay from X-ray texture goniometry data

We have developed a new method for estimating the contribution of a pure clay fraction (i.e., devoid of organic matter) to the total effective rock stiffness. The method is based on published clay mineral stiffness data and on an original preferred clay mineral orientation data set obtained by X-ray texture goniometry on 56 samples of Kimmeridgian and Devonian age from two North American shale plays. We find that (1) large variability in preferred orientation of clay results in moderate variability in effective clay elastic anisotropy and (2) the effect of variations in the preferred orientation on effective rock properties is small compared with the effects of variations in clay abundance. As a result, a single clay elastic tensor is computed to be used in effective medium models. In addition, to account for various degrees of hydration, water is incorporated into the dry clay tensor through inclusion models. In situations in which isotropic approximations are necessary, we also provide apparent bulk and shear moduli for a hydrated clay fraction as a function of porosity and propagation angle.

Initiation of Tectonic Earthquakes during Underground Mining

The influence of underground mine workings arranged nearby faults on the initiation of large seismic event is considered. Numerical modeling proves that amount of underground mine workings affects actual stiffness of rocks and initiates dynamic movements accompanied by intensive seismic radiation. As rock mass quality worsens, the effective shear modulus drops. The calculations show that the effective shear modulus lowers by 20% for the stopes on the same level, decreases 1.5 times in case of the stopes arranged on two levels and nearly halves for three levels. Such reduction in the actual shear stiffness of rock mass may be critical in terms of initiation of dynamic shift along a fault.

Modeling of System Energy of Rock Under Harmonic Vibro-Impact

Hamiltonian function is proposed and the modeling of system energy of rock under harmonic vibro-impact is undertaken in this study. The modeling includes two aspects, namely, energy equation of rock system with no damping and the one with damping. Also, the results of numerical simulation are presented. Four main control parameters are considered, including natural frequency of rock, impact frequency, impact force, damping coefficient. It is confirmed that the system energy of rock will increase with the increase of natural frequency impact frequency and impact force. While impact force, damping coefficient and stiffness of rock will mainly decide the vibration amplitude of system energy.

Origin of quartz in the lower Cambrian Niutitang Formation in south Hubei Province, upper Yangtze platform

Abstract Brittle minerals, especially quartz, play an important role in the quality of shale reservoir. The precipitation of authigenic quartz caused a significant change in the rock stiffness and porosity. However, the formation mechanism of authigenic quartz in shale is still unclear. Lower Cambrian Niutitang shale from Guchengcun outcrop has been examined with respect to quartz cement. Four different types of quartz have been identified using SEM/CL/EDS. Type 1 occurs as angular to sub-rounded silt-size quartz grains with uniform luminescence, indicative of detrital origin. Type 2 appears as relatively large quartz aggregates approximately 30–150 μm in size, which is composed of small quartz grains (1–3 μm) and abundant in siliceous shale. The petrological evidence and consideration of potential diagenetic process suggest that Type 2 quartz was formed by local re-crystallization of biogenic silica in syndiagenesis and preferentially precipitated in the axial cavities of sponge spicules. Type 3 occurs as quartz overgrowths that are essentially non-luminescent at the periphery of high luminescence detrital quartz grains. This type quartz is present in most investigated samples. Type 4 represents microcrystalline quartz embedded in the illitized clay matrix as discrete, short chains or small clusters/nests and they are most commonly observed in argillaceous shale. The petrological evidence and CL responses indicate that both Type 3 and Type 4 quartz are derived from precipitation of silica released during the smectite to illite dissolution–precipitation reaction. S-I transition can be driven by microbial metabolic processes in shallow buried diagenesis or by heat and pressure in late diagenesis. Some of Type 4 quartz may be originated from low-temperature microbial pathway in shallow buried diagenesis, while Type 3 quartz and the remaining Type 4 quartz were formed in late diagenesis. Siliceous shale contains less abundant detrital quartz than argillaceous shale, indicating that siliceous shale was deposited in deeper water and far from terrigenous input than argillaceous shale. Although identifying the exact cause for diagenetic silica deposition in shale is not a trivial matter, its recognition is important for the reconstruction of the depositional history of shale sequences and understanding the role of diagenesis in shale reservoirs development, moreover, it also has great potential for enhancing prediction of mechanical rock properties in shales.

Predicting pillar burst by an explicit modelling of kinetic energy

Violent pillar failures known as pillar bursts are suspected to be a possible cause of large collapses in underground mines. A classical stability criterion for mine pillars, based on the relative stiffness of the host rock and the pillars during their post-peak unloading, was proposed by Starfield & Fairhurst (1968)6 and further demonstrated by Salamon (1970)7. An energy balance indicates that an excess kinetic energy is generated when this pillar stability criterion is violated. The present study focuses on demonstrating how an explicit numerical modelling method may be used to calculate and locate the damping of this kinetic energy during pillar failure, considering simple 2D geometries. Arguments in favour of the validation of the numerical results are provided by comparison to analytical calculations and to an empirical classification of rockbursts proposed by Ortlepp (1997)1. The good correlation between numerical, analytical and empirical approaches suggest that explicit numerical modelling of kinetic energy damping, following a procedure proposed in this paper, could be a useful tool for predicting zones submitted to a pillar burst hazard in underground mines and for consequently optimizing the mining method.

