Coal Extraction Research Articles

Influence of plasma breakdown on pores and fractures in bituminous coal: A new characterization method of breakdown energy

Plasma technology has a potential application prospect in the field of coal seam permeability enhancement. However, the relationship between plasma breakdown energy and the improvement effect of coal pores and fractures is lack of in-depth research. This study proposed a novel method for characterizing the plasma breakdown energy, and three testing techniques, namely, particle size distribution, mercury intrusion porosimetry (MIP) and low-field nuclear magnetic resonance (NMR), were utilized to examine the pore and fracture distribution of coal samples obtained from Jiulong Mine under varying breakdown energy conditions. The influence between breakdown energy and pores and fractures development is revealed. The results show that: (1) The degree of coal sample fragmentation increases with the increase of plasma breakdown energy. (2) Different breakdown energy induced the development of different pore distribution patterns. At lower breakdown energy, an increase in the volume of macropores dominates. As the breakdown energy increases, there is a rapid increase in the volume of mesopores, a slight increase in minipores, and the least increase in micropores, indicating that plasma treatment primarily improves pores with diameters greater than 100 nm. The test results of the three techniques were mutually verified. (3) Compared with capacitance energy and voltage, the effective breakdown energy obtained by the integral method has a more significant linear relationship with the particle size distribution, total pore volume, and average pore diameter, indicating that the effective breakdown energy is more suitable for characterizing the crushing effect of plasma. During the plasma breakdown process, the expansion stress and thermal stress formed by the effective breakdown energy exceeded the local tensile strength of coal, leading to the generation and development of pores and fractures, which in turn led to the rupture of the coal body. The larger the breakdown energy, the larger the crushing circle formed around the ion channel, the finer the coal is crushed, and the more pore fractures are developed. These nascent pores and fractures provide channels for gas transport, which is extremely favorable for coal mine gas extraction. The research conclusions provide theoretical support for the application of plasma in fracturing and permeability enhancement in coal seams.

Biogenic Degradation of Lignite Coal from Pakistani Coal Mine and Extraction of Humic Acid through Pretreatment Strategies by Fungal Isolate

Biogenic Degradation of Lignite Coal from Pakistani Coal Mine and Extraction of Humic Acid through Pretreatment Strategies by Fungal Isolate

Biogenic Degradation of Lignite Coal from Pakistani Coal Mine and Extraction of Humic Acid through Pretreatment Strategies by Fungal Isolate

The utilization of white rot fungal strain for degradation of low rank coal from coal environments is considered to be the best choice for converting raw coal into different kinds of valuable by products. NF-1, a fungal strain was isolated from coal mine of Thar region of Pakistan. For enhancing the process of biodegradation, the indigenous fungal isolate was used in the study. The lignite (low rank) coal sample degradation initiated by NF-1 strain were undergone through optimization process and had shown considerable production of organics at 1.5% Glucose, 1% coal loading ratio and 7 days of incubation period. The FTIR analysis of untreated coal and treated coal after solubilization was performed in order to observe changes in structural pattern by NF-1 fungal isolate. NF1 has the ability to break down the aromatic side linkages and attacking the amine and carboxyl groups. Scanning electron microscopy (SEM) of the coal treated by NF-1 strain was analyzed to investigate the attachment and adherence of the fungal mycelium on the coal surface. At 200µm the NF-1 isolate hyphae has clearly entrapped the coal particles showing erosion and up to 50µm colonization and visible changes on the coal surface can be observed clearly. Moreover, the residual coal after fungal pretreatment was processed for extraction of humic acid as a byproduct for defining the effect of such biological pretreatments. The produced humic acid was analyzed on the basis of E4/E6 ratio and FTIR. The fungal pretreated humic acid has shown more improvement in E4/E6 ratio as well as presence of functional groups related to humic acid through FTIR. This explains that the isolate NF1 have ability to speed up the biodegradation process and shows an aptitude of producing valuable by products i.e. humic acid as an alternative fuel.

