Approximate solution for solute transport during spherical-flow push-pull tests

A new solution to transient single-well push-pull test with low-permeability non-Darcian leakage effects

An accurate solute transport model is critical to the interpretation of single-well push-pull (SWPP) test. Previous studies of SWPP test generally consider solitary aquifer that is confined by impermeable layers. Also, existing solutions for solute transport in aquifer-aquitard systems only consider the injection phase and over-simplify the flow field by assuming uniformly distributed velocity in the aquitard. In this study, we developed a numerical model with Dirichlet boundary condition for SWPP test affected by leakage described by a low-permeability non-Darcian expression involving a threshold pressure gradient (I₀). Our SWPP test model considered transient flow in multi-phases, which include injection, chase, rest and extraction phases. Finite-difference scheme was adopted to solve the models of flow and solute transport. The results indicate that an increasing hydraulic diffusivity leads to a greater peak value of breakthrough curve (BTC) while a medium with larger grain size results in less estimation error when using steady-state flow model to interpret the transient SWPP test. Additionally, A greater I₀ makes the solute stored in aquitard more difficult to be extracted out due to dispersion dominance, which results in higher BTC values. For the purpose of application, a lumped dimensionless index called the non-Darcian index (NDI) was proposed to quantify the overestimation degree by neglecting leakage, and the underestimation degree by accounting for Darcian leakage, when interpreting the SWPP test with low-permeability non-Darcian leakage. The long-term slope of breakthrough curve coupled with the NDI can be employed to determine the cases in which the low-permeability non-Darcian leakage should be considered.

A Straightforward Random Walk Model for Fast Push-Pull Tracer Test Evaluation

In this article, we present a straightforward random walk model for fast evaluation of push-pull tracer tests. By developing an adaptive algorithm, we overcome the problem of manually defining how many particles have to be used to simulate the transport problem. Beside this, we validate the random walk model by evaluating a push-pull tracer test with drift phase and confirm the results with MT3DMS. The random walk model took less than 1% of computational time of MT3DMS, thus allowing a remarkable faster evaluation of push-pull tracer tests.

Identification of small-scale low and high permeability layers using single well forced-gradient tracer tests: fluorescent dye imaging and modelling at the laboratory-scale

Heterogeneity in aquifer permeability, which creates paths of varying mass flux and spatially complex contaminant plumes, can complicate the interpretation of contaminant fate and transport in groundwater. Identifying the location of high mass flux paths is critical for the reliable estimation of solute transport parameters and design of groundwater remediation schemes. Dipole flow tracer tests (DFTTs) and push-pull tests (PPTs) are single well forced-gradient tests which have been used at field-scale to estimate aquifer hydraulic and transport properties. In this study, the potential for PPTs and DFTTs to resolve the location of layered high- and low-permeability layers in granular porous media was investigated with a pseudo 2-D bench-scale aquifer model. Finite element fate and transport modelling was also undertaken to identify appropriate set-ups for in situ tests to determine the type, magnitude, location and extent of such layered permeability contrasts at the field-scale. The characteristics of flow patterns created during experiments were evaluated using fluorescent dye imaging and compared with the breakthrough behaviour of an inorganic conservative tracer. The experimental results show that tracer breakthrough during PPTs is not sensitive to minor permeability contrasts for conditions where there is no hydraulic gradient. In contrast, DFTTs are sensitive to the type and location of permeability contrasts in the host media and could potentially be used to establish the presence and location of high or low mass flux paths. Numerical modelling shows that the tracer peak breakthrough time and concentration in a DFTT is sensitive to the magnitude of the permeability contrast (defined as the permeability of the layer over the permeability of the bulk media) between values of 0.01-20. DFTTs are shown to be more sensitive to deducing variations in the contrast, location and size of aquifer layered permeability contrasts when a shorter central packer is used. However, larger packer sizes are more likely to be practical for field-scale applications, with fewer tests required to characterise a given aquifer section. The sensitivity of DFTTs to identify layered permeability contrasts was not affected by test flow rate.

A Mathematical Model for the Analysis of the Pressure Transient Response of Fluid Flow in Fractal Reservoir

This study uses similar construction method of solution (SCMS) to solve mathematical models of fluid spherical flow in a fractal reservoir which can avoid the complicated mathematical deduction. The models are presented in three kinds of outer boundary conditions (infinite, constant pressure, and closed). The influence of wellbore storage effect, skin factor, and variable flow rate production is also involved in the inner boundary conditions. The analytical solutions are constructed in the Laplace space and presented in a pattern with one continued fraction—the similar structure of solution. The pattern can bring convenience to well test analysis programming. The mathematical beauty of fractal is that the infinite complexity is formed with relatively simple equations. So the relation of reservoir parameters (wellbore storage effect, the skin factor, fractal dimension, and conductivity index), the formation pressure, and the wellbore pressure can be learnt easily. Type curves of the wellbore pressure and pressure derivative are plotted and analyzed in real domain using the Stehfest numerical invention algorithm. The SCMS and type curves can interpret intuitively transient pressure response of fractal spherical flow reservoir. The results obtained in this study have both theoretical and practical significance in evaluating fluid flow in such a fractal reservoir and embody the convenience of the SCMS.

