Estimation of the Height of Complete Groundwater Drainage Above Mined Longwall Panels

The height of complete groundwater drainage above subsided longwall panels (referred to as H) at underground mines is determined using a data base of hydraulic head measurements made with multiple devices down the depth profile at each of a number of sites worldwide. H is shown to be relatively independent of most parameters except the geometry of the mined void and the overburden thickness. An empirical equation linking H to these parameters is developed using hydraulic head data, and confirmed using an independent data base of ground movement. H is shown to be the same as the height of the zone of major ground movement above a panel. H for special cases (above longwall chain pillars, above pillar extraction panels, and underneath significant water bodies) is invariably smaller than H above center panel for ordinary cases. A new caving model, from a groundwater perspective, is proposed for continuously sheared longwall panels at ordinary locations. It removes complexity and reduces the uncertainty in estimating H. The derived equation for H applies to a variety of strata types.     

Estimation of the Change in Storage Capacity above Mined Longwall Panels

Accurate estimation of the change in groundwater storage capacity (S) above mined longwall panels is vital for analysis of postmining void water level recovery in coal mines, and assessment of water quality impacts. At present, there is no generalized representation of the spatial distribution of changes in S around a panel. Current estimates are generally bulk averages with high uncertainty, precluding calculation of groundwater velocities in various parts of the subsurface. In this work, a recently published hydrogeological conceptual model of longwall caving is used in conjunction with observations from borehole extensometers, goaf height measurements, and pumping/drawdown records for mine pools to develop a subsurface spatial distribution of changes in S following longwall caving, with reduced uncertainty in their magnitudes. The assumption of saturation in the disturbed zone proved critical for obtaining accurate results and in reconciling widely varying published estimates of S. Results indicate that the goaf and collapsed zones each absorb over 30% of the mined volume, and about 20% is absorbed by the surface subsidence trough. The increase in S in the collapsed zone is inversely proportional to the amount of surface subsidence. The conceptual model is updated with these results to present the spatial distribution of S after caving. The results allow calculation of water velocities in various zones, and may provide greater accuracy in estimation of water level rebound and water quality processes. Most of the S participating in groundwater flows is provided by defects rather than the matrix.     

The Alabama,U.S.A., seismic event and strata collapse of May 7, 1986

On May 7, 1986, the residents of Tuscaloosa, Alabama, felt a seismic event of local magnitude 3.6 that occurred at the same time as a rock burst and roof collapse in an active longwall coal mine. Visual inspection of the seismograms reveals a deficiency in energy at frequencies above 20 Hz compared to tectonic earthquakes or surface blasts. The predominance of energy below 5 Hz may explain reports of body wave magnitudes (m _b ) greater than 4.2. Also, 1.0 Hz surface waves were more strongly excited than body waves and may explain local felt effects more typically associated with greater epicentral distances. All recorded first motions were dilatational. The concentration of stations in the northern hemisphere allows reverse motion on an east-trending near-vertical plane or strike-slip motion on northwest or southeast trending planes. The reverse focal mechanism is preferred, because the area of roof collapse and the area of active longwall mining are located between two east-striking loose vertical fracture zones. The characteristics of the seismic event suggest that it might have been sudden shear failure resulting from accumulated strain energy in overlying strata behind an active longwall. Although an alternate interpretation of the focal mechanism as an implosion or shear failure in the strata above previously mined out areas is also allowed by the first motion data, this alternate intepretation is not supported by geological data.     

Evaluation of the post-mining groundwater regime following longwall mining

A methodology for calculating strains that accompany mining is used to estimate the post-mining modification of the hydraulic conductivity field and the change in the regional and local subsurface water system. The techniques yield reasonable agreement with recorded changes in water levels for reasonable and defensible choices of material parameters in validation exercises at an instrumented longwall site. Water level changes recorded above the twin panel longwall configuration are complex and varied. However, they may be explained through consideration of the mining-modified conductivity field alone. Changes in hydraulic conductivity are independently corroborated from the results of in situ permeability tests, conducted before and after mining, that confirm the overall influence of mining-induced strains. These resulting patterns of hydraulic conductivity enhancement enable direct explanation of observed water level changes. © 1997 John Wiley & Sons, Ltd.     

