Geology topics

Stephen E. Silliman

Publications and source records attributed to Stephen E. Silliman.

5 recordsLinked to original sources

USGS2010

Laboratory investigation of longitudinal dispersion in anisotropic porous media

In this study, laboratory experiments were used to investigate mechanisms that may cause anisotropy in the dispersion coefficient and to investigate the relation between anisotropy in hydraulic conductivity and anisotropy in longitudinal dispersion. Measurements of sodium chloride concentration (used as a tracer) were made at 105 in situ sampling locations in a new type of sand box designed to allow flow in either of two perpendicular directions. Two types of hydraulic anisotropy were examined. The first consisted of structured zones of increased hydraulic conductivity within a lower-conductivity medium. The second type involved low-conductivity platelike inclusions within a homogeneous, isotropic medium. The plates were aligned such that the tortuosity was increased only in one principal direction of permeability. Results using two examples of the first type of media showed that the apparent longitudinal dispersivities for flow parallel to the high-conductivity direction were greater than those perpendicular to this direction. Two examples of the second type of media produced smaller apparent longitudinal dispersivities for flow parallel to the high-conductivity direction. The results suggest that the mechanisms causing dispersive anisotropy can be related, conceptually, to the factors causing hydraulic anisotropy.

Water Resources Research↗

USGS2000

Estimating the theoretical semivariogram from finite numbers of measurements

We investigate from a theoretical basis the impacts of the number, location, and correlation among measurement points on the quality of an estimate of the semivariogram. The unbiased nature of the semivariogram estimator ŷ ( r ) is first established for a general random process Z( x ). The variance of ŷ Z ( r ) is then derived as a function of the sampling parameters (the number of measurements and their locations). In applying this function to the case of estimating the semivariograms of the transmissivity and the hydraulic head field, it is shown that the estimation error depends on the number of the data pairs, the correlation among the data pairs (which, in turn, are determined by the form of the underlying semivariogram γ( r )), the relative locations of the data pairs, and the separation distance at which the semivariogram is to be estimated. Thus design of an optimal sampling program for semivariogram estimation should include consideration of each of these factors. Further, the function derived for the variance of ŷ Z ( r ) is useful in determining the reliability of a semivariogram developed from a previously established sampling design.

Water Resources Research↗

USGS2000

Estimating the variance and integral scale of the transmissivity field using head residual increments

A modification of previously published solutions regarding the spatial variation of hydraulic heads is discussed whereby the semivariogram of increments of head residuals (termed head residual increments HRIs) are related to the variance and integral scale of the transmissivity field. A first‐order solution is developed for the case of a transmissivity field which is isotropic and whose second‐order behavior can be characterized by an exponential covariance structure. The estimates of the variance σ Y 2 and the integral scale λ of the log transmissivity field are then obtained via fitting a theoretical semivariogram for the HRI to its sample semivariogram. This approach is applied to head data sampled from a series of two‐dimensional, simulated aquifers with isotropic, exponential covariance structures and varying degrees of heterogeneity (σ Y 2 = 0.25, 0.5, 1.0, 2.0, and 5.0). The results show that this method provided reliable estimates for both λ and σ Y 2 in aquifers with the value of σ Y 2 up to 2.0, but the errors in those estimates were higher for σ Y 2 equal to 5.0. It is also demonstrated through numerical experiments and theoretical arguments that the head residual increments will provide a sample semivariogram with a lower variance than will the use of the head residuals without calculation of increments.

Water Resources Research↗

USGS1981

A transient laboratory method for determining the hydraulic properties of 'tight' rocks-I. Theory

Transient pulse testing has been employed increasingly in the laboratory to measure the hydraulic properties of rock samples with low permeability. Several investigators have proposed a mathematical model in terms of an initial-boundary value problem to describe fluid flow in a transient pulse test. However, the solution of this problem has not been available. In analyzing data from the transient pulse test, previous investigators have either employed analytical solutions that are derived with the use of additional, restrictive assumptions, or have resorted to numerical methods. In Part I of this paper, a general, analytical solution for the transient pulse test is presented. This solution is graphically illustrated by plots of dimensionless variables for several cases of interest. The solution is shown to contain, as limiting cases, the more restrictive analytical solutions that the previous investigators have derived. A method of computing both the permeability and specific storage of the test sample from experimental data will be presented in Part II.

International Journal of Rock Mechanics and Mining↗

USGS1981

A transient laboratory method for determining the hydraulic properties of 'tight' rocks-II. Application

In Part I a general analytical solution for the transient pulse test was presented. Part II presents a graphical method for analyzing data from a test to obtain the hydraulic properties of the sample. The general solution depends on both hydraulic conductivity and specific storage and, in theory, analysis of the data can provide values for both of these hydraulic properties. However, in practice, one of two limiting cases may apply in which case it is possible to calculate only hydraulic conductivity or the product of hydraulic conductivity times specific storage. In this paper we examine the conditions when both hydraulic parameters can be calculated. The analyses of data from two tests are presented. In Appendix I the general solution presented in Part I is compared with an earlier analysis, in which compressive storage in the sample is assumed negligible, and the error in calculated hydraulic conductivity due to this simplifying assumption is examined.

International Journal of Rock Mechanics and Mining↗