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

Technical Geosciences Delft University of Technology, The Netherlands Objectives For experts: Introduce alternative equation for sorption interpretation Simpler calculation Easier error analysis For non-experts: Basic understanding of volumetric sorption isotherms measurements

Technical Geosciences Delft University of Technology, The Netherlands Outline Relevance Introduction to volumetric sorption Alternative formula for interpretation Comparison to original formula Conclusion

Technical Geosciences Delft University of Technology, The Netherlands Reasons for measuring sorption isotherms Determine Gas Storage Capacity Used for Gas In Place analysis Determine fluid-solid interaction Reservoir models Science

Technical Geosciences Delft University of Technology, The Netherlands 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

Technical Geosciences Delft University of Technology, The Netherlands 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

Technical Geosciences Delft University of Technology, The Netherlands Gas supply Valve 1 Valve 2 sample cell P 0 vacuum - Gas supply Sorption experimental procedure Representation of the two experimental steps in a sorption experiment From N. Siemons

Technical Geosciences Delft University of Technology, The Netherlands Pressure development during an experiment

Technical Geosciences Delft University of Technology, The Netherlands Sorption is a material balance difference calculation M: Measured point

Technical Geosciences Delft University of Technology, The Netherlands 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

Technical Geosciences Delft University of Technology, The Netherlands Alternative formulation for sorption interpretation simplifies error analysis Void volume ratio sample and reference cell (defines the dividing surface) Each parameter can separately be calculated

Technical Geosciences Delft University of Technology, The Netherlands 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

Technical Geosciences Delft University of Technology, The Netherlands Previous formulation is unnecessarily difficult Redundant terms in equilibrium amount Real gas law formulation unnecessarily complicated Void volume is not independently measured This unnecessarily complicates error analysis!

Technical Geosciences Delft University of Technology, The Netherlands 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

Technical Geosciences Delft University of Technology, The Netherlands Questions?

Technical Geosciences Delft University of Technology, The Netherlands Alternative formulation for sorption simplifies error analysis

Technical Geosciences Delft University of Technology, The Netherlands Experimental uncertainties from alternative equation (A.1) (A.9)

Technical Geosciences Delft University of Technology, The Netherlands Alternative formulation for sorption interpretation 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.

Technical Geosciences Delft University of Technology, The Netherlands Alternative formulations require unknown parameters

Technical Geosciences Delft University of Technology, The Netherlands 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.

Technical Geosciences Delft University of Technology, The Netherlands 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

Technical Geosciences Delft University of Technology, The Netherlands Introduce alternative formula for interpretation of volumetric sorption experiments Calculation is simpler Error analysis is easier More straightforward interpretation

Technical Geosciences Delft University of Technology, The Netherlands 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

Technical Geosciences Delft University of Technology, The Netherlands 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

Technical Geosciences Delft University of Technology, The Netherlands 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

Technical Geosciences Delft University of Technology, The Netherlands 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.

Technical Geosciences Delft University of Technology, The Netherlands 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

Technical Geosciences Delft University of Technology, The Netherlands Sorption is a material balance difference calculation