Calculating Groundwater Response Times for Flow in Heterogeneous Porous Media

Predicting the amount of time required for a transient groundwater response to take place is a practical question that is of interest in many situations. This time scale is often called the response time. In the groundwater hydrology literature, there are two main methods used to calculate the response time: (1) both the transient and steady‐state groundwater flow equations are solved, and the response time is taken to be amount of time required for the transient solution to approach the steady solution within some tolerance; and (2) simple scaling arguments are adopted. Certain limitations restrict both of these approaches. In this study, we outline a third method, based on the theory of mean action time. We derive the governing boundary value problem for both the mean and variance of action time for confined flow in two‐dimensional heterogeneous porous media. Importantly, we show that these boundary value problems can be solved using widely available software. Applying these methods to a test case reveals the advantages of the theory of mean action time relative to standard methods.     

An Experimenting Field Approach for the Numerical Solution of Multiphase Flow in Porous Media

In this work, we apply the experimenting pressure field technique to the problem of the flow of two or more immiscible phases in porous media. In this technique, a set of predefined pressure fields are introduced to the governing partial differential equations. This implies that the velocity vector field and the divergence at each cell of the solution mesh can be determined. However, since none of these fields is the true pressure field entailed by the boundary conditions and/or the source terms, the divergence at each cell will not be the correct one. Rather the residue which is the difference between the true divergence and the calculated one is obtained. These fields are designed such that these residuals are used to construct the matrix of coefficients of the pressure equation and the right‐hand side. The experimenting pressure fields are generated in the solver routine and are fed to the different routines, which may be called physics routines, which return to the solver the elements of the matrix of coefficients. Therefore, this methodology separates the solver routines from the physics routines and therefore results in simpler, easy to construct, maintain, and update algorithms.     

Thermodynamically Constrained Averaging Theory Approach for Modeling Flow and Transport Phenomena in Porous Medium Systems: 5. Single-Fluid-Phase Transport

This work is the fifth in a series of papers on the thermodynamically constrained averaging theory (TCAT) approach for modeling flow and transport phenomena in multiscale porous medium systems. The general TCAT framework and the mathematical foundation presented in previous works are used to develop models that describe species transport and single-fluid-phase flow through a porous medium system in varying physical regimes. Classical irreversible thermodynamics formulations for species in fluids, solids, and interfaces are developed. Two different approaches are presented, one that makes use of a momentum equation for each entity along with constitutive relations for species diffusion and dispersion, and a second approach that makes use of a momentum equation for each species in an entity. The alternative models are developed by relying upon different approaches to constrain an entropy inequality using mass, momentum, and energy conservation equations. The resultant constrained entropy inequality is simplified and used to guide the development of closed models. Specific instances of dilute and non-dilute systems are examined and compared to alternative formulation approaches.     

利用三维非均匀不稳定渗流场的数值解求解垂直井与水平井的联合开采

用差分的方法给出了三维非均匀不稳定渗流方程的离散方程组,将配斯曼（Peaceman）方程拓展成能够被用于同时求解垂直井与水平井联合开采问题的形式,利用迭代解法求解差分方程和配斯曼方程所组成的方程组,并以实际层状不均匀介质为例计算了其压强的空间分布。     

Coupling of a Column System with ICP‐MS for the Characterisation of Colloid‐mediated Metal(loid) Transport in Porous Media

In this work a coupling method for the characterisation of colloid‐mediated transport of the metal(loid) species in porous media was developed. For this transport experiments quartz sand was used as column packing material and the synthetic three‐layer clay mineral laponite as model colloid. The determination of colloids was conducted by means of UV detection. The quantification of the metal(loid) ions was carried out in two different ways: (1) The fractions collected at the column outlet were analysed with an inductively coupled plasma mass spectrometer (ICP‐MS) (offline measurements); (2) the column system was directly coupled with ICP‐MS (online measurements). In the column experiments the influence of laponite colloids on the transport of Cu, Pb, Zn, Pt and As species was investigated. In the offline experiments as a consequence of dilution during sample preparation no metal(loid) species at the column outlet could be found. Unlike this the breakthrough of all metal(loid)s could be detected under the same experimental column conditions in the coupling experiments. This coupling technique offers the online detection of the metal species and colloidal particles with high resolution even at low concentrations and without any time‐consuming preparation. The coupling experiments have shown that the laponite particles accelerate the transport of the cationic metals. For anionic metal(loid) species no influence of laponite on their transport behaviour was found.