Geology topics

A.F. Moench

Publications and source records attributed to A.F. Moench.

10 recordsLinked to original sources

USGS2010

A numerical inversion of the Laplace transform solution to radial dispersion in a porous medium

A special form of the numerical inversion of the Laplace transform described by Stehfest (1970) is applied to the transformed solution of dispersion in a radial flow system in a porous medium. The inversion is extremely simple to use because the weighting coefficients depend only on the number of terms used in the computation and not upon the transform solution as required by most numerical inversion techniques. The result obtained by use of this approximate inversion of the radial dispersion problem reproduced the curves obtained previously by Hoopes and Harleman (1967) with a finite difference scheme.

Water Resources Research↗

USGS2010

Laboratory investigations of steam flow in a porous medium

Experiments were carried out in the laboratory to test a theory of transient flow of pure steam in a uniform porous medium. This theory is used in modeling pressure transient behavior in vapor dominated geothermal systems. Transient, superheated steam flow experiments were run by bringing a cylinder of porous material to a uniform initial pressure and then making a step increase in pressure at one end of the sample while monitoring the pressure transient breakthrough at the other end. It was found in experiments run at 100°, 125°, and 146°C that the time required for steam pressure transients to propagate through an unconsolidated material containing sand, silt, and clay was 10–25 times longer than predicted by conventional superheated steam flow theory. It is hypothesized that the delay in the steam pressure transient was caused by adsorption of steam in the porous sample. In order to account for steam adsorption, a sink term was included in the conservation of mass equation. In addition, energy transfer in the system has to be considered because latent heat is released when steam adsorption occurs, increasing the sample temperature by as much as 10°C. Finally, it was recognized that the steam pressure was a function of both the temperature and the amount of adsorption in the sample. This function was assumed to be an equilibrium adsorption isotherm, which was determined by experiment. By solving the modified mass and energy equations numerically, subject to the empirical adsorption isotherm relationship, excellent theoretical simulation of the experiments was achieved.

Water Resources Research↗

USGS2008

Analytical and numerical analyses of an unconfined aquifer test considering unsaturated zone characteristics

A 7-d, constant rate aquifer test conducted by University of Waterloo researchers at Canadian Forces Base Borden in Ontario, Canada, is useful for advancing understanding of fluid flow processes in response to pumping from an unconfined aquifer. Measured data include not only drawdown in the saturated zone but also volumetric soil moisture measured at various times and distances from the pumped well. Analytical analyses were conducted with the model published in 2001 by Moench and colleagues, which allows for gradual drainage but does not include unsaturated zone characteristics, and the model published in 2006 by Mathias and Butler, which assumes that moisture retention and relative hydraulic conductivity (RHC) in the unsaturated zone are exponential functions of pressure head. Parameters estimated with either model yield good matches between measured and simulated drawdowns in piezometers. Numerical analyses were conducted with two versions of VS2DT: one that uses traditional Brooks and Corey functional relations and one that uses a RHC function introduced in 2001 by Assouline that includes an additional parameter that accounts for soil structure and texture. The analytical model of Mathias and Butler and numerical model of VS2DT with the Assouline model both show that the RHC function must contain a fitting parameter that is different from that used in the moisture retention function. Results show the influence of field-scale heterogeneity and suggest that the RHC at the Borden site declines more rapidly with elevation above the top of the capillary fringe than would be expected if the parameters were to reflect local- or core-scale soil structure and texture.

Water Resources Research↗

USGS2005

Importance of the Vadose Zone in analyses of unconfined aquifer tests

Analytical models commonly used to interpret unconfined aquifer tests have been based on upper-boundary (water table) conditions that do not adequately address effects of time-varying drainage from the vadose zone. As a result, measured and simulated drawdown data may not agree and hydraulic parameters may be inaccurately estimated. A 72-hour aquifer test conducted in Cape Cod, Massachusetts, in a slightly heterogeneous, coarse-grained, glacial outwash deposit was found to be a good candidate for testing models with different upper-boundary conditions. In general, under the commonly invoked assumption of instantaneous drainage, measured and simulated draw-downs were found to agree with one another only at late time and early time. In the intermediate-time range, because of delayed drainage, measured drawdowns always exceeded simulated values, most noticeably in piezometers located near the water table. To reduce these discrepancies, an analytical model was developed that can fully account for time-varying drainage given that the aquifer is not strongly heterogeneous. The approach is flexible as the model, which makes use of empirical relations, does not constrain drainage to follow any particular functional relation. By this approach, measured and simulated drawdowns agree over the complete time range, and the estimated parameters are consistent with prior studies and with what is known about the aquifer geometry, stratigraphy, and composition. By properly accounting for vadose zone drainage, it was found that realistic estimates of all hydraulic parameters, including specific yield, could be obtained with or without the use of late-time data.

