The borehole model, developed by Rembe Consulting, is a complex FEM-simulation modell on the basis of COMSOL Multiphysics®. It reproduces the well with its essential installation parts as tubings, casings, fluid filled annuli, cements, packer and others as well as the surrounding bed rock. The model calculates the time dependent heat balance and considers injection and extraction of fluids as well as storage caverns and solution mining caverns.

3D image of a storage cavern and the surrounding bed rock.


The model structure assures a separate parametrisation of the single components, for which the heat transfer shall be calculated. In this way, time dependent temperature – depth profiles can be calculated for each component separately.

linkage scheme

The model considers the heat exchange with the surrounding rock, the Joule-Thomson-effect as well as the interaction of injected and extracted fluids in the storage cavern. The pressure calculation, the mass- and heat balancing describe the cavern as a mass and heat reservoir, including heat transfer with the host rock. Thus, time dependent storage cycles (injection and extraction) can be simulated for years.

Fluid pathways in bore hole cements and along the borehole wall can be calculated with the Darcy-law of flow in porous media.

For the calculation any gaseous or liquid fluids may be chosen and can be parametrised. Specific gas parameters for natural gases are calculated on the basis of pseudo-reduced variables of state. The calculation of the Gas law deviation factors is done according to REDLICH-KWONG or STANDING & KATZ.

As results one obtains the temperature distribution in the surrounding rock, vertical temperature profiles of the bore hole installation components and the fluid filled interior spaces, temperature-time-extrusions as well as the time dependent state variables and balance quntities of the cavern. The single balance quatities (mass and heat flow, storage changes, sources and sinks) can be documented separately if required for balancing.

Vertical temperature profiles

The model is applicable for the recalculation of storage cycles and quantitative evaluation of temperature measurements (e.g. DTS-measurements) for the detection of leakages and fluid flows in cements and along the borehole wall. The following figure shows the temperature change-time-extrusion as a simulation result.

Temperature change-time-extrusion


BÜCKER, C.; GROSSWIG, S.; HURTIG, E.; REMBE, M. and N. STADT (2015): Processes in the Near Wellbore Reservoir Matrix during Formation Water Re-injection – Measurements and Simulation. Presentation at the DGMK Spring Conference in Celle/Germany, April 22.-23., 2015.

BÜCKER, C.; GROSSWIG, S.; HURTIG, E.; REMBE, M. and N. STADT (2015): Prozessabläufe im Speicherbereich bei der Injektion von Flüssigkeiten in Bohrungen - Messung und Simulation. Erdöl Erdgas Kohle 131. Jg. 2015, Heft 7/8, S. 278-284.