A comparative study of a heat and fluid flow problem using three models of different levels of sophistication

AbstractThree mathematical models of different levels of sophistication have been used to study a practical problem on underground heat and fluid flow, associated with the seasonal storage of hot water in an aquifer. A number of scenarios have been examined using the three models. For the basic problem the three models yield similar results, so use of the simplest is preferred. For several variations on the problem, only the more complicated models are adequate to properly address the problem. In general, the choice of an appropriate model is very problem-specific and requires not only experience with modelling methods, but also an understanding of the physics of the problem

Uncertainty in the Maximum Principal Stress Estimated from Hydraulic Fracturing Measurements Due to the Presence of the Induced Fracture

Abstract The classical theory for hydraulic fracturing stress measurements assumes an ideal case with a linear elastic, homogenous, and isotropic medium; and a fracture that reopens distinctly when the minimum tangential borehole stress is exceeded. The induced fracture disturbs this ideal picture in several aspects, which are important for the evaluation of the maximum horizontal principal stress using the fracture reopening pressure. This disturbance can be attributed to the fracture normal stiffness and the initial hydraulic fracture permeability. In this paper, the hydraulic fracturing reopening test is studied by coupled hydromechanical modeling that takes into account an induced fracture that is incompletely closed. The result shows that with realistic equipment compliance, the apparent fracture reopening evaluated from the well-pressure is close to the magnitude of the minimum horizontal principal stress with little or no correlation to the maximum horizontal principal stress. This observation suggests that determination of maximum principal stress by hydraulic fracturing using the reopening pressure is very uncertain

Coupled hydro-mechanical processes in crytalline rock and ininduratedand plastic clays: A comparative discussion

This paper provides a comparative discussion of coupledhydromechanical processes in three different geological formations:crystalline rock, plastic clay, and indurated clay. First, the importantprocesses and associated property characteristics in the three rock typesare discussed. Then, one particular hydromechanical coupling is broughtup for detailed consideration, that of pore pressure changes in nearbyrock during tunnel excavation. Three field experiments in the three rocktypes are presented and their results are discussed. It is shown that themain physical processes are common to all three rock types, but with verydifferent time constants. The different issues raised by these cases arepointed out, and the transferable lessons learned are identified. Suchcross fertilization and simultaneous understanding of coupled processesin three very different rock types help to greatly enhance confidence inthe state of science in this field

A Semi-Analytical Solution for Large-Scale Injection-Induced PressurePerturbation and Leakage in a Laterally Bounded Aquifer-AquitardSystem

A number of (semi-)analytical solutions are available to drawdown analysis and leakage estimation of shallow aquifer-aquitard systems. These solutions assume that the systems are laterally infinite. When a large-scale pumping from (or injection into) an aquifer-aquitard system of lower specific storativity occurs, induced pressure perturbation (or hydraulic head drawdown/rise) may reach the lateral boundary of the aquifer. We developed semi-analytical solutions to address the induced pressure perturbation and vertical leakage in a 'laterally bounded' system consisting of an aquifer and an overlying/underlying aquitard. A one-dimensional radial flow equation for the aquifer was coupled with a one-dimensional vertical flow equation for the aquitard, with a no-flow condition imposed on the outer radial boundary. Analytical solutions were obtained for (1) the Laplace-transform hydraulic head drawdown/rise in the aquifer and in the aquitard, (2) the Laplace-transform rate and volume of leakage through the aquifer-aquitard interface integrated up to an arbitrary radial distance, (3) the transformed total leakage rate and volume for the entire interface, and (4) the transformed horizontal flux at any radius. The total leakage rate and volume depend only on the hydrogeologic properties and thicknesses of the aquifer and aquitard, as well as the duration of pumping or injection. It was proven that the total leakage rate and volume are independent of the aquifer's radial extent and wellbore radius. The derived analytical solutions for bounded systems are the generalized solutions of infinite systems. Laplace-transform solutions were numerically inverted to obtain the hydraulic head drawdown/rise, leakage rate, leakage volume, and horizontal flux for given hydrogeologic and geometric conditions of the aquifer-aquitard system, as well as injection/pumping scenarios. Application to a large-scale injection-and-storage problem in a bounded system was demonstrated

Simple Model Representations of Transport in a Complex Fracture and Their Effects on Long-Term Predictions