Post Processing of Zone Budgets to Generate Improved Groundwater Influx Estimates Associated with Longwall Mining

Impacts of underground longwall mining on groundwater systems are commonly assessed using numerical groundwater flow models that are capable of forecasting changes to strata pore pressures and rates of groundwater seepage over the mine life. Groundwater ingress to a mining operation is typically estimated using zone budgets to isolate relevant parts of a model that represent specific mining areas, and to aggregate flows at nominated times within specific model stress periods. These rates can be easily misinterpreted if simplistic averaging of daily flow budgets is adopted. Such misinterpretation has significant implications for design of underground dewatering systems for a new mine site or it may lead to model calibration errors where measured mine water seepage rates are used as a primary calibration constraint. Improved estimates of groundwater ingress can be made by generating a cumulative flow history from zone budget data, then differentiating the cumulative flow history using a low order polynomial convolved through the data set.     

煤矿冲击地压的微地震监测研究

为了研究煤矿冲击地压与岩层在三维空间破裂之间的关系,进而探索依据岩层破裂规律预测和预报冲击地压的可能性,文中采用自行研制的防爆型微地震定位监测（MS）系统,基于定位原理,监测了山东华丰煤矿冲击地压煤层（四层煤）及其解放层（六层煤）开采过程中的岩层破裂过程和二次应力场分布变化的过程,得到了如下结论：冲击地压的发生与岩层破裂密切相关,四层煤下顺槽处于六层煤顶板破裂区的外边缘时,正处于高应力区内,在此处掘进容易引发冲击地压,必须将六层煤下顺槽位置向实体煤侧移动20 m以上,或将四层煤下顺槽位置内移20 m以上,才能消除四层煤的冲击地压;六层煤和四层煤开采时,工作面前方断层活化的距离分别为250 m和350 m左右,根据这一距离,及时对断层带进行卸压处理,可以消除由断层带引发的冲击地压;监测显示了工作面周围岩层的三维破裂形态和范围,为矿井确定防水煤柱的高度提供了可靠的依据;监测证明了厚层砾岩的破裂、断层活化、采场附近关键层的破裂是引起冲击地压的主要原因,证明了所研制的硬件和定位软件具有较高的精度和实用性,可以在煤矿和边坡、隧道等领域应用.     

The usefulness of outcrop analogue air permeameter measurements for analyzing aquifer heterogeneity: quantifying outcrop hydraulic conductivity and its spatial variability

Saturated hydraulic conductivity (K) is one of the most important parameters determining groundwater flow and contaminant transport in both unsaturated and saturated porous media. Although several well‐established laboratory methods exist for determining K, in situ measurements of this parameter remain very complex and scale dependent. Often, the limited accessibility of subsurface sediments for sampling means an additional impediment to our ability to quantify subsurface K heterogeneity. One potential solution is the use of outcrops as analogues for subsurface sediments. This paper investigates the use of air permeameter measurements on outcrops of unconsolidated sediments to quantify K and its spatial heterogeneity on a broad range of sediment types. The Neogene aquifer in northern Belgium is used as a case study for this purpose. To characterize the variability in K, 511 small‐scale air permeability measurements were performed on outcrop sediments representative over five of the aquifer's lithostratigraphic units. From these measurements, outcrop‐scale equivalent K tensors were calculated using numerical upscaling techniques. Validation of the air permeameter‐based K values by comparison with laboratory constant head K measurements reveals a correlation of 0.93. Overall, the results indicate that hand‐held air permeameters are very efficient and accurate tools to characterize saturated K, as well as its small‐scale variability and anisotropy on a broad range of unconsolidated sediments. The studied outcrops further provided a qualitative understanding of aquifer hydrostratigraphy and quantitative estimates about K variability at the centimetre‐scale to metre‐scale. Copyright © 2013 John Wiley & Sons, Ltd.     