Influence of mining on vegetation in semi-arid areas of western China based on the coupling of above ground and below ground – A case study of Daliuta coalfield

Underground mining operations are known to result in extensive surface subsidence, introducing a multitude of disturbances to surface vegetation, with particularly severe environmental impacts in the fragile ecosystems of arid and semi-arid regions. This study focuses on the Daliuta mining area located in semi-arid zones, selecting four distinct areas for data analysis. Areas A, B, and C fall within the mining perimeter and have all been affected by mining-related disturbances. Following coal extraction, Areas A and B underwent artificial rehabilitation measures, including fracture infilling and sea buckthorn plantation; Area C was left in its natural state without any artificial interference. Area D, unaffected by mining activities, was designated as the control group. The research utilized 60 Landsat satellite images spanning from 1988 to 2022. Employing the Normalized Difference Vegetation Index (NDVI) and the Fractional Vegetation Cover (FVC), the study classified the experimental zone’s vegetation cover and degradation into six levels, ranging from low to high. By comparing the average vegetation cover over an extended period, changes across different vegetation cover levels, and the degree of vegetation degradation before and after mining, the study assessed the impact of underground mining on surface vegetation. The conclusions drawn are as follows: Mining operations caused significant damage to the vegetation in Areas A and B, yet artificial restoration measures notably improved the vegetation quality, with an overcompensation effect observed in Area A, suggesting the potential for ecological restoration efforts to create a vegetative environment that exceeds its original condition in the long term. Mining activities also induced continuous ecological adverse effects in Area C, but the natural regeneration process progressively restored the vegetation to pre-mining levels over time. Based on these findings, the study reveals the spatiotemporal patterns of vegetation damage and recovery across different mining periods and land reclamation stages. It proposes a restoration strategy for mine areas in semi-arid regions that prioritizes natural regeneration supported by artificial guidance. This work provides valuable insights and guidance for assessing the impact of underground coal mining on surface vegetation in semi-arid areas, as well as for the rehabilitation and ecological reconstruction of mine areas, emphasizing the necessity and urgency of conducting environmental assessments and implementing restoration measures.

Storytelling in precarious landscapes: Insights from a photovoice project in rural Appalachia

The impacts of the coronavirus pandemic in the small central Appalachian town of Rainelle, West Virginia cannot be understood separately from the broader human-environment relationships of this place. These relationships are grounded in landscapes that hold tremendous natural beauty alongside the scars of coal and timber extraction, and which now face increased risk of flooding because of the changing climate those extractive industries helped create. Too often, stories of this place lack attention to this complexity because they do not account for the perspective and knowledge of the people who live and make their livelihoods there. This paper details findings from a photovoice project in Rainelle that captured life in the small town in Fall 2020, through the lenses of nine town residents. Their photos tell a story not just of the height of the pandemic in rural America, but also of what happened when the pandemic intersected with ongoing efforts to recover from a devastating flood in 2016 and decades of socio-economic hardship before that. The results show that photovoice is an effective method by which political ecologists can facilitate the telling of stories by and with research participants, while also offering insights for how we might envision more just climate futures with people not typically part of conversations about climate change, such as those from the precarious landscapes of rural Appalachia.

Petrology and organic geochemistry of the Middle Devonian cutinitic liptobioliths from Luquan region, Yunnan Province, China

The majority of Middle Devonian coal samples from Wujing (WJ), Damo (DM), and Batang (BT) areas in the Luquan region of China have cutinite content exceeding 50%, classifying them as typical cutinitic liptobioliths. These coals are notable for their thinly-bedded texture, which allows them to split readily into leaf-like laminae. However, coals from these areas display distinct macroscopic, microscopic, and geochemical features. The split laminae from WJ and DM coals are black and ribbon-like, with those from WJ being notably longer and wider. In contrast, BT coal laminae are irregular, small fragments with golden or brown hues. Correspondingly, the cutinite in WJ coals is predominantly thick-walled, DM coals primarily contain a medium-walled type, and BT coals are characterized by a thin-walled type. Additionally, BT coals are rich in sporinite, with some classified as sporinite-rich durain or sporinitic liptobiolith. Abundant tetracyclic diterpenoids were detected in the maltene fraction of all the coal extracts. The concentration and composition of these diterpenoids are influenced by the content and type of cutinite present in the coals. The presence of tetracyclic diterpenoids, with beyerane, atisane and kaurane skeletons, had already evolved in early land plants. This implies that the precursors of these compounds were likely significant components of the cuticles of early land plants or, at least coexisted alongside plant cuticles. The spore assemblages in coals and the microscopic features of cutinite suggest that the coal-forming plants of the Luquan cutinitic liptobioliths were early land plants, predominantly herbaceous lycopsids, rhyniopsids, Orestovia and Spongiophyton. However, it is important to note that the specific types of these coal-forming plants may vary by areas. This variation leads to the distinctive macroscopic and microscopic characteristics observed in coals from different locations.Cutinitic liptobiolith appears to have been exclusive to the Middle Devonian period, especially during the Givetian. The emergence of this distinct coal type is likely due to the unique structure of Devonian land plants. Specifically, the combination of well-developed cuticles and less developed woody tissues in these early land plants might have played a key role in the formation of cutinitic liptobioliths.

