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Meaning of fugacity in GWB (difference between two reaction paths, simple and sliding)


Neda
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Hello,

 

I am struggling with the meaning of fugacity and the way it is defined in GWB and I appreciate if you could help me to clarify my confusion.

 

I am simulating gas injection into a closed system (minerals and brine) that is initially at equilibrium. I found I can add the gas as a reactant substance to my system either using simple or sliding (fugacity) option.

 

The partial pressure of the gas is needed to reach to a certain value. By doing simple calculations for my system, to have a partial pressure of 3.5 bar, I need 0.5 mole of the gas. Fugacity coefficient in my case is 1.02, so fugacity is almost equal to the partial pressure.

 

 

I created two models using different reaction paths for an identical system. In the first model I added 0.5 of gas using simple option and in the second model I used sliding and set the fugacity to 3.5, the value that should be reached by adding 0.5 mole gas. Results I got from these simulations are hugely different. When I plotted the result from the first simulation I found 0.5 mole injected gas creates fugacity of order of 1e-6 in the gas phase while I was expecting a value of 3.5.

 

I really need to understand the meaning of fugacity in GWB to be able to have a realistic model to represent operational condition for my system. It seems setting small value for fugacity through sliding modelling acts as if I added huge amount of gas (in terms of mole) and I don't understand the reason. I would greatly appreciate your help. Thanks.

 

Best,

 

Neda

 

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Hi Neda,

 

When you add a gas as a simple reactant, it doesn't all stay in the gas phase. All it does is change the composition of the fluid-rock system, which is then free to evolve (i.e. minerals can precipitate or dissolve, buffering reactions can occur, etc.). In fact, the nature of the simple reactant doesn't affect the calculation. It could be an aqueous species, a mineral, a gas, or even an oxide with no thermodynamic stability. All that matters is the bulk composition of the simple reactant.

 

There's no harm in setting a larger simple reactant mass than you think you need. Just run the model, plot X reacted on the x axis and fugacity of X gas on the y axis, and you'll be able to see how much reactant is needed to reach a certain fugacity. You may need to adjust delxi, the maximum time step in reaction progress, if the system's chemistry is changing very rapidly.

 

For more on simple reactants, please see Chapter 13, Mass transfer, in the Geochemical and Biogeochemical Reaction Modeling text. For an explanation of delxi, please see the React section of the GWB Reference Manual.

 

Hope this helps,

 

Brian Farrell

Aqueous Solutions

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Dear Brian,

 

Thanks for your reply, I very much appreciate it.

 

The fact is that I am doing geochemical simulations for a gas storage study and my objective is to somehow represent the operational condition in my simulations. Having total size of the reservoir, gas injection rate and duration of injection, total mass of the stored gas which is inside the reservoir is known. The intention of my work is to see how this gas would disturb brine-mineral equilibrium in different conditions. As I mentioned before by downscaling the reservoir scale to the study scale, 0.5 mole gas should provide almost 3.5 bar partial pressure or fugacity for my system.

 

 

I understand that all introduced gas through simple option doesn’t stay in the gas phase, but to have fugacity of 3.5 bar almost 135 mole of gas is needed (I found this value after plotting fugacity and reactant mass). The results then vary extremely in these cases and I am very confused which one is actually consistent and reliable for my case. I also played with the delxi value but it doesn’t have much influence on the final results.

 

 

I started to make an equilibrium model in which both minerals and gas are modelled at equilibrium, then I made kinetic model for minerals and in the end I introduced gas kinetically. In all simulations, operational range (either gas mass or fugacity) is crucial for my results and conclusions.

 

 

I would appreciate your advice and recommendations for this case study to find the most consistent way to represent the stated operational condition. Thanks so much in advance for your reply.

 

Best regards,

Neda

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Hi Neda,


Regarding the sliding fugacity path vs. titration path, both should yield qualitatively similar results, at least in terms of what has happened by the end of a reaction path. In my mind, at least, the sliding fugacity path helps one with "what if" type questions, whereas a titration path helps with "how". I would probably go with the titration path in this case. For more on sliding fugacity paths, including an interesting note on sliding a value vs. its logarithm, please see section 14.3, Sliding activity and fugacity paths, in the GBRM text.