Infiltration and runoff generation processes in fire‐affected soils

Post‐wildfire runoff was investigated by combining field measurements and modelling of infiltration into fire‐affected soils to predict time‐to‐start of runoff and peak runoff rate at the plot scale (1 m²). Time series of soil‐water content, rainfall and runoff were measured on a hillslope burned by the 2010 Fourmile Canyon Fire west of Boulder, Colorado during cyclonic and convective rainstorms in the spring and summer of 2011. Some of the field measurements and measured soil physical properties were used to calibrate a one‐dimensional post‐wildfire numerical model, which was then used as a ‘virtual instrument’ to provide estimates of the saturated hydraulic conductivity and high‐resolution (1 mm) estimates of the soil‐water profile and water fluxes within the unsaturated zone. Field and model estimates of the wetting‐front depth indicated that post‐wildfire infiltration was on average confined to shallow depths less than 30 mm. Model estimates of the effective saturated hydraulic conductivity, K_s, near the soil surface ranged from 0.1 to 5.2 mm h^?1. Because of the relatively small values of K_s, the time‐to‐start of runoff (measured from the start of rainfall), t_p, was found to depend only on the initial soil‐water saturation deficit (predicted by the model) and a measured characteristic of the rainfall profile (referred to as the average rainfall acceleration, equal to the initial rate of change in rainfall intensity). An analytical model was developed from the combined results and explained 92–97% of the variance of t_p, and the numerical infiltration model explained 74–91% of the variance of the peak runoff rates. These results are from one burned site, but they strongly suggest that t_p in fire‐affected soils (which often have low values of K_s) is probably controlled more by the storm profile and the initial soil‐water saturation deficit than by soil hydraulic properties. Published 2013. This article is a U.S. Government work and is in the public domain in the USA.     

Scale‐dependency of hydraulic conductivity: an example from Thorne Moor,a raised mire in South Yorkshire,UK

The hydraulic conductivity (K) of many low permeability materials is strongly scale‐dependent. In raised mires and other types of peat deposit the effects of features such as abandoned infilled ditches, root holes and localized woody material, cause K to be heterogeneous and scale‐dependent. Despite this, field measurements are routinely made using auger hole (slug) tests at the scale of only a few tens of centimetres. Such measurements are locally valid, but where the regional subsurface movement of water through peat bogs is simulated using groundwater models, typically at the scale of hundreds of metres, they give rise to a systematic underestimate of flows and an overprediction of water table elevations. Until now, techniques to obtain values at a scale sufficiently large to include the effects of localized features of higher permeability have not been applied routinely. Research at Thorne Moor, a large raised mire, demonstrates that the K of peat varies over several orders of magnitude when measured at different scales, using a variety of techniques. Laboratory and auger hole tests cannot be relied upon to provide results that represent the hydraulic conductivity of large expanses of peatland. This has significant implications for the management and long‐term restoration of peatlands where both regional and local control of water levels is crucial. For groundwater models to be used successfully to plan such schemes, it is essential to apply the K values relevant to the scale of the simulation. This paper describes and tests novel techniques, using ditches, for the derivation of K at large scales which overcome many of the problems that have been identified with conventional techniques and are capable of producing estimates that are appropriate to the application of physically based regional flow models. Copyright © 2004 John Wiley & Sons, Ltd.     

Hydromechanical Heterogeneities of a Mature Fault Zone: Impacts on Fluid Flow

In this paper, fluid flow is examined for a mature strike‐slip fault zone with anisotropic permeability and internal heterogeneity. The hydraulic properties of the fault zone were first characterized in situ by microgeophysical (V_P and σ_c) and rock‐quality measurements (Q‐value) performed along a 50‐m long profile perpendicular to the fault zone. Then, the local hydrogeological context of the fault was modified to conduct a water‐injection test. The resulting fluid pressures and flow rates through the different fault‐zone compartments were then analyzed with a two‐phase fluid‐flow numerical simulation. Fault hydraulic properties estimated from the injection test signals were compared to the properties estimated from the multiscale geological approach. We found that (1) the microgeophysical measurements that we made yield valuable information on the porosity and the specific storage coefficient within the fault zone and (2) the Q‐value method highlights significant contrasts in permeability. Fault hydrodynamic behavior can be modeled by a permeability tensor rotation across the fault zone and by a storativity increase. The permeability tensor rotation is linked to the modification of the preexisting fracture properties and to the development of new fractures during the faulting process, whereas the storativity increase results from the development of micro‐ and macrofractures that lower the fault‐zone stiffness and allows an increased extension of the pore space within the fault damage zone. Finally, heterogeneities internal to the fault zones create complex patterns of fluid flow that reflect the connections of paths with contrasting properties.     