Non-invasive geophysical methods for monitoring the shallow aquifer based on time-lapse electrical resistivity tomography, magnetic resonance sounding, and spontaneous potential methods

The Ningdong coalfield has played a pivotal role in advancing local economic development and meeting national energy. Nevertheless, mining operations have engendered ecological challenges encompassing subterranean water depletion, land desertification, and ground subsidence, primarily stemming from the disruption of coal seam roof strata. Consequently, the local ecosystem has incurred substantial harm. Water-preserved coal mining presently constitutes the pivotal technology in mitigating this problem. The primary challenge of this technique lies in identifying critical aquifer layers and understanding the heights of water-conducting fracture zones. To obtain a precise comprehension of the seepage patterns within the upper coal seam aquifer during mining, delineate the extent of water-conducting fracture zones, non-invasive geophysical techniques such as time-lapse electrical resistivity tomography (TL-ERT), magnetic resonance sounding (MRS), and spontaneous potential (SP) have been employed to monitor alterations within the shallow coalfield’s aquifer throughout the mining process in the Ningdong coalfield. By conducting meticulous examinations of fluctuations in resistivity, moisture content, and self-potential within the superjacent strata during coal seam extraction, the predominant underground water infiltration strata were ascertained, concurrently enabling the estimation of the development elevation of water-conducting fracture zones. This outcome furnishes a geophysical underpinning for endeavors concerning local water-preserved coal mining and ecological rehabilitation.

Gangue grouting filling in subsequent space of coal green mining: methodology and case study

Underground backfilling stands out as a crucial technological strategy for the eco-friendly and effective management of solid waste in mining operations. However, existing backfilling techniques have led to increased production processes at the working face, resulting in a reduction in coal extraction efficiency. Addressing the temporal and spatial interference between mine solid waste backfilling and coal mining is essential. To overcome this challenge, this study introduces a novel post-mining spatial gangue slurry backfilling method. Radar detection was employed to ascertain the typical characteristics of the subsequent space collapse roof shape. Stress monitoring and compaction experiments were conducted to establish the relationship between stress and the bulking coefficient of the overlying rock mass, identifying subsequent spatial void structure characteristics. The development of a CO2 mineralized coal-based solid waste filling material, utilizing conventional low-calcium fly ash under normal temperature and pressure conditions, was presented. This paper provides a comprehensive understanding of the post-mining spatial gangue slurry backfilling method, outlines the spatial layout approach for the corresponding system, and analyzes research challenges associated with gangue slurry backfilling materials and the technology of slurry injection borehole layout. The research aims to innovate an efficient underground disposal model for gangue, contributing to the refinement of the technical system for the comprehensive disposal and utilization of gangue.

Re-attaching to coal in a Climate Emergency: The case of the Whitehaven mine

This paper draws on the concept of ‘attachment’ to examine pro-coal sentiment in Whitehaven – an English town at the centre of global political controversy because of a plan to open a coal mine in the area. Drawing on fieldwork data, I show that pro-mine persuasions among some residents are underpinned by a process of ‘re-attaching’ to coal. I argue that the case of the Whitehaven mine is a warning about how fossil fuels might re-emerge as promissory objects in other parts of the world, even when a transition away from fossil fuels has been completed. Paradoxically, the very disorientations and deepening traumas that climate change is causing threaten to spur on the rise of fossil fuel (re-)attachments. The paper also examines how pro-coal discourses linked to wider vested interests are received in a context where coal exists as ‘afterlife’. Consequently, local actors construct narratives that legitimise new coal extraction by (re)articulating discourses of delay. My findings are thus a reminder of the need to guard against over-valorising ‘the grassroots’, arguably a risk in environmental justice scholarship. I conclude by calling for further empirical research on the way attachments to high-carbon objects are (re/de)composed, an urgent task given the need for rapid societal decarbonisation – one which has received very little attention to date.

