Allen M. Shapiro, Ph.D. (Former Employee)
Science and Products
Filter Total Items: 68
An exact solution of solute transport by one-dimensional random velocity fields
The problem of one-dimensional transport of passive solute by a random steady velocity field is investigated. This problem is representative of solute movement in porous media, for example, in vertical flow through a horizontally stratified formation of variable porosity with a constant flux at the soil surface. Relating moments of particle travel time and displacement, exact expressions for the a
Authors
V.D. Cvetkovic, G. Dagan, A.M. Shapiro
Comment on “Flow and tracer transport in a single fracture: A stochastic model and its relation to some field observations” by L. Moreno et al.
Moreno et al. [1988] (hereinafter referred to as MT) used a particle-tracking scheme to investigate the physics of solute movement in a variable-aperture planar fracture. The spatially heterogeneous fluid velocity was assumed to be the only mechanism of solute movement; local or pore scale dispersion and molecular diffusion were assumed to be negligible. The particle-tracking scheme used by MT con
Authors
Daniel J. Goode, Allen M. Shapiro
A comparison of two- and three-dimensional stochastic models of regional solute movement
Recent models of solute movement in porous media that are based on a stochastic description of the porous medium properties have been dedicated primarily to a three-dimensional interpretation of solute movement. In many practical problems, however, it is more convenient and consistent with measuring techniques to consider flow and solute transport as an areal, two-dimensional phenomenon. The physi
Authors
A.M. Shapiro, V.D. Cvetkovic
Solute advection in stratified formations
Advection‐dominated solute movement in stratified formations is investigated using a Lagrangian interpretation of particle motion. A probability density function (pdf) for particle position quantifies the expected depth‐integrated resident concentration. A pdf for particle arrival time quantifies the expected depth‐integrated rate of mass arrival, from which the flux‐averaged concentration can be
Authors
V.D. Cvetkovic, Allen M. Shapiro
Assessing the validity of the channel model of fracture aperture under field conditions
In recent investigations of fluid and solute movement in discrete fractures, spatial heterogeneity of the fracture aperture has been conceptualized as a series of noninterconnecting constant aperture flow paths, or channels. Two methods of estimating the distribution of the aperture sizes are presented using information from a single-hole pumping test and a radially converging tracer test. The fir
Authors
Allen M. Shapiro, James R. Nicholas
Interpretation of oscillatory water levels in observation wells during aquifer tests in fractured rock
Oscillatory water levels in observation wells have commonly been recorded at the beginning of aquifer tests in highly transmissive fractured formations. In this paper, oscillatory water levels are predicted by the equations coupling the fluid movement in the observation well and the fluid movement in the surrounding formation. The equivalent-porous medium and dual-porosity models of fractured rock
Authors
Allen M. Shapiro
Stochastic analysis of solute arrival time in heterogeneous porous media
Longitudinal advective solute movement in heterogeneous porous media is investigated by considering the solute arrival time at a plane perpendicular to the mean fluid velocity. The moments of the solute arrival time are defined in terms of the stochastic properties of a statistically anisotropic hydraulic conductivity field. The flux‐averaged concentration is specified by introducing the moments o
Authors
Allen M. Shapiro, V.D. Cvetkovic
Simulation of steady-state flow in three-dimensional fracture networks using the boundary-element method
An efficient method for simulating steady-state flow in three-dimensional fracture networks is formulated with the use of the boundary-element method. The host rock is considered to be impervious, and the fractures can be of any orientation and areal extent. The fractures are treated as surfaces where fluid movement is essentially two-dimensional. Fracture intersections are regarded as one-dimensi
Authors
A.M. Shapiro, J. Andersson
Non-USGS Publications**
Pinder, G. F. and Shapiro, A. 1982. Physics of Flow in Geothermal Systems, in Recent Trends in Hydrogeology. ed. T. N. Narasimhan. Geological Society of America, Boulder, CO. p. 25-30. https://doi.org/10.1130/SPE189-p25.
