Andy Louwyck

Simulation of axi-symmetric flow towards wells: A finite-difference approach

A detailed finite-difference approach is presented for the simulation of transient radial flow in multi-layer systems. The proposed discretization scheme simulates drawdown within the well more accurately than commonly applied schemes. The solution is compared to existing (semi) analytical models for the simulation of slug tests and pumping tests with constant discharge in single- and multi-layer systems. For all cases, it is concluded that the finite-difference model approximates drawdown to acceptable accuracy. The main advantage of finite-difference approaches is the ability to account for the varying saturated thickness in unconfined top layers. Additionally, it is straightforward to include radial variation of hydraulic parameters, which is useful to simulate the effect of a finite-thickness well skin. Aquifer tests with variable pumping rate and/or multiple wells may be simulated by superposition. The finite-difference solution is implemented in MAxSym, a MATLAB tool which is designed specifically to simulate axi-symmetric flow. Alternatively, the presented equations can be solved using a standard finite-difference model. A procedure is outlined to apply the same approach with MODFLOW. The required modifications to the input parameters are much larger for MODFLOW than for MAxSym, but the results are virtually identical. The presented finite-difference solution may be used, for example, as a forward model in parameter estimation algorithms. Since it is applicable to multi-layer systems, its use is not limited to the simulation of traditional pumping and slug tests, but also includes advanced aquifer tests, such as multiple pumping tests or multi-level slug tests.

SEAWAT-Based Simulation of Axisymmetric Heat Transport

Simulation of heat transport has its applications in geothermal exploitation of aquifers and the analysis of temperature dependent chemical reactions. Under homogeneous conditions and in the absence of a regional hydraulic gradient, groundwater flow and heat transport from or to a well exhibit radial symmetry, and governing equations are reduced by one dimension (1D) which increases computational efficiency importantly. Solute transport codes can simulate heat transport and input parameters may be modified such that the Cartesian geometry can handle radial flow. In this article, SEAWAT is evaluated as simulator for heat transport under radial flow conditions. The 1971, 1D analytical solution of Gelhar and Collins is used to compare axisymmetric transport with retardation (i.e., as a result of thermal equilibrium between fluid and solid) and a large diffusion (conduction). It is shown that an axisymmetric simulation compares well with a fully three dimensional (3D) simulation of an aquifer thermal energy storage systems. The influence of grid discretization, solver parameters, and advection solution is illustrated. Because of the high diffusion to simulate conduction, convergence criterion for heat transport must be set much smaller (10(-10) ) than for solute transport (10(-6) ). Grid discretization should be considered carefully, in particular the subdivision of the screen interval. On the other hand, different methods to calculate the pumping or injection rate distribution over different nodes of a multilayer well lead to small differences only.

MODFLOW procedure to simulate axisymmetric flow in radially heterogeneous and layered aquifer systems

A procedure is outlined to simulate axisymmetric groundwater flow in radially heterogeneous and layered aquifer systems using the unmodified version of MODFLOW. The procedure is straightforward, as it only requires correction of some of the input parameters. In contrast to other MODFLOW procedures to simulate axisymmetric flow, no restrictions are imposed on the type of flow, the discretization of radial distance, or the parameter values. Hence, the method can deal with both confined and unconfined flow, wellbore storage, and axisymmetric aquifer inhomogeneities including effects of finite-thickness skin and gravel pack. Several test cases are presented, which compare the calculated results with existing analytical solutions, the analytic element solver TTim, and the axisymmetric, finite-difference model MAxSym. It is concluded that the MODFLOW procedure is capable of simulating accurately axisymmetric flow in radially heterogeneous multi-aquifer systems.RésuméUne procédure est présentée pour simuler l’écoulement axisymétrique d’eau souterraine dans des systèmes aquifères hétérogènes radialement et stratifiés au moyen de la version non modifiée de MODFLOW. La procédure est simple car elle ne requiert que la correction de quelques paramètres d’entrée. Contrairement à d’autres procédures MODFLOW destinées à simuler un écoulement axisymétrique, aucune restriction n’est imposée au type d’écoulement, à la discrétisation de la distance radiale ou aux valeurs des paramètres. Par conséquent, la méthode peut s’appliquer tant aux écoulements libres que captifs, à l’effet de capacité au puits et aux hétérogénéités de l’aquifère axisymétrique, incluant les effets de skin d’épaisseur finie et du massif de gravier. Plusieurs cas d’étude sont présentés qui comparent les résultats calculés avec des solutions analytiques existantes, le solveur d’éléments analytiques TTim et le modèle aux différences finies axisymétrique MAxSym. Il en est conclu que la procédure MODFLOW est capable de simuler précisément l’écoulement axisymétrique dans des systèmes multi-aquifères radialement hétérogènes.ResumenSe describe un procedimiento para simular los flujos de agua subterránea axisimétricos en sistema acuíferos estratificados y radialmente heterogéneos usando la versión no modificada del MODFLOW. El procedimiento es directo ya que solamente requiere la corrección de alguno de los parámetros de entrada. En contraste con otros procedimientos de MODFLOW para simular flujos axisimétricos, no se imponen restricciones en el tipo de flujo, la discretización de las distancias radiales, o los valores de los parámetros. Por lo tanto, que el método puede tratar tanto con flujo no confinado como confinado, almacenamiento en el pozo, e inhomogeneidades axisimétricas del acuífero incluyendo los efectos de películas de espesores finitos y empaque de gravas. Se presentan varios casos de ensayos, que comparan resultados calculados con soluciones analíticas existentes, la resolución del elemento analítico TTim, y el modelo axisimétrico de diferencias finitas MAxSym. Se concluye que el procedimiento de MODFLOW es capaz de simular con exactitud el flujo axisimétrico en sistemas multiacuíferos radialmente heterogéneos.摘要本文概述了采用未更改的MODFLOW软件模拟放射状非均匀和层状含水层系统中轴对称地下水流的过程。过程非常简单,因为只需要修改一些输入的参数。与其它MODFLOW模拟轴对称流的过程相比,对水流类型、放射状距离的离散化或参数值没有什么限制。因此,这个方法可以处理承压和非承压水流,钻井孔存储、以及轴对称含水层非均质性包括有限厚度--和砾料的影响。展示了几个实验案例,与用目前的解析方法,解析元TTim方法和轴对称有限差模型MAxSym得到的计算结果进行了对比。结论是MODFLOW的过程能够准确模拟放射状非均匀和层状含水层系统中轴对称流。ResumoDescreve-se o procedimento utilizado para simular o escoamento assimétrico de águas subterrâneas em sistemas aquíferos multi-camada radialmente heterogéneos, usando a versão não modificada do MODFLOW. O procedimento é simples, na medida em que apenas requer a correção de alguns dos parâmetros de entrada. Em contraste com outros procedimentos do MODFLOW para simular o escoamento assimétrico de eixos, aqui não é imposta nenhuma restrição nem para o tipo de escoamento, nem para a discretização da distância radial, nem para os valores dos parâmetros. Assim, o método pode lidar com ambas as situações de escoamento confinado e não confinado, armazenamento do poço, e heterogeneidades assimétricas do aquífero, incluindo efeitos de espessura de pele de poço (zona de baixa permeabilidade circundante ao furo) e de filtro de areão calibrado. São testados vários casos que comparam os resultados calculados com soluções analíticas existentes, o elemento analítico da solução TTim, e a simetria axial do modelo de diferenças finitas MAxSym. Conclui-se que o procedimento do MODFLOW é capaz de simular com precisão o escoamento assimétrico em sistemas multi-aquífero radialmente heterogéneos.