PAMM · Proc. Appl. Math. Mech. 13, 589 – 590 (2013) / DOI 10.1002/pamm.201310275

Multi-Fracture Reservoir Simulations for Long Time Physical Processes

Georg-Peter Ostermeyer1,∗ and Tarin Srisupattarawanit1,∗∗

1 Institute of Dynamics and Vibrations, Technical University Braunschweig, Schleinitz str. 20, 38106, Braunschweig

Reservoirs with multi-fracture techniques are developed and frequently used for oil and gas industry. Recently, they are alsoused for deep geothermal reservoirs especially for Hot Dry Rock (HDR). The analysis of the reservoir is generally interestedin long time physical properties (10–100 years), e.g. fluid flow, heat transport etc. Typical CFD simulations are limited in thiscontext. Here we developed a fluid flow and heat transport modeling in a multi-fracture reservoir based on the so-called MixedDimensional Model (MDM), which describes the different characteristic flows and the heat transport in different dimensions.In the mathematical point of view, these models are discretized based on the Cellular Automaton (CA) method combined withother necessary numerical techniques. The different cases of fluid flow and heat transport in multi-fracture reservoirs havebeen simulated and shown physical results very reasonably with less computational time.

c© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

1 Multi-Dimensional Model for Heat and Flow in Rock Fracture

There is difficult in order to simulate fluid flow and heat transfer in multi–fractures geothermal reservoir, especially whenlong time simulation is necessary. The different scale in space and time are the main challenges to deal with such kindof the problem. In this article, we presented the flow model and heat transport in multi–fractures system for long timesimulation (more than 50 years). The model is the so–called Multi–Dimensional Model (MDM)—in which the flow and heattransport are modeled in different dimensional based on the characteristic of physical properties, see in Fig. (1). On this MDMthe flow modeling can be summarized as, 1D model for fluid flow in pipe, this can be modeled based on the potential flow andstreamline function. The velocity field in long time simulation are obtained by means of Bernoulli’s equation. 2D model forfluid in rock fracture, this flow is modeled as potential flow with doublet condition for inflow and out flow. First we obtainedthe solution by means of Laplace’equation analytically. This model is suitable for the case of doublet is far from the boundaryline of fracture, but most of practical cases are near the boundary line. We extended the model by using cellular automata [1].

Fig. 1: (Left) shown multi-dimensional Model; (Right) shown cellular automata model

The heat transport modeling consist of heat transfer in fluid, heat transfer in rock close to the fracture and heat transferremote to the fracture. The heat transfer in fluid includes the effect of heat conduction, heat convection and heat transportform rock to fluid at the near field. These are modeled based on different cellular automata model. Considering heat on therock close to fracture, it is modeled based on heat conduction inside rock combine with effect of heat convection from fluidinside fracture. The rock far from fracture is also include with the cellular automata model. All three part of heat modeling arecoupled iteratively to cover the short time(heat at near field rock) and long time effect such as the cooling down of reservoir.

∗ Corresponding author: Email gp.ostermeyer@tu-bs.de, phone +49 531 391 7000, fax +49 531 391 7017∗∗ Email t.srisupattarawanit@tu-bs.de, phone +49 531 391 7001, fax +49 531 391 7017

c© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

590 Section 22: Scientific computing

2 Simulation of Multi-Fractures Geothermal Reservoir

The simulation of flow in multi–fractures geothermal reservoir have been done based on the MDM which are described before.The geometry of reservoir is shown in Fig. (2), which reservoir is 6000 m. down from surface, the inflow temperature is 20celcuis. The Simulation run for long time period (more than 50 years real time), the results of output temperature on the surfaceare shown in Fig. (3). We can observe the characteristic of the line shown the reduction of output temperature exponentiallywhich are reasonable results of cooling down effect in reservoir. This example requires approximately 16 minute on CPUtime, with Window XP system,Intel(R)Core(TM) i7 CPU Q740 1.73 GHz, 3.24 GB RAM. Furthermore we shown the caseof optimizing flow with regulator, see Fig. (3), the number of active fracture is increase and higher output temperature couldbe gained. However in such case the flow velocity is reduced significantly and might be a problem in long time operation bysedimentation inside fracture. These we are working on and the results will be published somewhere else.

Fig. 2: Domain of Heat and flow in multi–fractures geothermal reservoir

Fig. 3: Solution of heat transport; line shown output temperature on the surface over time, below shown the temperature inside the firstfracture

3 Conclusion

The modeling of heat and flow in multi–fracture reservoir have been described based on MDM and cellular automata. the 3Dflow modeling can be represented by a coupled 1D and 2D model, in which can be completed iteratively based on Kirchhoff’stheory, the local flow in fracture is modeled based on the Cellular Automaton model. The heat transfer in 3D can be modeledas three sub-models, heat inside fracture, heat on rock near to fracture and heat on rock far from fracture, these models arecoupled iteratively. These MDM given very fast simulation and suitable for long time behavior of 3D multi–fracture reservoir,including reasonable result in physics.

References[1] G. -P. Ostermeyer, and T. Srisupattarawanit, Multi–Scale Simulation of Heat and Flow in Geothermal Reservoir, Oil Gas European

Magazine, Pg 40-42, (1/2013).

c© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim www.gamm-proceedings.com