Limitations of Upper Protective Layers as Pressure Relief Measures for Extra-Thick Coal Seam Mining: Insights from a Case Study

Upper protective layer (UPL) mining is extensively utilised as a pressure relief strategy to prevent outbursts and coal bursts. However, when the excavation height of the protected layer is substantial, the depressurisation efficacy of the protective layer may be diminished. This paper takes the Haishiwan coal mine in China as a case study and explores the stress evolution and influencing factors in the mining of extra-thick coal seam beneath the protective layer through theoretical analysis, numerical simulation, and field observation. The results indicate that increasing the excavation height of the coal seam will lead to the upward development of the collapse zone in the overburden of the goaf, with the “masonry beam” structure formed at a higher position by key strata blocks. The overburden above the masonry beam will be supported by the coal rock masse on both sides of the structure, leading to increased stress on the coal seam near the goaf and eliminating the depressurisation effect of the protective layer. Numerical simulation shows that factors such as faults, protective layers, interlayer spacing, and the height of coal seam excavation significantly affect the stress distribution in the protected layer. With the increase in interlayer spacing and the thickness of coal seam extraction, the stress reduction phenomenon of the UPL gradually decreases, especially with an abnormal stress concentration of the gob-side coal seam. Observations of Surface subsidence and the distribution of mining-induced seismic events corroborate the conclusions of theoretical analysis and numerical simulations. The results offer valuable guidance for the mining of extra-thick coal seams and the selection of the UPL.

Study on the Inhibition Characteristics of Coal Spontaneous Combustion by Silica Gel Foam.

The spontaneous combustion of residual coal in abandoned mining areas severely affects the safe and efficient extraction of coal, employee occupational health, and regional environmental ecology. A technical measure for preventing and controlling the spontaneous combustion of residual coal involves injecting antispontaneous combustion materials into abandoned areas. In this study, the composition, preparation, and mechanism of action of silica gel foam, a material used to suppress spontaneous combustion during coal mining, were investigated to improve the performance of materials designed to prevent spontaneous combustion in abandoned areas. The inhibitory efficiency improved, and the mechanical strength and stability of the foam liquid film increased upon adding modified antioxidants and nanosilica particles to the gel foam. Macro performance tests, microstructural characterization, and chemical inhibition mechanism analyses verified the efficacy of silica gel foam for suppressing spontaneous combustion. The air leakage resistance of the silica gel foam effectively increased the air leakage resistance of the coal samples at different pressures. New radicals formed during the spontaneous combustion of coal comprising different inhibitors, as indicated by the g-factor results of electron paramagnetic resonance (EPR) spectroscopy analysis; the formation of radicals initially decreased and then increased when the inhibitor material changed. The concentration of free radicals decreased markedly during the spontaneous combustion process of both raw and inhibited coal samples at low oxidation temperatures (∼60-100 °C), indicating a marked inhibitory effect.

Study on the Vertical Stability of Drilling Wellbore under Optimized Constraints

With the development of coal resource extraction and wellbore construction proceeding towards deeper depths, the stability of drilling wellbore structures has become increasingly severe, even posing a barrier to the use of drilling method technology in deep wellbore construction. To address this issue, this study raised an optimized constraints method involving pre-throwing cement slurry to the bottom before wellbore decent, altering bottom constraints. Firstly, the critical depth and instability criterion of this optimized method was derived by catastrophe theory. Subsequently, the role of single-factor and multi-factor sensitivity analyses on critical depth was discussed. The engineering effects of optimized constraint methods were contrasted and examined in several drilling projects. Finally, the characteristic values of real engineering were computed using numerical techniques and ABAQUS2020 software, and the efficacy of optimization approaches was examined and validated. The results revealed that the critical depth increased by 41.39 ± 5%. The influence factors described in order of the degree were the counterweight water height, the elastic modulus, the thickness of the wellbore, and the self-weight of the wellbore, sequentially. The conclusion on structural stability between the numerical calculation solution and theoretical calculation solution was completely the same. The optimized constraints method can effectively improve the stability of the wellbore structure.

