Yoojin Jung

A closed-form analytical solution for thermal single-well injection-withdrawal tests

A closed-form analytical solution for thermal single-well injection-withdrawal tests Yoojin Jung 1 and Karsten Pruess 1 [ 1 ] Thermal single-well injection-withdrawal (SWIW) tests entail pumping cold water into a hot and usually fractured reservoir, and monitoring the temperature recovery during subsequent backflow. Such tests have been proposed as a potential means to characterize properties of enhanced geothermal systems (EGS), such as fracture spacing, connectivity, and porosity. In this paper we develop an analytical solution for thermal SWIW tests, using an idealized model of a single vertical fracture with linear flow geometry embedded in impermeable conductive wall rocks. The analytical solution shows that the time dependence of temperature recovery is dominated by the heat exchange between fracture and matrix rock, but strong thermal diffusivities of rocks as compared to typical solute diffusivities are not necessarily advantageous for characterizing fracture-matrix interactions. The effect of fracture aperture on temperature recovery during backflow is weak, particularly when the fracture aperture is smaller than 0.1 cm. The solution also shows that temperature recovery during backflow is independent of the applied injection and backflow rates. This surprising result implies that temperature recovery is independent of the height of the fracture, or the specific fracture-matrix interface areas per unit fracture length, suggesting that thermal SWIW tests will not be able to characterize fracture growth that may be achieved by stimulation treatments. 1. Introduction [ 2 ] Enhanced geothermal systems (EGS) are engineered reservoirs that may be developed to produce energy from hot rock formations that are otherwise not economically viable for heat mining [Ge´rard et al., 2006]. To achieve a practically useful production capacity, the development of EGS commonly requires stimulation treatments, which usually involve water injection under high pressure. By applying stimulation treatments, we expect to increase the aperture, permeability, and size of pre-existing fractures and make additional fractures accessible to the injected fluid. [ 3 ] While increased fracture permeability is advanta- geous for improving the production of thermal energy, rapid migration of the injected water through preferential paths with insufficient heat transfer from the rock may result in premature thermal breakthrough at production wells, which would reduce the lifetime of the geothermal reservoir. For both success and sustainability of EGS, it is critical to ascertain the effectiveness of stimulation treat- ments for enhancing the fracture-rock matrix interface area, reducing flow impedance in the reservoir, and increasing flow rates of production wells. Earth Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California, USA. [ 4 ] Tracer tests have been proposed as a means to esti- mate fracture-matrix interface areas. Such tests generally involve the injection of aqueous solutes into one or more injection wells, and monitoring of tracer returns in fluids produced from offset observation or production wells [Shook, 2001 ; Sanjuan et al., 2006]. Interdiffusion of sol- ute tracers between fractures and rock matrix produces characteristic tails in tracer breakthrough curves that may permit the determination of fracture-matrix interface areas [Pruess, 2002 ; Pruess et al., 2005 ; Shan and Pruess, 2005]. However, because tracer breakthrough at offset ob- servation wells may be weak and slow, interwell tracer tests (ITT) may require fluid sampling over extended time peri- ods of weeks or even months. Also, suitable observation wells may not always be available. [ 5 ] Single-well injection-withdrawal (SWIW) tests, variously referred to as ‘‘huff and puff,’’ ‘‘push-pull,’’ or ‘‘injection-backflow’’ tests, can be an alternative to ITT. During an SWIW test, fluid with tracers is injected into a well and, after some quiescent or rest period, is produced out of the same well [Kocabas and Horne, 1987 ; Haggerty et al., 2001 ; Nalla and Shook, 2005 ; Ghergut et al., 2006, 2009 ; Neretnieks, 2007]. SWIW tests typically require a much shorter test duration from hours to a few days as com- pared to weeks or months for ITT. This holds out the prom- ise of obtaining test results much more quickly, which would provide significant economic benefits. Another potential advantage is that SWIW tests are much less affected than ITT by heterogeneities in the fracture network, potentially providing a clearer signal of matrix properties 1 of 12

TOUGH3: A new efficient version of the TOUGH suite of multiphase flow and transport simulators

The TOUGH suite of nonisothermal multiphase flow and transport simulators has been updated by various developers over many years to address a vast range of challenging subsurface problems. The increasing complexity of the simulated processes as well as the growing size of model domains that need to be handled call for an improvement in the simulators computational robustness and efficiency. Moreover, modifications have been frequently introduced independently, resulting in multiple versions of TOUGH that (1) led to inconsistencies in feature implementation and usage, (2) made code maintenance and development inefficient, and (3) caused confusion to users and developers. TOUGH3—a new base version of TOUGH—addresses these issues. It consolidates both the serial (TOUGH2 V2.1) and parallel (TOUGH2-MP V2.0) implementations, enabling simulations to be performed on desktop computers and supercomputers using a single code. New PETSc parallel linear solvers are added to the existing serial solvers of TOUGH2 and the Aztec solver used in TOUGH2-MP. The PETSc solvers generally perform better than the Aztec solvers in parallel and the internal TOUGH3 linear solver in serial. TOUGH3 also incorporates many new features, addresses bugs, and improves the flexibility of data handling. Due to the improved capabilities and usability, TOUGH3 is more robust and efficient for solving tough and computationally demanding problems in diverse scientific and practical applications related to subsurface flow modeling.

iTOUGH2: A multiphysics simulation-optimization framework for analyzing subsurface systems

Abstract iTOUGH2 is a simulation-optimization framework for the TOUGH suite of nonisothermal multiphase flow models and related simulators of geophysical, geochemical, and geomechanical processes. After appropriate parameterization of subsurface structures and their properties, iTOUGH2 runs simulations for multiple parameter sets and analyzes the resulting output for parameter estimation through automatic model calibration, local and global sensitivity analyses, data-worth analyses, and uncertainty propagation analyses. Development of iTOUGH2 is driven by scientific challenges and user needs, with new capabilities continually added to both the forward simulator and the optimization framework. This review article provides a summary description of methods and features implemented in iTOUGH2, and discusses the usefulness and limitations of an integrated simulation-optimization workflow in support of the characterization and analysis of complex multiphysics subsurface systems.

Reply to comment by Maier and Kocabas on “A closed‐form analytical solution for thermal single‐well injection‐withdrawal tests”

Reply to comment by Maier and Kocabas on “A closed-form analytical solution for thermal single-well injection-withdrawal tests” Yoojin Jung and Karsten Pruess Earth Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA 1. Introduction We appreciate the comment by Maier and Kocabas (2012) on our research article (Jung and Pruess, 2012). In their comment, they raise the following issues: (1) their solutions presented in Kocabas (2010) and Maier and Kocabas (2012) are mathematically simpler and computationally more efficient than our analytical solutions and (2) the insensitivity of thermal breakthrough curve to the flow velocity, which is one of the important conclusions of our study, only holds for the special case where the injection and the withdrawal flow rate is identical. We address each of these comments, along with a few other relatively minor comments and suggestions, below. 2.1. Efficiency of the Analytical Solution Regarding the computational efficiency of the analytical solutions, we agree that the solutions developed by Kocabas (2010) and Maier and Kocabas (2012) using the iterated Laplace transform have a simpler form than our solutions and therefore need a shorter