A complex fracture model for fluid flow and tracer transport was previously developed that incorporates many of the important physical effects of a realistic fracture, including advection through a heterogeneous fracture plane, partitioning of flow into multiple subfractures in the third dimension, and diffusion and sorption into fracture-filling gouge, small altered rock matrix blocks within the fracture zone, and the unaltered semi-infinite rock matrix on both sides of the fracture zone (Tsang and Doughty, 2003). It is common, however, to represent the complex fracture by much simpler models consisting of a single fracture, with a uniform or heterogeneous transmissivity distribution over its plane and bounded on both sides by a homogeneous semi-infinite matrix. Simple-model properties are often inferred from the analysis of short-term (one to a few days) site characterization (SC) tracer-test data. The question addressed in this paper is: How reliable is the temporal upscaling of these simplified models? Are they adequate are for long-term calculations that cover thousands of years? In this study, a particle-tracking approach is used to calculate tracer-test breakthrough curves (BTCs) in a complex fracture model, incorporating all the features described above, for both a short-term SC tracer test and a 10,000-year calculation. The results are considered the 'real-world'. Next, two simple fracture models, one uniform and the other heterogeneous, are introduced. Properties for these simple models are taken either from laboratory data or found by calibration to the short-term SC tracer-test BTCs obtained with the complex fracture model. Then the simple models are used to simulate tracer transport at the long-term time scale. Results show that for the short-term SC tracer test, the BTCs calculated using simple models with laboratory-measured parameters differ significantly from the BTCs obtained with the complex fracture model. By adjusting model properties, the simple models can be calibrated to reproduce the peak arrival time and height of the complex-fracture-model BTCs, but the overall match remains quite poor. Using simple models with short-term SC-calibrated parameters for long-term calculations causes order-of-magnitude errors in tracer BTCs: peak arrival time is 10-100 times too late, and peak height is 50-300 times too small. On the other hand, using simple models with laboratory-measured properties of unfractured rock samples for 10,000-year calculations results in peak arrivals and heights up to a factor of 50 too early and large, respectively. The actual magnitudes of the errors made by using the simple models depend on the parameter values assumed for the complex fracture model, but in general, simple models are not expected to provide reliable long-term predictions. The paper concludes with some suggestions on how to improve long-term prediction calculations

Shear-slip analysis in multiphase fluid-flow reservoir engineeringap plications using TOUGH-FLAC

This paper describes and demonstrates the use of the coupledTOUGH-FLAC simulator for geomechanical shear-slip (failure) analysis inmultiphase fluid-flow reservoir-engineering applications. Two approachesfor analyzing shear-slip are described, one using continuum stress-strainanalysis and another using discrete fault analysis. The use of shear-slipanalysis in TOUGH-FLAC is demonstrated on application examples related toCO2 sequestration and geothermal energy extraction. In the case of CO2sequestration, the shear-slip analysis is used to evaluate maximumsustainable CO2-injection pressure under increasing reservoir pressure,whereas in the case of geothermal energy extraction, the shear-slipanalysis is used to study induced seismicity during steam productionunder decreasing reservoir pressure and temperature

Evaluating Potential for Large Releases from CO2 StorageReservoirs: Analogs, Scenarios, and Modeling Needs

While the purpose of geologic storage of CO{sub 2} in deep saline formations is to trap greenhouse gases underground, the potential exists for CO{sub 2} to escape from the target reservoir, migrate upward along permeable pathways, and discharge at the land surface. Such discharge is not necessarily a serious concern, as CO{sub 2} is a naturally abundant and relatively benign gas in low concentrations. However, there is a potential risk to health, safety and environment (HSE) in the event that large localized fluxes of CO{sub 2} were to occur at the land surface, especially where CO{sub 2} could accumulate. In this paper, we develop possible scenarios for large CO{sub 2} fluxes based on the analysis of natural analogues, where large releases of gas have been observed. We are particularly interested in scenarios which could generate sudden, possibly self-enhancing, or even eruptive release events. The probability for such events may be low, but the circumstances under which they might occur and potential consequences need to be evaluated in order to design appropriate site selection and risk management strategies. Numerical modeling of hypothetical test cases is needed to determine critical conditions for such events, to evaluate whether such conditions may be possible at designated storage sites, and, if applicable, to evaluate the potential HSE impacts of such events and design appropriate mitigation strategies

Reply to Comments by Veling on “A Semi-Analytical Solution for Large-Scale Injection-Induced Pressure Perturbation and Leakage in a Laterally Bounded Aquifer–Aquitard System” by Zhou, Birkholzer, and Tsang

Veling (2010) pointed to 'a serious mistake' and 'mathematical inconsistency' in Zhou et al. (2009) because the dimensionless flow equations in Equation 4 (in terms of dimensionless hydraulic head rise in the aquifer and the aquitard) would give rise to additional terms when back converting to the groundwater flow equations, in the case that initial conditions for hydraulic head were spatially variable. He added, however, that the conclusions of the paper remain valid when uniform initial conditions are assumed. We accept this comment because we have indeed assumed uniform initial conditions in the system but failed to state this explicitly in the publication, partially because this assumption is very common in groundwater hydrology when deriving analytical and semi-analytical solutions. The same assumption was employed, for example, by Veling in Veling and Maas (2009), as stated 'For the ease of presentation we assume from here on that {phi}{sub i0} (r, z) ... are all equal to zero. An arbitrary initial function ... will complicate the solution, but not essentially'. We shall emphasize that with this assumption, our semi-analytical solutions and their derivations are correct

Large releases from CO2 storage reservoirs: Analogs, scenarios,and modeling needs

While the purpose of geologic storage in deep salineformations is to trap greenhouse gases underground, the potential existsfor CO2 to escape from the target reservoir, migrate upward alongpermeable pathways, and discharge at the land surface. In this paper, weevaluate the potential for such CO2 discharges based on the analysis ofnatural analogs, where large releases of gas have been observed. We areparticularly interested in circumstances that could generate sudden,possibly self enhancing release events. The probability for such eventsmay be low, but the circumstances under which they occur and thepotential consequences need to be evaluated in order to designappropriate site-selection and risk-managementstrategies. Numericalmodeling of hypothetical test cases is suggested to determine criticalconditions for large CO2 releases, to evaluate whether such conditionsmay be possible at designated storage sites, and, if applicable, toevaluate the potential impacts of such events as well as designappropriate mitigation strategies