Modeling Deep Geothermal Reservoirs: Recent Advances and Future Problems

Ilyasov, Maxim; Ostermann, Isabel; Punzi, Alessandro

doi:10.1007/978-3-642-01546-5_22

Cited by 8 publications

(6 citation statements)

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“…Developing models that can consistently predict the behavior of the system treating it as a whole and without expecting many data concerning its geometric properties are therefore of critical impotence. For an in-depth review of the current methods in use for modeling geothermal reservoirs we refer the reader to Ilyasov et al (2010). Hydrothermal and petrothermal are the two main categories of geothermal reservoirs.…”

Section: Physical Problem and Current Modelsmentioning

confidence: 99%

Modeling anomalous heat transport in geothermal reservoirs via fractional diffusion equations

Luchko

Punzi

2011

Int J Geomath

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The aim of this article is to give an overview of the current research towards applications of fractional partial differential equations for the modeling of anomalous heat transfer in porous media. We start with presenting a physical background behind the anomalous processes described by the Continuous Time Random Walk (CTRW) model and arguing its feasibility for modeling of heat transport processes in heterogeneous media. From the CTRW model on the microscopic level, a macroscopic model in form of a generalized fractional diffusion equation is then deduced. Both mathematical analysis of the generalized fractional diffusion equations and some methods for their numerical treatment are presented. Finally, some open questions and directions for further work are suggested

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Section: Physical Problem and Current Modelsmentioning

confidence: 99%

Modeling anomalous heat transport in geothermal reservoirs via fractional diffusion equations

Luchko

Punzi

2011

Int J Geomath

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“…This system is characterized by a less invasive procedure, as well as lower stress levels inside and in the vicinity of the reservoir compared to the case of petrothermal reservoirs. For a characterization of reservoir models the reader is referred, e.g., to Ilyasov et al (2010) and the references therein. Small earthquakes can be the consequences of a highly stressed rock formation.…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional modeling of heat transport in deep hydrothermal reservoirs

Ostermann

2011

Int J Geomath

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The need for alternative energy increases steadily-especially due to the climate change and the limited availability of fossil fuels. Geothermal power uses the intrinsic heat which is stored in the accessible part of the Earth's crust. Its importance among the renewable energy resources originates from the almost unlimited energy supply of the Earth and its independence from external influences such as seasonal or even daily climatic variability. Nevertheless, there are risks which have to be assessed. From a mathematical point of view there are four building blocks of the characterization of deep geothermal systems: seismic exploration, gravimetry, modeling transport processes, and modeling the stress field. In particular, local depletion poses a significant risk during the industrial utilization of geothermal reservoirs. In order to reduce this risk, reliable techniques to predict the heat transport and the production temperature are required. To this end, a three-dim ensional model to simulate the heat transport in hydrothermal systems is developed which is based on a transient advection-diffusion-equation for a two-phase porous medium. The existence, uniqueness, and continuity of the weak solution of the resulting initial boundary value problem is verified. For the numerical realization, a Galerkin scheme is introduced on the basis of scalar kernels. Its convergence is proven. Furthermore, exemplary applications of this method are investigated for the biharmonic kernel

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“…In dieser Arbeit werden -basierend auf den Betrachtungen in [3,28,30,33,35,37,45,46,59,68,69] -zuerst kurz der geothermische Hintergrund und insbesondere die relevanten Reservoirtypen dargestellt. Im Anschluss werden für diese Reservoirtypen die den einzelnen Säulen zugrundeliegenden Differential-und Integralgleichungen beschrieben.…”

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“…1) heraus. Modelle und (numerische) Lösungsansätze zu den beschriebenen Problemen im Bereich der Transportprozesse findet man unter anderem in[21,43,46,53,54,59,68,69,71] und der darin aufgeführten Literatur.…”

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