Hydraulic Tomography: 3D Hydraulic Conductivity,Fracture Network,and Connectivity in Mudstone

We present the first demonstration of hydraulic tomography (HT) to estimate the three-dimensional (3D) hydraulic conductivity (K) distribution of a fractured aquifer at high-resolution field scale (HRFS), including the fracture network and connectivity through it. We invert drawdown data collected from packer-isolated borehole intervals during 42 pumping tests in a wellfield at the former Naval Air Warfare Center, West Trenton, New Jersey, in the Newark Basin. Five additional tests were reserved for a quality check of HT results. We used an equivalent porous medium forward model and geostatistical inversion to estimate 3D K at high resolution (K blocks <1 m³), using no strict assumptions about K variability or fracture statistics. The resulting 3D K estimate ranges from approximately 0.1 (highest-K fractures) to approximately 10⁻¹³ m/s (unfractured mudstone). Important estimated features include: (1) a highly fractured zone (HFZ) consisting of a sequence of high-K bedding-plane fractures; (2) a low-K zone that disrupts the HFZ; (3) several secondary fractures of limited extent; and (4) regions of very low-K rock matrix. The 3D K estimate explains complex drawdown behavior observed in the field. Drawdown tracing and particle tracking simulations reveal a 3D fracture network within the estimated K distribution, and connectivity routes through the network. Model fit is best in the shallower part of the wellfield, with high density of observations and tests. The capabilities of HT demonstrated for 3D fractured aquifer characterization at HRFS may support improved in situ remediation for contaminant source zones, and applications in mining, repository assessment, or geotechnical engineering.     

NMR Logging to Estimate Hydraulic Conductivity in Unconsolidated Aquifers

Nuclear magnetic resonance (NMR) logging provides a new means of estimating the hydraulic conductivity (K) of unconsolidated aquifers. The estimation of K from the measured NMR parameters can be performed using the Schlumberger‐Doll Research (SDR) equation, which is based on the Kozeny–Carman equation and initially developed for obtaining permeability from NMR logging in petroleum reservoirs. The SDR equation includes empirically determined constants. Decades of research for petroleum applications have resulted in standard values for these constants that can provide accurate estimates of permeability in consolidated formations. The question we asked: Can standard values for the constants be defined for hydrogeologic applications that would yield accurate estimates of K in unconsolidated aquifers? Working at 10 locations at three field sites in Kansas and Washington, USA, we acquired NMR and K data using direct‐push methods over a 10‐ to 20‐m depth interval in the shallow subsurface. Analysis of pairs of NMR and K data revealed that we could dramatically improve K estimates by replacing the standard petroleum constants with new constants, optimal for estimating K in the unconsolidated materials at the field sites. Most significant was the finding that there was little change in the SDR constants between sites. This suggests that we can define a new set of constants that can be used to obtain high resolution, cost‐effective estimates of K from NMR logging in unconsolidated aquifers. This significant result has the potential to change dramatically the approach to determining K for hydrogeologic applications.     

Spatio‐temporal distribution of near‐surface and root zone soil moisture at the catchment scale

Soil moisture is highly variable both spatially and temporally. It is widely recognized that improving the knowledge and understanding of soil moisture and the processes underpinning its spatial and temporal distribution is critical. This paper addresses the relationship between near‐surface and root zone soil moisture, the way in which they vary spatially and temporally, and the effect of sampling design for determining catchment scale soil moisture dynamics. In this study, catchment scale near‐surface (0–50 mm) and root zone (0–300 mm) soil moisture were monitored over a four‐week period. Measurements of near‐surface soil moisture were recorded at various resolutions, and near‐surface and root zone soil moisture data were also monitored continuously within a network of recording sensors. Catchment average near‐surface soil moisture derived from detailed spatial measurements and continuous observations at fixed points were found to be significantly correlated (r² = 0·96; P = 0·0063; n = 4). Root zone soil moisture was also found to be highly correlated with catchment average near‐surface, continuously monitored (r² = 0·81; P < 0·0001; n = 26) and with detailed spatial measurements of near‐surface soil moisture (r² = 0·84). The weaker relationship observed between near‐surface and root zone soil moisture is considered to be caused by the different responses to rainfall and the different factors controlling soil moisture for the soil depths of 0–50 mm and 0–300 mm. Aspect is considered to be the main factor influencing the spatial and temporal distribution of near‐surface soil moisture, while topography and soil type are considered important for root zone soil moisture. The ability of a limited number of monitoring stations to provide accurate estimates of catchment scale average soil moisture for both near‐surface and root zone is thus demonstrated, as opposed to high resolution spatial measurements. Similarly, the use of near‐surface soil moisture measurements to obtain a reliable estimate of deeper soil moisture levels at the small catchment scale was demonstrated. Copyright © 2007 John Wiley & Sons, Ltd.     

