The calculation of relative humidity in tunnels is a fundamental task when designing a repository ventilation system in a clay host rock. It requires complex numerical modeling of transient (forced) convective and conductive heat and fluid transport. The humidity of the tunnel air primarily depends (along with the meteorological conditions at the entrance) upon the thermal-hygric transitional conditions at the exposed rock surface of the tunnel walls. Some portions receive water influx while others receive heat influx from the waste already emplaced in other parts of the host rock.

The coupling between the transport processes in the host rock and the transfer processes along the tunnel wall are treated in a simplified manner. The processes described by coefficients for heat (Nusselt number) and vapor (Sherwood number) both depend on the ventilation velocity (Reynolds number). We discuss an approach involving supportive TOUGH2 computations for complex transport problems in the host rock. The results are processed and applied to the transient analysis of temperature and humidity changes in the ventilation air.

Analysis of the evaporation along a tunnel wall is supported by a one-dimensional radially symmetric EOS9 model. Results from the TOUGH2 computations with different Sherwood numbers are parameterized accordingly. The prevailing humidity along the tunnel wall is then determined with an iterative approach, whereby the humidity is controlled by either the ventilation (i.e., through the Sherwood number) or the leakage capacity of the host rock. Finally, the humidity changes in the ventilation air are derived from the computed diffusion of vapor along the boundary layer.

To calculate the heat transfer into the tunnel along its walls, we used the results from a complex geometric TOUGH2 model. The model considers different thermophysical parameters as well as the transient rates of heat production by the waste. At any given time, the heat transfer along the tunnel wall - with consideration of the then-prevailing heat production and ventilation velocity - causes a rise in air temperature and a corresponding decrease in relative humidity.