CO2 charged brines changed rock strength and stiffness at Crystal Geyser, Utah: Implications for leaking subsurface CO2 storage reservoirs

CO2 geological storage in saline aquifers results in acidification of resident brine. Chemical reactions between acidified brine and rock minerals lead to dissolution and precipitation of minerals at various time scales. Mineral dissolution and precipitation are often neglected in assessing the mechanical integrity of target storage formations, yet, changes in rock strength and deformational behavior can impact trapping mechanisms. This study shows the impact of exposure to CO2-charged brine on shear strength and stiffness of various outcrop rocks evaluated through triaxial testing. The tested rocks were exposed to CO2-charged brine over geological time at a naturally occurring near-surface seepage along the Little Grand Wash Fault and Salt Wash Grabens, which include the Crystal Geyser site near the town of Green River, Utah. Prior work suggests that this site provides a near-surface structural analog for possible fault-controlled CO2 leakage over time scales that exceed expected injection time scales (10–100 years). Results show mechanical alteration in various aspects: (1) CO2-charged brine alteration at near-surface conditions results in mineral dissolution/precipitation and reduction of shear strength and brittleness of Entrada sandstone and Summerville siltstone samples, and (2) carbonate precipitation in fractured Mancos shale leads to matrix stiffening and fracture mineralization resulting in overall stiffer and likely tighter shale. Additional discrete element simulations coupled with a bonded-particle-model confirm the role of cement bond size alteration as one of the main controls for rock chemo-mechanical alteration in sandstones. The chemo-mechanical alteration path that mimics cement dissolution (under stressed subsurface conditions) results in vertical compaction and lateral stress relaxation. Overall, results show that rock exposure to CO2-charged brine can impart distinct petrophysical and geomechanical changes according to rock lithology and location with respect to major CO2 conduits. While mineral dissolution in the storage rock may result in undesired reservoir strains and changes of stresses, mineral precipitation downstream from a leakage path can help seal potentially induced fractures.

Quantifying Rock Weakening Due to Decreasing Calcite Mineral Content by Numerical Simulations.

The quantification of changes in geomechanical properties due to chemical reactions is of paramount importance for geological subsurface utilisation, since mineral dissolution generally reduces rock stiffness. In the present study, the effective elastic moduli of two digital rock samples, the Fontainebleau and Bentheim sandstones, are numerically determined based on micro-CT images. Reduction in rock stiffness due to the dissolution of 10% calcite cement by volume out of the pore network is quantified for three synthetic spatial calcite distributions (coating, partial filling and random) using representative sub-cubes derived from the digital rock samples. Due to the reduced calcite content, bulk and shear moduli decrease by 34% and 38% in maximum, respectively. Total porosity is clearly the dominant parameter, while spatial calcite distribution has a minor impact, except for a randomly chosen cement distribution within the pore network. Moreover, applying an initial stiffness reduced by 47% for the calcite cement results only in a slightly weaker mechanical behaviour. Using the quantitative approach introduced here substantially improves the accuracy of predictions in elastic rock properties compared to general analytical methods, and further enables quantification of uncertainties related to spatial variations in porosity and mineral distribution.

Correlating mode-I fracture toughness and mechanical properties of heat-treated crystalline rocks

For the effect of thermal treatment on the mode-I fracture toughness (FT), three crystalline rocks (two basalts and one tonalite) were experimentally investigated. Semi-circular bend specimens of the rocks were prepared following the method suggested by the International Society for Rock Mechanics (ISRM) and were treated at various temperatures ranging from room temperature (25 °C) to 600 °C. Mode-I FT was correlated with tensile strength (TS), ultrasonic velocities, and Young's modulus (YM). Additionally, petrographic and X-ray diffraction analyses were carried out to find the chemical changes resulting from the heat treatment. Further, scanning electron microscopy (SEM) was conducted to observe the micro structural changes when subjected to high temperatures. These experiments demonstrate that heat treatment has a strong negative impact on the FT and mechanical properties of the rocks. From room temperature to 600 °C, mode-I FT values of massive basalt, giant plagioclase basalt, and tonalite were reduced by nearly 52%, 68%, and 64%, respectively. Also, at all temperature levels, FT and mechanical properties are found to be exponentially correlated. However, the exact nature of the relationship mainly depends on rock type. Besides, TS was found to be a better indicator of degradation degree than the mode-I FT. SEM images show that micro crack density and structural disintegration of the mineral grains increase with temperature. These physical changes confirm the observed reduction in the stiffness of heat-treated crystalline rocks.

