7/27/2019 Analytical Study of Gas Slippage

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1 BACKGROUND

Alireza Ashrafi Moghadam; Rick ChalaturnykUniversity of Alberta

Analytical Study of Gas Slippage

When the mean free path of the gas molecules is comparable tothe pore size, the classic zero velocity assumption at the pore wallsfails. Therefore the velocity at the wall has a non-zero value. Thiscondition is referred to as slip flow. !Flow in low permeability porous media typically lies in the Slip Flow

regime, therefore it can not be described by Darcy equation.!!

Klinkenberg (1941) proposed an equation to take slippage intoaccount. This equation has been the industry standard for 70 years.

Slip flow was only observed in the laboratory analysis for

conventional reservoirs. However, in Shale Gas reservoirs slip flowis also present in reservoir condition.

2 Why / PURPOSE

4 RESULTS!

Ashrafi Moghadam,A.,Chalaturnyk, R.,2013. A New Analytical Approach to Gas Slip Theory.Journal Coal Geology,InPress.;Klinkenberg, L.J 1941.The permeability of porous media to liquids and gases.APIDrilling and Production Practice,200-2 13.;Darabi, H.,Ettehad,A., Javadpour,F.,Sepehrnoori,K., 2012.Gas Flow in Ultra-Tight ShaleStrata.Journal of Fluid Mechanics,710, 641-658.;Tanikawa W.,Shimamoto,T.,2009. Comparison of Klinkenberg-Corrected Gas Permeability and Water Permeability in Sedimentary Rocks.International journal of Rock Mechanics & Mining Sciences 46,229-238.; Li,S., Dong,M., Li,Z., 2009.Measurement and Revised Interpretation of

Gas Flow Behaviour in Tight Reservoir Cores. Journal of Petroleum Science and Engineering 65,81-88.; Dong,M., Li,Z., Li,S.,Yao,J., 2012.Permeabilities of Tight Reservoir Cores Determined for Gaseous and Liquid CO2 and C2H6 Using Minimum Backpressure Method.Journal of natural Gas Science and Engineering 5, 1-5;Javadpour,F.,Fisher,D.,Unsworth, M.,2007. Nanoscale gas flow in shale gas sediments.Journal of Canadian Petroleum Technology.46(10), 5561. !!!!

Klinkenbergs Equation!

While Klinkenbergs equation is accurate for conventionalpermeabilities, deviations have been observed for ultra-low permeability

media.!!It is observed that b in Klinkenbergs equation increases withincreasing mean pressure. !!Several investigators have reported overestimation of permeability byKlinkenbergs equation. !!In Klinkenbergs analysis, a constant velocity gradient is assumed in thepores. This assumption does not hold particularly for the case of a shalepore. !

Deviation from straight line!

The assumption of constant velocity gradient is removed from Klinkenbergsanalysis. The boundary condition in a circular tube becomes: !

The equation of motion assuming continuous laminar flowof a Newtonian fluid is:!

Using the new boundary condition and comparing to Darcy and Poiseuilles equation: !

which explains why b in Klinkenbergs equation increases with pressure!

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