Pinder, G. F. and Shapiro, A. 1979. A new collocation method for the solution of the convection-dominated transport equation. Water Resources Research 15(5): 1177-1182. https://doi.org/10.1029/WR015i005p01177.
Pinder, G. F. and Shapiro, A. 1980. Reply to comment on "A new collocation method for the solution of the convection-dominated transport equation". Water Resources Research 16(6): 1137. https://doi.org/10.1029/WR016i006p01137.
Shapiro, A. and Pinder, G. F. 1981. Analysis of an upstream weighted collocation approximation to the transport equation. Journal of Computational Physics 39(1): 46-71. https://doi.org/10.1016/0021-9991(81)90136-4.
Andersson, J. and Shapiro, A. M. 1983. Stochastic analysis of one-dimensional steady state unsaturated flow: A Comparison of Monte Carlo and Perturbation Methods. Water Resources Research 19(1): 121-133. 10.1029/WR019i001p00121.
Shapiro, A. M. and Andersson, J. 1983. Steady state fluid response in fractured rock: A boundary element solution for a coupled, discrete fracture continuum model. Water Resources Research 19(4): 959-969. 10.1029/WR019i004p00959.
Andersson, J., Shapiro, A. M. and Bear, J. 1984. A Stochastic Model of a Fractured Rock Conditioned by Measured Information. Water Resources Research 20(1): 79-88. 10.1029/WR020i001p00079.
Bear, J. and Shapiro, A. M. 1984. On the shape of the non-steady interface intersecting discontinuities in permeability. Advances in Water Resources 7(3): 106-112. https://doi.org/10.1016/0309-1708(84)90037-X.
Bear, J., Shamir, U., Gamliel, A. and Shapiro, A. M. 1985. Motion of the seawater interface in a coastal aquifer by the method of successive steady states. Journal of Hydrology 76(1): 119-132. https://doi.org/10.1016/0022-1694(85)90093-9.
**Disclaimer: The views expressed in Non-USGS publications are those of the author and do not represent the views of the USGS, Department of the Interior, or the U.S. Government.
Science and Products
Filter Total Items: 68
An exact solution of solute transport by one-dimensional random velocity fields
The problem of one-dimensional transport of passive solute by a random steady velocity field is investigated. This problem is representative of solute movement in porous media, for example, in vertical flow through a horizontally stratified formation of variable porosity with a constant flux at the soil surface. Relating moments of particle travel time and displacement, exact expressions for the a
Authors
V.D. Cvetkovic, G. Dagan, A.M. Shapiro
Comment on “Flow and tracer transport in a single fracture: A stochastic model and its relation to some field observations” by L. Moreno et al.
Moreno et al. [1988] (hereinafter referred to as MT) used a particle-tracking scheme to investigate the physics of solute movement in a variable-aperture planar fracture. The spatially heterogeneous fluid velocity was assumed to be the only mechanism of solute movement; local or pore scale dispersion and molecular diffusion were assumed to be negligible. The particle-tracking scheme used by MT con
Authors
Daniel J. Goode, Allen M. Shapiro
A comparison of two- and three-dimensional stochastic models of regional solute movement
Recent models of solute movement in porous media that are based on a stochastic description of the porous medium properties have been dedicated primarily to a three-dimensional interpretation of solute movement. In many practical problems, however, it is more convenient and consistent with measuring techniques to consider flow and solute transport as an areal, two-dimensional phenomenon. The physi
Authors
A.M. Shapiro, V.D. Cvetkovic
Solute advection in stratified formations
Advection‐dominated solute movement in stratified formations is investigated using a Lagrangian interpretation of particle motion. A probability density function (pdf) for particle position quantifies the expected depth‐integrated resident concentration. A pdf for particle arrival time quantifies the expected depth‐integrated rate of mass arrival, from which the flux‐averaged concentration can be
Authors
V.D. Cvetkovic, Allen M. Shapiro
Assessing the validity of the channel model of fracture aperture under field conditions
