How to apply this unique Mix of Neuman + Dirichlet Boundary conditions, for Temperature & Pressure, 1-d Problem

Hello everyone
I am trying to setup a 1-D validation problem from a research paper for validating experimental results.
In short, I need to apply Neuman & Dirichlet Boundary conditions, for Pressure & Temperature
For Neuman: I need to set the block as Inactive, its done Neuman!!! (P,T both )
For Dirichlet i need to set INCON
But the problem is At one boundary: I need to set Temp as Neuman & Pressure as Dirichlet, How to do this???
Kindly see the pic...attached
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I think the trick on the right side is to connect that boundary to an element with VERY large volume (~1.0E50). This will hold both the pressure and temperature constant at that boundary. Let me ask you this before I fully commit to this response... is this an isothermal simulation? I see there is no heat flux entering or exiting the system through the boundaries. Does the temperature within the elements also remain fixed over time? If so, there's a much easier (and more efficient) way of solving your problem.
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So what you're aiming to get is an isobaric, adiabatic boundary on the other side. This trick can be done. This trick can be done by assigning the large volume element imposing Dirichlet conditions to a material type with a large heat capacity as well. You'll still get a heat flux through into that element, but it will be absorbed with negligible temperature changes by the large heat capacity. This setting can be changed in the SPHT variable at the end of the first line of the ROCKS block listing. Make sure this element has a very large volume (1.0E50) in the ELEME block and very small (1.0E-10) distance to the interface on the CONNE block. I cannot tell you what to do about anything specific to TOUGH+Hydrate, but I believe this should address the original issue you brought up here.