Sensitivity of soil parameters in unsaturated zone modelling and the relation between effective,laboratory and in situ estimates

Simulation of soil moisture content requires effective soil hydraulic parameters that are valid at the modelling scale. This study investigates how these parameters can be estimated by inverse modelling using soil moisture measurements at 25 locations at three different depths (at the surface, at 30 and 60 cm depth) on an 80 by 20 m hillslope. The study presents two global sensitivity analyses to investigate the sensitivity in simulated soil moisture content of the different hydraulic parameters used in a one‐dimensional unsaturated zone model based on Richards' equation. For estimation of the effective parameters the shuffled complex evolution algorithm is applied. These estimated parameters are compared to their measured laboratory and in situ equivalents. Soil hydraulic functions were estimated in the laboratory on 100 cm³ undisturbed soil cores collected at 115 locations situated in two horizons in three profile pits along the hillslope. Furthermore, in situ field saturated hydraulic conductivity was estimated at 120 locations using single‐ring pressure infiltrometer measurements. The sensitivity analysis of 13 soil physical parameters (saturated hydraulic conductivity (K_s), saturated moisture content (θ_s), residual moisture content (θ_r), inverse of the air‐entry value (α), van Genuchten shape parameter (n), Averjanov shape parameter (N) for both horizons, and depth (d) from surface to B horizon) in a two‐layer single column model showed that the parameter N is the least sensitive parameter. K_s of both horizons, θ_s of the A horizon and d were found to be the most sensitive parameters. Distributions over all locations of the effective parameters and the distributions of the estimated soil physical parameters from the undisturbed soil samples and the single‐ring pressure infiltrometer estimates were found significantly different at a 5% level for all parameters except for α of the A horizon and K_s and θ_s of the B horizon. Different reasons are discussed to explain these large differences. Copyright © 2004 John Wiley & Sons, Ltd.     

Bootstrap Calibration and Uncertainty Estimation of Downhole NMR Hydraulic Conductivity Estimates in an Unconsolidated Aquifer

Characterization of hydraulic conductivity (K) in aquifers is critical for evaluation, management, and remediation of groundwater resources. While estimates of K have been traditionally obtained using hydraulic tests over discrete intervals in wells, geophysical measurements are emerging as an alternative way to estimate this parameter. Nuclear magnetic resonance (NMR) logging, a technology once largely applied to characterization of deep consolidated rock petroleum reservoirs, is beginning to see use in near‐surface unconsolidated aquifers. Using a well‐known rock physics relationship—the Schlumberger Doll Research (SDR) equation—K and porosity can be estimated from NMR water content and relaxation time. Calibration of SDR parameters is necessary for this transformation because NMR relaxation properties are, in part, a function of magnetic mineralization and pore space geometry, which are locally variable quantities. Here, we present a statistically based method for calibrating SDR parameters that establishes a range for the estimated parameters and simultaneously estimates the uncertainty of the resulting K values. We used co‐located logging NMR and direct K measurements in an unconsolidated fluvial aquifer in Lawrence, Kansas, USA to demonstrate that K can be estimated using logging NMR to a similar level of uncertainty as with traditional direct hydraulic measurements in unconsolidated sediments under field conditions. Results of this study provide a benchmark for future calibrations of NMR to obtain K in unconsolidated sediments and suggest a method for evaluating uncertainty in both K and SDR parameter values.     

Changes in Entrapped Gas Content and Hydraulic Conductivity with Pressure

Water table fluctuations continuously introduce entrapped air bubbles into the otherwise saturated capillary fringe and groundwater zone, which reduces the effective (quasi‐saturated) hydraulic conductivity, K_quasi, thus impacting groundwater flow, aquifer recharge and solute and contaminant transport. These entrapped gases will be susceptible to compression or expansion with changes in water pressure, as would be expected with water table (and barometric pressure) fluctuations. Here we undertake laboratory experiments using sand‐packed columns to quantify the effect of water table changes of up to 250 cm on the entrapped gas content and the quasi‐saturated hydraulic conductivity, and discuss our ability to account for these mechanisms in ground water models. Initial entrapped air contents ranged between 0.080 and 0.158, with a corresponding K_quasi ranging between 2 and 6 times lower compared to the K_s value. The application of 250 cm of water pressure caused an 18% to 26% reduction in the entrapped air content, resulting in an increase in K_quasi by 1.16 to 1.57 times compared to its initial (0 cm water pressure) value. The change in entrapped air content measured at pressure step intervals of 50 cm, was essentially linear, and could be modeled according to the ideal gas law. Meanwhile, the changes in K_quasi with compression–expansion of the bubbles because of pressure changes could be adequately captured with several current hydraulic conductivity models.     