Ground Water↗

USGS2005

Flow to a well in a water-table aquifer: An improved laplace transform solution

An alternative Laplace transform solution for the problem, originally solved by Neuman, of constant discharge from a partially penetrating well in a water-table aquifer was obtained. The solution differs from existing solutions in that it is simpler in form and can be numerically inverted without the need for time-consuming numerical integration. The derivation invloves the use of the Laplace transform and a finite Fourier cosine series and avoids the Hankel transform used in prior derivations. The solution allows for water in the overlying unsaturated zone to be released either instantaneously in response to a declining water table as assumed by Neuman, or gradually as approximated by Boulton's convolution integral. Numerical evaluation yields results identical with results obtained by previously published methods with the advantage, under most well-aquifer configurations, of much reduced computation time.

Ground Water↗

USGS2003

Estimation of hectare-scale soil-moisture characteristics from aquifer-test data

Analysis of a 72-h, constant-rate aquifer test conducted in a coarse-grained and highly permeable, glacial outwash deposit on Cape Cod, Massachusetts revealed that drawdowns measured in 20 piezometers located at various depths below the water table and distances from the pumped well were significantly influenced by effects of drainage from the vadose zone . The influence was greatest in piezometers located close to the water table and diminished with increasing depth. The influence of the vadose zone was evident from a gap, in the intermediate-time zone, between measured drawdowns and drawdowns computed under the assumption that drainage from the vadose zone occurred instantaneously in response to a decline in the elevation of the water table. By means of an analytical model that was designed to account for time-varying drainage, simulated drawdowns could be closely fitted to measured drawdowns regardless of the piezometer locations. Because of the exceptional quality and quantity of the data and the relatively small aquifer heterogeneity, it was possible by inverse modeling to estimate all relevant aquifer parameters and a set of three empirical constants used in the upper-boundary condition to account for the dynamic drainage process. The empirical constants were used to define a one-dimensional (1D) drainage versus time curve that is assumed to be representative of the bulk material overlying the water table. The curve was inverted with a parameter estimation algorithm and a 1D numerical model for variably saturated flow to obtain soil-moisture retention curves and unsaturated hydraulic conductivity relationships defined by the Brooks and Corey equations. Direct analysis of the aquifer-test data using a parameter estimation algorithm and a two-dimensional, axisymmetric numerical model for variably saturated flow yielded similar soil-moisture characteristics. Results suggest that hectare-scale soil-moisture characteristics are different from core-scale predictions and even relatively small amounts of fine-grained material and heterogeneity can dominate the large-scale soil-moisture characteristics and aquifer response.

Journal of Hydrology↗

USGS2000

Aquifer response to stream-stage and recharge variations. II. Convolution method and applications

In this second of two papers, analytical step-response functions, developed in the companion paper for several cases of transient hydraulic interaction between a fully penetrating stream and a confined, leaky, or water-table aquifer, are used in the convolution integral to calculate aquifer heads, streambank seepage rates, and bank storage that occur in response to streamstage fluctuations and basinwide recharge or evapotranspiration. Two computer programs developed on the basis of these step-response functions and the convolution integral are applied to the analysis of hydraulic interaction of two alluvial stream-aquifer systems in the northeastern and central United States. These applications demonstrate the utility of the analytical functions and computer programs for estimating aquifer and streambank hydraulic properties, recharge rates, streambank seepage rates, and bank storage. Analysis of the water-table aquifer adjacent to the Blackstone River in Massachusetts suggests that the very shallow depth of water table and associated thin unsaturated zone at the site cause the aquifer to behave like a confined aquifer (negligible specific yield). This finding is consistent with previous studies that have shown that the effective specific yield of an unconfined aquifer approaches zero when the capillary fringe, where sediment pores are saturated by tension, extends to land surface. Under this condition, the aquifer's response is determined by elastic storage only. Estimates of horizontal and vertical hydraulic conductivity, specific yield, specific storage, and recharge for a water-table aquifer adjacent to the Cedar River in eastern Iowa, determined by the use of analytical methods, are in close agreement with those estimated by use of a more complex, multilayer numerical model of the aquifer. Streambank leakance of the semipervious streambank materials also was estimated for the site. The streambank-leakance parameter may be considered to be a general (or lumped) parameter that accounts not only for the resistance of flow at the river-aquifer boundary, but also for the effects of partial penetration of the river and other near-stream flow phenomena not included in the theoretical development of the step-response functions.Analytical step-response functions, developed for several cases of transient hydraulic interaction between a fully penetrating stream and a confined, leaky, or water-table aquifer, are used in the convolution integral to calculate aquifer heads, streambank seepage rates, and bank storage that occur in response to stream-stage fluctuations and basinwide recharge or evapotranspiration. Two computer programs developed on the basis of these step-response functions and the convolution integral are applied to the analysis of hydraulic interaction of two alluvial stream-aquifer systems. These applications demonstrate the utility of the analytical functions and computer programs for estimating aquifer and streambank seepage rates and bank storage.

