## 1. Introduction

[2] In a recent paper [*Mukhopadhyay and Tsang*, 2008], hereinafter referred to as paper 1, we presented a simple conceptual model and a semianalytical solution to analyze the data from flowing fluid temperature logging (FFTL). In paper 1, we also presented a procedure to estimate the effective permeability of the fractured rock using the temperature data from FFTL (see section 2 for a recapitulation of FFTL). The conceptual model described in paper 1 assumes single-phase flow of air and ignores the presence of the water phase in the unsaturated rock. The model includes heat transfer by convection but neglects heat conduction. It also assumes that pumping of air from the borehole during FFTL does not change the pressure and temperature in the surrounding rock (a reasonable assumption, considering the short duration of the test and the large volume of the surrounding rock compared to the volume of the borehole). However, it is possible that these simplifying assumptions could introduce some uncertainties into the estimated permeability value. The primary objective of this paper is to analyze these uncertainties, and to refine the estimated permeability values from paper 1. In addition, as a result of this study, we are also able to estimate additional transport parameters from FFTL data.

[3] In FTTL performed in unsaturated fractured rock, the recorded pressure and temperature data communicate the underlying multiphase flow and transport processes in response to the applied perturbation (i.e., pumping of air). A full and complete analysis of FFTL data requires a systematic investigation using a conceptual model that will encompass anticipated multiphase flow and heat-transport processes in a fractured porous medium. These include water and vapor flow, heat transport by conduction and convection, and plausible changes in the physical condition of the rock matrix and fractures surrounding the borehole being pumped. Many of these factors were assumed to be negligible in the conceptual model presented in paper 1, based on intuition and plausibility arguments. In this paper, we reexamine these hypotheses put forth in paper 1, and seek to affirm or negate some of those assumptions, based on a systematic numerical study. This approach is also useful in providing quantitative estimates of uncertainties associated with ignoring a particular process or feature.

[4] In this paper, data from FFTL are analyzed using the numerical flow and transport simulator TOUGH2 [*Pruess*, 1991; *Pruess et al.*, 1999]. TOUGH2 is a general purpose simulation program for multidimensional fluid and heat flows of multiphase, multicomponent fluid mixtures in porous and fractured media. In addition, we conduct statistical analysis of the data and parameter estimation by using the optimization and inversion software package *i*TOUGH2 [*Finsterle*, 1999a, 1999b, 1999c] (http://esd.lbl.gov/iTOUGH2), which is based on the TOUGH2 code. *i*TOUGH2 has been extensively used in unsaturated and multiphase inverse modeling of both laboratory and field test data; see *Finsterle* [2004] for a review of *i*TOUGH2 applications. More specifically and with more relevance for this paper, *i*TOUGH2 has been successfully used for parameter estimation in gas flow and transport experiments [*Finsterle and Persoff*, 1997; *Ahlers et al.*, 1999; *Unger et al.*, 2004] and nonisothermal two-phase flow [*Finsterle et al.*, 1998, 2000; *Engelhardt et al.*, 2003; *White et al.*, 2003; *Björnsson et al.*, 2003; *Finsterle*, 2005; *Zarrouk et al.*, 2007].

[5] A model is a simplified, abstracted, and parameterized conceptualization of a natural system. Model conceptualization and parameterization are related [*Finsterle*, 2004], and both are needed to capture and reduce the complexity of the natural system. As long as a process is suitably parameterized, it can be subjected to uncertainty analysis and parameter estimation. Parameterization need not be restricted to hydrologic properties only (in the context of FFTL). It may include aspects of the conceptual model that are considered uncertain (such as the initial and boundary conditions of the model). Even though there is no upper limit to the number of parameters employed for uncertainty analysis, it is not appropriate to determine a large number of strongly correlated parameters for inverse modeling and parameter estimation, given limited data of insufficient sensitivity.

[6] The first step of our investigation is to develop a conceptual model that is a reasonable representation of the multiphase flow and transport processes occurring in the natural system in response to FFTL. Data obtained from an actual FFTL, and other prior information about the natural system (such as permeability of the rock determined from previous independent testing) is used to constrain the model. In the next step, we perform a systematic sensitivity study to determine the parameters that have the strongest influence on a FFTL response. In the last step, we use *i*TOUGH2 for estimation of these parameters and analysis of uncertainties in the estimated values.