Here's another thought. I’m assuming you’re still talking about adding H2(g). Does your estimate of 0.5 moles of gas ignore chemical reaction? The H2 fugacity is tied to the H2(aq) concentration (or rather, its activity), so try taking a look at the concentration of the H2(aq) species as you titrate in the H2(g). If its concentration is not increasing as you titrate in the gas, it must be consumed by reaction. Do you have any HCO3- or SO4 in the water that are being reduced to CH4 or HS-? Are minerals dissolving? Take a look at what changes in your system and consider whether those reactions would be expected in the real world. If they wouldn’t occur, you may need to prevent them from forming by suppressing them. If they’d occur slowly, but perceptibly, you may need to incorporate more kinetic reactions.


Hope this helps,

Brian
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Hi Brian,

 

Thanks for your reply.

 

Yes I am still working on H2 (g) storage problem. As you might remember we already did some studies (at equilibrium) using GEMS (http://gems.web.psi.ch). I set up the same model in GWB and despite using different thermodynamic database and using different models for gas, at equilibrium I got consistent results with my previous model in GEMS which made me sure that the setup of the model was done correctly. In our previous work we didn’t consider operational condition range in real storage operation and now with GWB and by having kinetic modelling option this study is possible.

 

In the equilibrium model, adding 0.5 mole has really negligible effect on the system. In fact I can define a window for operational condition [0.5 to 10 mole (maximum pressure that can be reached for hydrogen)]. In case of adding 10 mole H2(g), changes in the system are minor but noticeable. In all cases HCO3- and SO4 in the water were reduced to CH4 and HS-.

 

I integrated kinetic rates of minerals to my model as my second study. For the time span of the study that I considered one year, kinetics highly restricts any precipitation or dissolution, but pH is strongly under influence of hydrogen (in comparison with the equilibrium model, kinetic model results to higher H2(aq) concentration, H2(g) fugacity, and pH while changes of mineral abundance is much more less. So in this case knowing the operational window is even more critical.

 

In my third study, I decided to add hydrogen kinetically to limit its dissolution in water and prevent the high increase of pH. In this case I can only work with fugacity as GWB only take fugacity as the input. So I need to properly understand the relation between added H2 and fugacity. If I use the H2 (g) fugacity value that I get after running kinetic model (1e-5 to 1e-3) then adding hydrogen could have almost zero impact on the system while using 3.5 bar fugacity can be considered tricky and at some level problematic for the real operations. I attached some of the plots of the equilibrium and kinetic model (case study of 0.5 mole added H2(g)) for your consideration. Thank you.

 

Best,

 

Neda

 

results_kinetic_ equilibrium_ 0.5 mole H2.compressed.pdf

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  • 2 weeks later...

Hi Neda,

 

Thanks for the scripts. I took a look at them, but you're using a non-default thermo dataset so I couldn't run them. I managed to replicate one of them closely by ignoring the mineral Ankerite, which I don't have in any thermo dataset. After playing around, I have some thoughts. It seems quite a bit of the H2 is consumed reducing carbonate to methane and that the associated fluid changes are causing most of the carbonate mineral dissolution in your models. The carbonate minerals replenish carbonate to the fluid as they dissolve, so there's always some available to react with the H2. I'm not sure how quickly the H2 and carbonate would react in your reservoir, but you might benefit by considering the kinetics of a redox reaction like 4*H2(aq) + HCO3- + H+ -> CH4(aq) + 3*H2O. If you disable other redox coupling reactions, (for example, between HCO3- and acetate), then you'll limit how much of the H2 is consumed and potentially allow its fugacity to build up.

 

Regards,

Brian

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Dear Brian,

 

Thanks so much for the reply. My sincere apologies for not having attached the thermo dataset. Unfortunately my license is expired and I can’t proceed with further modelling. Thank you so much again for all the support.

 

Best,

Neda

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