Influence of subsurface injection on time‐lapse seismic: laboratory studies at seismic and ultrasonic frequencies

ABSTRACTSeismic monitoring of reservoir and overburden performance during subsurface CO2 storage plays a key role in ensuring efficiency and safety. Proper interpretation of monitoring data requires knowledge about the rock physical phenomena occurring in the subsurface formations. This work focuses on rock stiffness and elastic velocity changes of a shale overburden formation caused by both reservoir inflation induced stress changes and leakage of CO2 into the overburden. In laboratory experiments, Pierre shale I core plugs were loaded along the stress path representative for the in situ stress changes experienced by caprock during reservoir inflation. Tests were carried out in a triaxial compaction cell combining three measurement techniques and permitting for determination of (i) ultrasonic velocities, (ii) quasistatic rock deformations, and (iii) dynamic elastic stiffness at seismic frequencies within a single test, which allowed to quantify effects of seismic dispersion. In addition, fluid substitution effects connected with possible CO2 leakage into the caprock formation were modelled by the modified anisotropic Gassmann model. Results of this work indicate that (i) stress sensitivity of Pierre shale I is frequency dependent; (ii) reservoir inflation leads to the increase of the overburden Young's modulus and Poisson's ratio; (iii) in situ stress changes mostly affect the P‐wave velocities; (iv) small leakage of the CO2 into the overburden may lead to the velocity changes, which are comparable with one associated with geomechanical influence; (v) non‐elastic effects increase stress sensitivity of an acoustic waves; (iv) and both geomechanical and fluid substitution effects would create significant time shifts, which should be detectable by time‐lapse seismic.

Numerical investigation of the efficiency of emission reduction and heat extraction in a sedimentary geothermal reservoir: a case study of the Daming geothermal field in China.

The utilization of geothermal energy is clean and has great potential worldwide, and it is important to utilize geothermal energy in a sustainable manner. Mathematical modeling studies of geothermal reservoirs are important as they evaluate and quantify the complex multi-physical effects in geothermal reservoirs. However, previous modeling efforts lack the study focusing on the emission reduction efficiency and the deformation at geothermal wellbores caused by geothermal water extraction/circulation. Emission efficiency is rather relevant in geothermal projects introduced in areas characterized by elevated air pollution where the utilization of geothermal energy is as an alternative to burning fossil fuels. Deformation at geothermal wellbores is also relevant as significant deformation caused by water extraction can lead to geothermal wellbore instability and can consequently decrease the effectiveness of the heat extraction process in geothermal wells. In this study, the efficiency of emission reduction and heat extraction in a sedimentary geothermal reservoir in Daming County, China, are numerically investigated based on a coupled multi-physical model. Relationships between the efficiency of emission reduction and heat extraction, deformation at geothermal well locations, and geothermal field parameters including well spacing, heat production rate, re-injection temperature, rock stiffness, and geothermal well placement patterns are analyzed. Results show that, although large heat production rates and low re-injection temperatures can lead to decreased heat production in the last 8years of heat extraction, they still improve the overall heat production capacity and emission reduction capacity. Also, the emission reduction capacity is positively correlated with the heat production capacity. Deformation at geothermal wellbore locations is alleviated by smaller well spacing, lower heat production rates, and smaller numbers of injectors in the well pattern, and by placing wells at locations with higher rock stiffness. Compared with the reference case with coal burning for heating purposes, the yearly emission reduction capacity can reach 1 × 107kg by switching to the direct utilization of geothermal energy in Daming field.

Stiff cement, soft cement: Nonlinearity, arching effect, hysteresis, and irreversibility in CO2-well integrity and near-well geomechanics

During geologic CO2 storage, integrity of injection wells is of utmost importance. Tensile radial stresses at casing-cement and cement-rock interfaces caused by relatively cold CO2 flowing down the tubing may induce debonding and create microannuli. Microannuli represent potential leakage paths. Thermal stresses can be reduced by using softer cement (“flexible cement”). Numerical simulations show that benefits of soft cement are more pronounced in relatively hard (stiff) rocks. In a very soft rock, there might be as good as no effect of lowered cement stiffness on thermal stresses, while tensile strength of such cement might be severely reduced. Thus, to fully benefit from soft (flexible) cement in CO2-injection wells, such cement should be set against sufficiently stiff rock. Effect of rock stiffness on tensile radial stress build-up during cooling is stronger than that of cement stiffness. As a result, the benefits of carefully adjusting the cement stiffness might be offset by natural variation in the rock properties. Soft cement also reduces the stress build-up in the cement sheath caused by far-field in-situ stress variation during injection. The mechanism here is the arching effect in the near-well area: the rock effectively shields the cement sheath from in-situ stress changes. In order to fully exploit benefits of soft cement here, the rock again must be sufficiently stiff.