Alternative equation for sorption data interpretation Patrick van Hemert & K-H.A.A. Wolf

1. Alternative equation for sorption data interpretationPatrick van Hemert & K-H.A.A. Wolf International Symposium CBM, Tuscaloosa May 25, 2006

2. Objectives • For experts: • Introduce alternative equation for sorption interpretation • Simpler calculation • Easier error analysis • For non-experts: • Basic understanding of volumetric sorption isotherms measurements

3. Outline • Relevance • Introduction to volumetric sorption • Alternative formula for interpretation • Comparison to original formula • Conclusion

4. Reasons for measuring sorption isotherms • Determine Gas Storage Capacity • Used for Gas In Place analysis • Determine fluid-solid interaction • Reservoir models • Science

5. Typical laboratory output: The Langmuir • X-axis is usually pressure in either bar, psia or Mpa. • Y-axis is usually sorbed gas in mol/kg, or SCF/Ton

6. What are volumetric isotherms? • Isothermal experiments. • Material balance calculations from P,T,V data • Procedure consist of two steps, isolated(1) and connected(2) • Sorbed amount is the difference between the total amount and the equilibrium amount of gas

7. vacuum Valve 1 P Valve 2 sample cell 0 Sorption experimental procedure Representation of the two experimental steps in a sorption experiment Gas supply Gas supply - - 2 1 From N. Siemons

8. Pressure development during an experiment

9. Sorption is a material balance differencecalculation M: Measured point

10. Determination of volume ratio from material balance conservation • For micro-porous solids needs to be experimentally determined • Helium sorption experiments with the assumption that helium sorption is negligible

11. Alternative formulation for sorption interpretationsimplifies error analysis Total Equilibrium Sorbed Scale Void volume ratio sample and reference cell (defines the dividing surface) Each parameter can separately be calculated

12. High pressure volumetric isotherms are very sensitive • Changes in the volume ratio have a large effect • The use of an wrong densities has large effects

13. Previous formulation is unnecessarily difficult Total Sorbed Scale Scale Equilibrium • Redundant terms in equilibrium amount • Real gas law formulation unnecessarily complicated • Void volume is not independently measured • This unnecessarily complicates error analysis!

14. The alternative equation for volumetric sorption interpretation has the following advantages: • Physical interpretation is straightforward • Easy to calculate • Simple error analysis • Contains only independent parameters

15. Questions?

16. Alternative formulation for sorption simplifies error analysis

17. (A.1) Experimental uncertainties from alternative equation (A.9)

18. Alternative formulation for sorption interpretation Total Equilibrium Sorbed Scale Volume ratio sample and reference cell The sorbed amount is calculated from the difference in material balance between the total amount of gas and the equilibrium amount of gas.

19. Alternative formulations require unknown parameters

20. Gibbs sorption is the only rigorous thermodynamic framework for adsorption equilibrium • The extent and density of the sorbed phase can not be measured independently or directly. • Gibbs suggested the mathematical transformation that all fluid-solid interaction is attributed to a dividing surface. • In micro-porous solids measuring the dividing surface is an experimental challenge. • This constitutes an ill-defined problem.

21. What causes the considerable differences between inter-laboratory sorption experiment? • Investigation into the nature of the measurements • Quantification of the accuracy and precision of the measurements

22. Introduce alternative formula for interpretation of volumetric sorption experiments • Calculation is simpler • Error analysis is easier • More straightforward interpretation

23. Enhanced Coalbed Methane production may be a commercial energy source • Underground coal contains ,mainly sorbed, methane • Coalbed Methane projects (CBM) produce methane by pumping gas and water from the reservoir • Enhanced Coalbed Methane (ECBM) projects may enhance production by injecting gas • Gas-solid interactions determine production behavior

24. Optimizing ECBM requires knowledge of gas-coal interactions • Equilibrium adsorption data quantify fluid-solid interaction • Pure component isotherms are the simplest form of adsorption equilibrium data • Methane isotherms on coal are already used to quantify the amount of methane producible

25. Sorption isotherms are measured volumetrically • Volumetric technique is very widespread • Procedures and apparatus are easily obtainable • Actively used in the field of (E)CBM • Gravimetric sorption measurements are less common • More complex equipment and procedures

26. Reliability of sorption isotherms is often omitted • Every measurement has an associated uncertainty • This uncertainty quantifies the measurements’ significance • Reliability estimates from error analysis and repeated experiments should concur.

27. Inter-laboratory isotherms differ considerably • Repeated (inter-laboratory) experiments are the best reliability estimators • The associated experimental errors must be specified. • The cause of the difference must be investigated

28. Sorption is a material balance difference calculation