Radiolaria‐dated Lower Permian clastic‐rock sequence in the Fukuji area of the Hida‐gaien terrane,central Japan,and its inter‐terrane correlation across Southwest Japan

The stratigraphy and radiolarian age of the Mizuyagadani Formation in the Fukuji area of the Hida‐gaien terrane, central Japan, represent those of Lower Permian clastic‐rock sequences of the Paleozoic non‐accretionary‐wedge terranes of Southwest Japan that formed in island arc–forearc/back‐arc basin settings. The Mizuyagadani Formation consists of calcareous clastic rocks, felsic tuff, tuffaceous sandstone, tuffaceous mudstone, sandstone, mudstone, conglomerate, and lenticular limestone. Two distinctive radiolarian faunas that are newly reported from the Lower Member correspond to the zonal faunas of the Pseudoalbaillella u‐forma morphotype I assemblage zone to the Pseudoalbaillella lomentaria range zone (Asselian to Sakmarian) and the Albaillella sinuata range zone (Kungurian). In spite of a previous interpretation that the Mizuyagadani Formation is of late Middle Permian age, it consists of Asselian to Kungurian tuffaceous clastic strata in its lower part and is conformably overlain by the Middle Permian Sorayama Formation. An inter‐terrane correlation of the Mizuyagadani Formation with Lower Permian tuffaceous clastic strata in the Kurosegawa terrane and the Nagato tectonic zone of Southwest Japan indicates the presence of an extensive Early Permian magmatic arc(s) that involved almost all of the Paleozoic non‐accretionary‐wedge terranes in Japan. These new biostratigraphic data provide the key to understanding the original relationships among highly disrupted Paleozoic terranes in Japan and northeast Asia.     

Estimation of evapotranspiration and its components from an apple orchard in northwest China using sap flow and water balance methods

Field experiments were conducted to investigate the effects of leaf area index and soil moisture content on evapotranspiration and its components within an apple orchard in northwest China for 2 years. Evapotranspiration in the non‐rainfall period was estimated using two approaches: the soil water balance method based on tube‐type time‐domain reflection measurements, and sap flow plus micro‐lysimeter methods. The two methods were in good agreement, with differences usually less than 10%. The components of evapotranspiration varied with canopy development. During spring and autumn, soil evaporation was dominating as result of low leaf area index. In summer, plant transpiration became significant, with an average transpiration to evapotranspiration ratio of 0·87. The crop coefficient K_c showed a strong linear dependence on leaf area index. The water stress coefficient K_s was around 1·0 when soil moisture was above 23% and started to decrease linearly after that. This study demonstrates that prediction of evapotranspiration in apple orchards can be made using the Food and Agriculture Organization's crop coefficient method from commonly available meteorological data in the area. Copyright © 2006 John Wiley & Sons, Ltd.     

Application of 1D paleo‐fluvial process modelling at a basin scale to augment sparse borehole data: example of a Permian formation in the Galilee Basin,Australia

The heterogeneous hydraulic conductivity (K) in water‐bearing formations controls subsurface flow and solute transport processes. Geostatistical techniques are often employed to characterize the K distribution in space based on the correlation between K measurements. However, at the basin scale, there are often insufficient measurements for inferring the spatial correlation. This is a widespread problem that we address in this study using the example of the Betts Creek Beds (BCB) in the Galilee Basin, Australia. To address the lack of data, we use a 1D stochastic fluvial process‐based model (SFPM) to quantify the total sediment thickness, Z( x ), and the sandstone proportion over the total thickness, P_s( x ), in the BCB. The semivariograms of Z( x ) and P_s( x ) are then extracted and used in sequential Gaussian simulation to construct the 2D spatial distribution of Z( x ) and P_s( x ). P_s( x ) can be converted to a K distribution based on classical averaging methods. The results demonstrate that the combination of SFPM and geostatistical simulation allows for the evaluation of upscaled K distribution with a limited number of K measurements. Copyright © 2015 John Wiley & Sons, Ltd.