An Emergency Of Black Diamonds

Abstract: This essay offers a literary history of the black diamond, pertinent to Appalachian coal. Coal extraction is more than anything a massive engorgement of aesthetics, a tool by which human life is reproduced and expanded in styles of domination. The black diamond shorthands mineral enslavement and the fungibility of Blackened flesh, the gendered and racialized compression of danger and attachment. What I’m trying to understand is how a stubborn politics of the remnant comes to signify in the black diamond, how remaining inside the idea of Appalachia seems like the right thing to do for contemporary “Appalachians,” even after that very identity was consummated in the kiln of extractive violence. What kind of love operates so strangely to turn material fungibility into an erotics of fugitivity, a desire to flee into the absolute stillness of stone?

Economic impacts of the coal extraction sector on the South Korean national economy: An input-output analysis

This article applies input-output (IO) techniques to appraising the role and economic impacts of the coal extraction sector (CES) in South Korea. IO tables for five years, namely 2000, 2005, 2010, 2015, and 2019, are used. Three IO models are utilized to deal with various economic impacts by treating the CES included in the endogenous sectors as an exogenous one. The impacts of a production or investment in the CES on inducing production, value-added, and wages in the national economy have been gradually increasing, which is interpreted as the result of the restructuring of the CES that the South Korean government has promoted over the past 20 years. However, the value-added coefficient, employment coefficient, and employment creation impact have gradually decreased, which seems to be due to the worsening profitability due to the gradual phasing out of the CES. Both the impact of production disruptions in the CES on other sectors’ production and the impact of a change in the output price of the CES on that of other sectors have been gradually decreasing. Thus, the government can continue to phase out the CES without creating the burden of production disruptions and inflationary pressure in the national economy.

The impact of employment restriction on the risk of an accident at work in the mining industry in Poland

Abstract The European Union's energy policy has necessitated a reduction in coal mining, with significant consequences for occupational safety within the industry. This study investigates the correlation between employment reduction and accident risk within Poland's mining sector during 2006-2020, a period marked by over a 40% decrease in coal extraction and a corresponding 30% decrease in mining employment. An escalation in the relative risk (RR) of accidents was observed, increasing from 1.28 to 2.33. More critically, the RR of fatal accidents rose from 2.54 to 8.22 by 2019. Analysis revealed a critical employment threshold: a fall in mining employment below 140,000 is associated with a marked increase in accident risk, particularly fatal accidents. A linear model was developed to suggest that a reduction in the RR of accidents to 0.7 is requisite to achieve a national average risk for fatal accidents (RR = 1). The findings advocate for targeted safety interventions and propose a preventive strategy model. The implications are vital for policymakers and industry stakeholders aiming to improve worker safety in response to employment changes within the mining sector.

Application of a Variable Weight Time Function Combined Model in Surface Subsidence Prediction in Goaf Area: A Case Study in China

To attain precise forecasts of surface displacements and deformations in goaf areas (a void or cavity that remains underground after the extraction of mineral resources) following coal extraction, this study based on the limitations of individual time function models, conducted a thorough analysis of how the parameters of the model impact subsidence curves. Parameter estimation was conducted using the trust-region reflective algorithm (TRF), and the time function models were identified. Then we utilized a combined model approach and introduced the sliding window mechanism to assign variable weights to the model. Based on this, the combined model was used for prediction, followed by the application of this composite prediction to engineering scenarios for the dynamic forecasting of surface movements and deformations. The results indicated that, in comparison with DE, GA, PSO algorithms, the TRF exhibited superior stability and convergence. The parameter models obtained using this method demonstrated a higher level of predictive accuracy. Moreover, the predictive precision of the variable-weight time function combined model surpassed that of corresponding individual time function models. When employing six different variable-weight combination prediction models for point C22, the Weibull-MMF model demonstrated the most favorable fitting performance, featuring a root mean square error (RMSE) of 32.98 mm, a mean absolute error (MAE) of 25.66 mm, a mean absolute percentage error (MAPE) of 7.67%; the correlation coefficient R2 reached 0.99937. These metrics consistently outperformed their respective individual time function models. Additionally, in the validation process of the combined model at point C16, the residuals were notably smaller than those of individual models. This reaffirmed the accuracy and reliability of the proposed variable-weight combined model. Given that the variable-weight combination model was an evolution from individual time function models, its applicability extends to a broader range, offering valuable guidance for the dynamic prediction of surface movement and deformation in mining areas.

