J. E. Capilla

Stochastic simulation of transmissivity fields conditional to both transmissivity and piezometric data—I. Theory

Abstract The generation of equally likely realizations of transmissivity fields conditional to both transmissivity and piezometric data is achieved using an iterative technique that couples geostatistics and optimization. By conditioning to both transmissivity fields and piezometric data we mean that the transmissivity field generated honours the transmissivity data and that the solution to the flow equation reproduces the measured piezometric heads. By equally likely realizations we mean that all realizations display the same patterns of spatial variability as observed in the field, as opposed to the transmissivity fields obtained by interpolation or by inverse modelling which are oversmooth, unrealistic, representations of the real field. In this regard, any realization could be the real but unknown transmissivity field. To achieve this goal, first a transmissivity field is generated conditional only to the transmissivity data, then the transmissivity field (and possibly the boundary conditions), are modified without destroying the spatial patterns of variability of transmissivity until the piezometric data are also honoured. The methodology is presented for steady-state flow in a confined two-dimensional aquifer. The details of the implementation are given for finite-differences solution over an aquifer discretized in square blocks.

AQUATOOL, A GENERALIZED DECISION-SUPPORT SYSTEM FOR WATER-RESOURCES PLANNING AND OPERATIONAL MANAGEMENT

Abstract This paper describes a generic decision-support system (DSS) which was originally designed for the planning stage of dicision-making associated with complex river basins. Subsequently, it was expanded to incorporate modules relating to the operational stage of decision-making. Computer-assisted design modules allow any complex water-resource system to be represented in graphical form, giving access to geographically referenced databases and knowledge bases. The modelling capability includes basin simulation and optimization modules, an aquifer flow modelling module and two modules for risk assessment. The Segura and Tagus river basins have been used as case studies in the development and validation phases. The value of this DSS is demonstrated by the fact that both River Basin Agencies currently use a version for the efficient management of their water resources.

Stochastic simulation of transmissivity fields conditional to both transmissivity and piezometric data 2. Demonstration on a synthetic aquifer

In the first paper of this series a methodology for the generation of transmissivity fields conditional to both transmissivity and piezometric head data was presented. This methodology, termed the self-calibrated approach, consists of two steps: first, the generation of a seed transmissivity field conditioned only to transmissivity data, and second, the perturbation of the seed field up until the piezometric head data are reproduced. The methodology is now demonstrated on a set of controlled numerical experiments carried out on synthetic aquifers. The objective of these experiments is not just to show that the methodology works, but also to explore its robustness under different situations. A total of 12 experiments have analyzed the performance of the method as a function of: (i) the log10 T transmissivity variance (from 0.2 to 2.0); (ii) the number of log10 T conditioning data (from 10 to 30); (iii) the number of piezometric head data (from 30 to 90); (iv) the number of master points (from 25 to 1000); (v) the magnitude of allowed departure of the final T field from the seed field (up to four times the kriging standard deviation). In all cases, the method was able to generate transmissivity fields conditional to both transmissivity and head measurements, at the same time preserving the spatial variability of the transmissivity field. It was found that the performance of the method increases with both the number of log10 T data and the number of master points, whereas it decreases as either the log10 T variance or the number of piezometric head data increases.

A program to create permeability fields that honor single-phase flow rate and pressure data

Abstract Accurate prediction (or simulation) of reservoir performance or contaminant transport in groundwater requires a realistic geological model representative of the reservoir/aquifer heterogeneity. Geostatistics provides tools for constructing such complex geological models constrained by different types of available (hard and soft) data and providing an assessment of related uncertainty. Permeability and flow data are nonlinearly related through the flow equations. Derivation of permeability models that honor flow response data is typically an inverse problem. This paper presents a FORTRAN program for generating permeability fields conditional to multiple-well single-phase flow rate and pressure data through an iterative inverse technique, called the sequential self-calibration (SSC) method. The SSC method is geostatistically-based, that is, it generates multiple equiprobable realizations that honor the input geostatistics of permeability and match pressure data for the given flow rate, under the given boundary conditions. The unique aspects of SSC are: (1) the master point concept that reduces the amount of computation, (2) a propagation mechanism based on kriging that accounts for spatial correlations of perturbations and (3) a fast method for computing all sensitivity coefficients within a single flow simulation run. Results from running the SSC code using an example data set are presented.

Stochastic Simulation of Non-Gaussian 3D Conductivity Fields in a Fractured Medium with Multiple Statistical Populations: Case Study

This paper applies a stochastic inverse method, named as gradual conditioning (GC) method, to the fractured site of Aspo, Sweden, which is an underground hard rock laboratory initially designed as a potential future deep geological repository for spent nuclear fuel. The aim of this paper is (1) the verification of GC method in a real three-dimensional (3D) fractured rock medium, showing that the GC method is a competitive stochastic tool in highly heterogeneous aquifers, furthermore, it gathers a set of capabilities so far not included in any existing method; (2) to characterize the site as adequately as possible, experimental data are reproduced closely; (3) to provide measures on the uncertainty of the estimates by means of using multiple equally likely realizations, thus showing the importance of conditioning to as much information as possible in order to reduce the uncertainty; (4) to prove that this fractured media can be adequately modeled by assuming a (pseudo-) continuum media, or equivalent porou...

AQUATOOL: A Computer-Assisted Support System for Water Resources Research Management Including Conjunctive Use

Aquatool, a computer-assisted support system for water resources research and management, is presented. The system includes three main modules: 1) a module for water resources schemes optimization, 2) a module for the simulation of the management of water resources systems, including the conjunctive use of surface and groundwater, and 3) a module for groundwater model preprocessing designed to include distributed aquifer submodels in the simulation model. Interactive graphic input data interfaces and postprocessors facilitate the entering of schemes and data as well as the analysis of results. The application to the Segura River Basin in Spain demonstrates the usefulness of the programs when dealing with complex systems as tools to obtain design and management guidelines and realtime aids to decision making.

Stochastic Inverse Problems In GroundwaterModeling

The inverse problem is, by its own definition, an ill-posed problem that requires assumptions about the structure of the unknown parameters. Yet, it has been traditionally addressed in a somehow deterministic way, searching for an optimum or best estimate solution that reproduces the available data. The impossibility of measuring hydrodynamic parameters and variables all over the aquifer makes groundwater-modeling results uncertain at any given conceivable situation. This fact has been the motivation to the development of stochastic hydrogeology. In this framework, hydrodynamic parameters are treated as realizations of a stochastic process conditioned to available data and characterized by a random function model inferred from the own data. In practical cases, the difficulty to solve the stochastic partial differential equations resulting from this approach leads to proceed simulating multiple equally likely conditional parameter fields, solving the classic deterministic equations, and then analyzing the ensemble of results. In order to obtain more realistic results, the stochastic conditional parameter fields have to honor the available variable measurements (usually of head and concentrations). The implementation of new methodologies to reach this goal has defined a new field generally referred to as stochastic inverse modeling. In this paper we present some of the most advance state-of-the-art methods showing their application to a real case of risk assessment. It corresponds to a low pervious dolomite formation that might constitute the fastest pathway to the biosphere for radionuclides escaped from a nuclear waste repository. Hydraulic Engineering Software VIII, C.A. Brebbia & W.R. Blain (Editors)