Journal of Hydrology↗

USGS2000

Estimation of hydraulic parameters from an unconfined aquifer test conducted in a glacial outwash deposit, Cape Cod, Massachusetts

An aquifer test conducted in a sand and gravel, glacial outwash deposit on Cape Cod, Massachusetts was analyzed by means of a model for flow to a partially penetrating well in a homogeneous, anisotropic unconfined aquifer. The model is designed to account for all significant mechanisms expected to influence drawdown in observation piezometers and in the pumped well. In addition to the usual fluid-flow and storage processes, additional processes include effects of storage in the pumped well, storage in observation piezometers, effects of skin at the pumped-well screen, and effects of drainage from the zone above the water table. The aquifer was pumped at a rate of 320 gallons per minute for 72-hours and drawdown measurements were made in the pumped well and in 20 piezometers located at various distances from the pumped well and depths below the land surface. To facilitate the analysis, an automatic parameter estimation algorithm was used to obtain relevant unconfined aquifer parameters, including the saturated thickness and a set of empirical parameters that relate to gradual drainage from the unsaturated zone. Drainage from the unsaturated zone is treated in this paper as a finite series of exponential terms, each of which contains one empirical parameter that is to be determined. It was necessary to account for effects of gradual drainage from the unsaturated zone to obtain satisfactory agreement between measured and simulated drawdown, particularly in piezometers located near the water table. The commonly used assumption of instantaneous drainage from the unsaturated zone gives rise to large discrepancies between measured and predicted drawdown in the intermediate-time range and can result in inaccurate estimates of aquifer parameters when automatic parameter estimation procedures are used. The values of the estimated hydraulic parameters are consistent with estimates from prior studies and from what is known about the aquifer at the site. Effects of heterogeneity at the site were small as measured drawdowns in all piezometers and wells were very close to the simulated values for a homogeneous porous medium. The estimated values are: specific yield, 0.26; saturated thickness, 170 feet; horizontal hydraulic conductivity, 0.23 feet per minute; vertical hydraulic conductivity, 0.14 feet per minute; and specific storage, 1.3x10-5 per foot. It was found that drawdown in only a few piezometers strategically located at depth near the pumped well yielded parameter estimates close to the estimates obtained for the entire data set analyzed simultaneously. If the influence of gradual drainage from the unsaturated zone is not taken into account, specific yield is significantly underestimated even in these deep-seated piezometers. This helps to explain the low values of specific yield often reported for granular aquifers in the literature. If either the entire data set or only the drawdown in selected deep-seated piezometers was used, it was found unnecessary to conduct the test for the full 72-hours to obtain accurate estimates of the hydraulic parameters. For some piezometer groups, practically identical results would be obtained for an aquifer test conducted for only 8-hours. Drawdowns measured in the pumped well and piezometers at distant locations were diagnostic only of aquifer transmissivity.

Massachusetts↗

USGS1982

Laboratory investigations of the physics of steam flow in a porous medium

Experiments were carried out in the laboratory to test a theory of transient flow of pure steam in a uniform porous medium. This theory is used extensively in modeling pressure-transient behavior in vapor-dominated geothermal systems. Transient, superheated steam-flow experiments were run by bringing a cylinder of porous material to a uniform initial pressure, and then making a step increase in pressure at one end of the sample, while monitoring the pressure-transient breakthrough at the other end. It was found in experiments run at 100?, 125?, and 146?C that the time required for steam-pressure transients to propagate through an unconsolidated material containing sand, silt, and clay was 10 to 25 times longer than predicted by theory. It is hypothesized that the delay in the steam-pressure transient was caused by adsorption of steam in the porous sample. In order to account for steam adsorption, a sink term was included in the conservation of mass equation. In addition, energy transfer in the system has to be considered because latent heat is released when steam adsorption occurs, increasing the sample temperature by as much as 10?C. Finally, it was recognized that the steam pressure was a function of both the temperature and the amount of adsorption in the sample. For simplicity, this function was assumed to be in equilibrium adsorption isotherm, which was determined by experiment. By solving the modified mass and energy equations numerically, subject to the empirical adsorption isotherm relationship, excellent theoretical simulation of the experiments was achieved. The experiments support the hypothesis that adsorption of steam can strongly influence steam pressure-transient behavior in porous media; the results suggest that the modified steam-flow theory, which includes steam adsorption terms, should be used in modeling steam flow in vapor-dominated geothermal systems.

Open-File Report↗

USGS1978

Transient-pressure analysis in geothermal steam reservoirs with an immobile vaporizing liquid phase

A finite-difference model for the radial horizontal flow of steam through a porous medium is used to evaluate transient-pressure behavior in the presence of an immobile vaporizing or condensing liquid phase. Graphs of pressure drawdown and buildup in terms of dimensionless pressure and time are obtained for a well discharging steam at a constant mass flow rate for a specified time. The assumptions are made that the steam is in local thermal equilibrium with the reservoir rocks, that temperature changes are due only to phase change, and that effects of vapor-pressure lowering are negligible. Computations show that when a vaporizing liquid phase is present the pressure drawdown exhibits behavior similar to that observed in noncondensable gas reservoirs, but delayed in time. A theoretical analysis allows for the computation of this delay and demonstrates that it is independent of flow geometry. The response that occurs upon pressure buildup is markedly different from that in a noncondensable gas system. This result may provide a diagnostic tool for establishing the existence of phase-change phenomena within a reservoir. ?? 1979.

Geothermics↗