In recent investigations of fluid and solute movement in discrete fractures, spatial heterogeneity of the fracture aperture has been conceptualized as a series of noninterconnecting constant aperture flow paths, or channels. Two methods of estimating the distribution of the aperture sizes are presented using information from a single-hole pumping test and a radially converging tracer test. The fir
Authors
Allen M. Shapiro, James R. Nicholas
Interpretation of oscillatory water levels in observation wells during aquifer tests in fractured rock
Oscillatory water levels in observation wells have commonly been recorded at the beginning of aquifer tests in highly transmissive fractured formations. In this paper, oscillatory water levels are predicted by the equations coupling the fluid movement in the observation well and the fluid movement in the surrounding formation. The equivalent-porous medium and dual-porosity models of fractured rock
Authors
Allen M. Shapiro
Stochastic analysis of solute arrival time in heterogeneous porous media
Longitudinal advective solute movement in heterogeneous porous media is investigated by considering the solute arrival time at a plane perpendicular to the mean fluid velocity. The moments of the solute arrival time are defined in terms of the stochastic properties of a statistically anisotropic hydraulic conductivity field. The flux‐averaged concentration is specified by introducing the moments o
Authors
Allen M. Shapiro, V.D. Cvetkovic
Simulation of steady-state flow in three-dimensional fracture networks using the boundary-element method
An efficient method for simulating steady-state flow in three-dimensional fracture networks is formulated with the use of the boundary-element method. The host rock is considered to be impervious, and the fractures can be of any orientation and areal extent. The fractures are treated as surfaces where fluid movement is essentially two-dimensional. Fracture intersections are regarded as one-dimensi
Authors
A.M. Shapiro, J. Andersson
Non-USGS Publications**
Pinder, G. F. and Shapiro, A. 1982. Physics of Flow in Geothermal Systems, in Recent Trends in Hydrogeology. ed. T. N. Narasimhan. Geological Society of America, Boulder, CO. p. 25-30. https://doi.org/10.1130/SPE189-p25.
Pinder, G. F. and Shapiro, A. 1979. A new collocation method for the solution of the convection-dominated transport equation. Water Resources Research 15(5): 1177-1182. https://doi.org/10.1029/WR015i005p01177.
Pinder, G. F. and Shapiro, A. 1980. Reply to comment on "A new collocation method for the solution of the convection-dominated transport equation". Water Resources Research 16(6): 1137. https://doi.org/10.1029/WR016i006p01137.
Shapiro, A. and Pinder, G. F. 1981. Analysis of an upstream weighted collocation approximation to the transport equation. Journal of Computational Physics 39(1): 46-71. https://doi.org/10.1016/0021-9991(81)90136-4.
Andersson, J. and Shapiro, A. M. 1983. Stochastic analysis of one-dimensional steady state unsaturated flow: A Comparison of Monte Carlo and Perturbation Methods. Water Resources Research 19(1): 121-133. 10.1029/WR019i001p00121.
Shapiro, A. M. and Andersson, J. 1983. Steady state fluid response in fractured rock: A boundary element solution for a coupled, discrete fracture continuum model. Water Resources Research 19(4): 959-969. 10.1029/WR019i004p00959.
Andersson, J., Shapiro, A. M. and Bear, J. 1984. A Stochastic Model of a Fractured Rock Conditioned by Measured Information. Water Resources Research 20(1): 79-88. 10.1029/WR020i001p00079.
Bear, J. and Shapiro, A. M. 1984. On the shape of the non-steady interface intersecting discontinuities in permeability. Advances in Water Resources 7(3): 106-112. https://doi.org/10.1016/0309-1708(84)90037-X.
Bear, J., Shamir, U., Gamliel, A. and Shapiro, A. M. 1985. Motion of the seawater interface in a coastal aquifer by the method of successive steady states. Journal of Hydrology 76(1): 119-132. https://doi.org/10.1016/0022-1694(85)90093-9.
**Disclaimer: The views expressed in Non-USGS publications are those of the author and do not represent the views of the USGS, Department of the Interior, or the U.S. Government.