Analysis of the spatiotemporal variation of groundwater storage in Ordos Basin based on GRACE gravity satellite data

Groundwater is the primary source for drinking, agriculture, irrigation, industrial, and municipal uses in Ordos Basin, a regional energy and heavy chemical industrial base in China. In recent decades, groundwater levels in the basin have declined due to climate change and anthropogenic activity. Analyses of the spatiotemporal variation of groundwater storage are crucial to regional sustainability. This study conducts the analysis utilizing GRACE gravity satellite data and GLDAS model data, employing methods that include the generalized three-cornered hat, Augmented Dickey-Fuller (ADF) test, and wavelet analysis to investigate the spatiotemporal variation of groundwater storage in the basin. The analysis results indicate that (1) before 2008, the climate had a significant influence on groundwater storage, with minimal impact from human activities, while after 2008, human activities have caused a noticeable decline in groundwater storage, particularly in the eastern region. (2) The eastern region of the basin experienced a decline in groundwater storage with a rate of −1.86 cm/yr, the middle region with a rate of −1.24 cm/yr, and the western region with a rate of −0.63 cm/yr. The extensive extraction of petroleum, natural gas, coal, and mineral resources in the basin has contributed to this pattern. (3) Human activities have altered the hydrological processes from precipitation infiltration, groundwater propagation, and groundwater distribution, leading to an increasingly complex groundwater system. (4) Human activities affect groundwater in the saturated zone more extensively than in the unsaturated zone. The research findings highlight that human activities are the main factor driving the variation in groundwater storage in the basin and provide crucial scientific evidence for protecting groundwater resources.

Living with coal in India: A temporal study of livelihood changes

This article asks what it is like for the rural poor to live with coal over time as mines expand and agriculture and forest-dependent ways of living inevitably become more restricted. Research on the expansion of open pit coal mining in India shows a widespread inability to appropriately compensate the rural poor for lost land and access to common property resources. Yet it is simultaneously clear that the growth of coal extraction over time ensures increased community dependence on mainly informal, coal-based livelihoods. What then happens over the long-term for people who live in and around the coalfields? Drawing on evidence from 2011 to 2022, this article explores longer term changes for mine-affected people next to major coal mines in Telangana state, India. Specifically, it examines a) the acquisition of forest and agricultural lands for the expanding mines, b) the operating mines and their environmental implications, but also improved job opportunities, and c) mine closure as an opportunity to rehabilitate the landscape and return the land for alternative community uses post mining. The results add to the understanding of the long-term changes that large-scale mining brings to rural communities, and the challenges to a just transition once coal mining inevitably comes to an end.

Experimental Investigations on Enhanced Coal Seam Methane Extraction by Injecting Gas: A Review

Experimental Investigations on Enhanced Coal Seam Methane Extraction by Injecting Gas: A Review

DETERMINATION BY NUMERICAL MODELING OF STRESS-STRAIN VARIATIONS RESULTING FROM GALLERY CROSS-SECTION CHANGES IN A LONGWALL TOP COAL CAVING PANEL

As a major pillar of global energy production, coal mining requires continuous advancements in efficiency to contribute to the broader goal of energy sustainability, all the while the shift towards more sustainable energy sources is underway. Mechanized excavation systems employed in underground coal mines, particularly within the longwall mining method, enable high-tonnage coal production. The Longwall Top Coal Caving (LTCC) method, one of the longwall mining techniques, has been developed for the effective extraction of coal from thick coal seams. However, as mining operations delve deeper, various complex issues, such as gallery cross-sectional variation, emerge. Gallery cross-sectional variation can increase the risk of collapse by affecting the stress distribution in the rock mass, posing a threat to worker safety. This study centers on the numerical modeling and analysis of gallery cross-sectional variation in the Ömerler underground mine, operated by the Turkish Coal Enterprises (TKI), West Lignite Enterprise (GLI). To achieve this objective, an extensive database was established through field and laboratory rock mechanics studies. This database was then utilized in the Fast Lagrangian Analysis of Continua 3D (FLAC3D) (v6.0) program to simulate the cross-sectional variations of the A6 panel in the Ömerler underground mine. The numerical simulation results provide valuable insights into the secondary stress-deformation changes associated with gallery cross-sectional variation.