Fluorescent dye imaging of the volume sampled by single well forced-gradient tracer tests evaluated in a laboratory-scale aquifer physical model

This study presents a new method to visualise forced-gradient tracer tests in 2-D using a laboratory-scale aquifer physical model. Experiments were designed to investigate the volume of aquifer sampled in vertical dipole flow tracer tests (DFTT) and push-pull tests (PPT), using a miniature monitoring well and straddle packer arrangement equipped with solute injection and recovery chambers. These tests have previously been used to estimate bulk aquifer hydraulic and transport properties for the evaluation of natural attenuation and other remediation approaches. Experiments were performed in a silica glass bead-filled box, using a fluorescent tracer (fluorescein) to deduce conservative solute transport paths. Digital images of fluorescein transport were captured under ultraviolet light and processed to analyse tracer plume geometry and obtain point-concentration breakthrough histories. Inorganic anion mixtures were also used to obtain conventional tracer breakthrough histories. Concentration data from the conservative tracer breakthrough curves was compared with the digital images and a well characterised numerical model. The results show that the peak tracer breakthrough response in dipole flow tracer tests samples a zone of aquifer close to the well screen, while the sampling volume of push-pull tests is limited by the length of the straddle packers used. The effective sampling volume of these single well forced-gradient tests in isotropic conditions can be estimated with simple equations. The experimental approach offers the opportunity to evaluate under controlled conditions the theoretical basis, design and performance of DFTTs and PPTs in porous media in relation to measured flow and transport properties.

Transient divergent flow and transport in an infinite anisotropic porous formation

When seeking to predict plume geometry resulting from fluid injection through partially penetrating wells, it is common to assume a steady-state spherically diverging flow field. In reality, the flow field is transient. The steady-flow assumption is likely to cause overestimation of injection plume radius since the accommodation of fluid by increases in porosity and fluid density is ignored. In this paper, a transient solution is developed, resulting in a nonlinear ordinary differential equation expressing plume radius as a function of time. It is shown that the problem can be fully described by one type curve. A critical time, t(c), is identified at which the percentage error of the steady-state flow solution compared to the fully dynamic problem is less than 1%. Only for large injection rates and low permeabilities, does t(c) become greater than 1 h. Nevertheless, an improved approximate solution is obtained by a simple linearization procedure. The critical time, t(c) for the new approximate solution is 0.3% of that required for the steady-state flow solution.

Modeling axisymmetric flow and transport

Unmodified versions of common computer programs such as MODFLOW, MT3DMS, and SEAWAT that use Cartesian geometry can accurately simulate axially symmetric ground water flow and solute transport. Axisymmetric flow and transport are simulated by adjusting several input parameters to account for the increase in flow area with radial distance from the injection or extraction well. Logarithmic weighting of interblock transmissivity, a standard option in MODFLOW, can be used for axisymmetric models to represent the linear change in hydraulic conductance within a single finite-difference cell. Results from three test problems (ground water extraction, an aquifer push-pull test, and upconing of saline water into an extraction well) show good agreement with analytical solutions or with results from other numerical models designed specifically to simulate the axisymmetric geometry. Axisymmetric models are not commonly used but can offer an efficient alternative to full three-dimensional models, provided the assumption of axial symmetry can be justified. For the upconing problem, the axisymmetric model was more than 1000 times faster than an equivalent three-dimensional model. Computational gains with the axisymmetric models may be useful for quickly determining appropriate levels of grid resolution for three-dimensional models and for estimating aquifer parameters from field tests.

Transport of methane and noble gases during gas push-pull tests in dry porous media

A field method called the gas push-pull test (GPPT) was previously developed and tested for the in situ quantification of aerobic methane (CH4) oxidation by soil microorganisms. The GPPT consists of an injection followed by extraction of reactant and tracer gases into and out of the soil. Quantification of microbial activities from GPPTs requires insight in the transport of reactant and tracer gases under diverse field conditions. We investigated how the transport of differenttracer gases (He, Ne, and Ar) compares to that of the reactant gas CH4 during GPPTs conducted in a well-defined, dry porous media that mimicked an open system. Transport of gaseous components during GPPT is mainly driven by advection resulting from injection and extraction and diffusion driven by concentration gradients. Regardless of the advective component (selected injection/ extraction, flow rates 0.2-0.8 L min(-1)), diffusion was the dominant transport mechanism for gaseous components. This resulted in dissimilar transport of CH4 and the tracers He and Ne. Numerical simulations of GPPTs showed that similar transport of these components is only achieved at very high injection/extraction rates that, in practice, are not feasible since they would imply extremely short duration times of GPPTs to allow for consumption of a measurable amount of reactant(s) by soil microorganisms. However, Ar transport was similar to that of CH4. Hence, Ar may be a good tracer provided that it is injected at high concentrations (e.g., >25% [v/v]) to overcome its background concentration in soil air. Using moderate injection/ extraction rates (e.g., 0.6 L min(-1)) with injected volumes of 10-30 L will result in GPPT durations of 1-3 h, which would suffice to attain a measurable consumption of reactant(s) in soils having relatively high (e.g., first-order rate constants >0.3 h(-1)) microbial activities.