Groundwater Flow Modeling in Karst Aquifers: Coupling 3D Matrix and 1D Conduit Flow via Control Volume Isogeometric Analysis—Experimental Verification with a 3D Physical Model

Abstract

A novel numerical model for groundwater flow in karst aquifers is presented. A discrete-continuum (hybrid) approach, in which a three-dimensional matrix flow is coupled with a one-dimensional conduit flow, was used. The laminar flow in the karst matrix is described by a variably saturated flow equation to account for important hydrodynamic effects in both the saturated and unsaturated zones. Turbulent conduit flow for both free surface and pressurized flow conditions was captured via the noninertia wave equation, whereas the coupling of two flow domains was established through an exchange term proportional to head differences. The novel numerical approach based on Fup basis functions and control-volume formulation enabled us to obtain smooth and locally conservative numerical solutions. Due to its similarity to the isogeometric analysis concept (IGA), we labeled it as control-volume isogeometric analysis (CV-IGA). Since realistic verification of the karst flow models is an extremely difficult task, the particular contribution of this work is the construction of a specially designed 3D physical model ( dimensions: 5.66 × 2.95 × 2.00 m) in order to verify the developed numerical model under controlled laboratory conditions. Heterogeneous porous material was used to simulate the karst matrix, and perforated pipes were used as karst conduits. The model was able to capture many flow characteristics, such as the interaction between the matrix and conduit, rainfall infiltration through the unsaturated zone, direct recharge through sinkholes, and both free surface and pressurized flow in conduits. Two different flow experiments are presented, and comparison with numerical results confirmed the validity of the developed karst flow model under complex laboratory conditions.

Adaptive numerical modeling using the hierarchical Fup basis functions and control volume isogeometric analysis

“…Rather, here in (8), we use Fup basis functions and the CV formulation (test functions as in (9)). We refer to this method as control volume isogeometric analysis (CV-IGA), first developed using only low order Fup 1 and uniform nonadaptive discretization in Malenica et al, 45 and applied to multiphysics model of the flow in karst aquifers. The main idea of CV-IGA is to utilize the powerful approximation and adaptive properties of Fup basis functions for numerical solutions of engineering problems that arise in the field of fluid mechanic with the conservation properties of the CV formulation (as in CVFEM).…”

Spectral Decomposition and a Waveform Cluster to Characterize Strongly Heterogeneous Paleokarst Reservoirs in the Tarim Basin, China

“…The general characteristics of karst systems have been extensively published, and modern cave systems are well-studied [89][90][91][92][93][94][95]. The distribution of fracture-cavity channel systems formed by the action of paleo-karst water can be divided into network, dendritic, pinnate, single-pipe, individual, and other forms [88].…”

Three-Dimensional Geophysical Characterization of Deeply Buried Paleokarst System in the Tahe Oilfield, Tarim Basin, China

“…According to the above approach, we traced the paleocaves in the well T403 area and obtained its 3D structural features. The paleocaves in this area have strong heterogeneity [60][61][62][63][64][65][66]:…”