Predicting Dead Pore-Volume in a Porous Media fromSingle Tracer Experiment

Jyoti Phirani1, Harish Jagat Pant2 and Shantanu Roy1

1:Department of Chemical Engineering, Indian Institute of Technology - Delhi, New Delhi 110016, India

2:Isotope and Radiation Application Division, Bhabha Atomic Research Centre, Mumbai 400085, India

ID: B01-03

Dead pore volume in flow

Source: Weatherford Source: United States Geological survey

Pore space

Packed grains

Flow path

Dead volume

Reservoir scale Core scalePore scale

Pore with dead volume

• In oil reservoirs dead volume fraction can be high due to heterogeneity• Fluid is present in the pore volume, flow is negligible• Mode of transport: diffusion for solute• Leads to a long tail in a tracer impulse study

Challenge: Identifying the dead volume and flowing volume

Impact on tracer study

Flow path

Dead volume

Factors impacting the tracer study• Volume governing average residence time• Flow rate• Dispersion• Diffusion to dead volume

How do we find the dead volume?

conc

time

Diffusion in and out are slow from dead volume

Coats-Smith Method : Two tests with tracer

Two experiments not possible in real systems

Flow path

Dead volume

Flow path

Dead volume

Very slow flow rateAll volume traced

High flow rateDead volume not traced

High flow rate Slow flow rate

con

cen

trat

ion

time

Flow path

Dead volume

Medium flow rateDead volume partially traced

Need of single tracer test

Oil and gas reservoirs• Testing with two flow rates is not possible in real reservoirs• In lab studies flow rate may change dead volume of pores

Approach to find the dead volume using single tracer test• Full tracer curves are available (Theory)• Truncated tracer curves are available (Application)

Method if full tracer curve is available (ADM)

Advection dispersion model in dimensionless form

v

con

cen

trat

ion

time

Advection dispersion model with no dead volume

Two parameters to be determined Pe and τ

For closed-closed boundary conditions

Governing equations of transport with dead volume

Advection dispersion model in dimensionless form

vco

nce

ntr

atio

n

time

Advection dispersion model with dead volume

• Mean, variance, skewnessand kurtosis are required

• Laplace transform used to find the parametric values

Da

Cumulative RTD

Cumulants of the moment generating function

Moment generating function is

Cumulants

The above equations can be solved to find the parameters f, Pe, Da and τ

Truncation time will have impact on mean, variance, skewness and kurtosis of the residence time distribution

f

Given Pe =100Given td=12

Impact of truncation in experiments

Conclusions

• The dead volume impacts the residence time distribution curve and we need to find the dead volume fraction and mass transfer coefficient in the dead volume to interpret the flow behaviour in porous media

• Mean, variance, skewness and kurtosis are found, from which flow parameters can be determined for full residence time distribution curve

• The truncation error can be huge, which have been found for a few given parameters

• Generalization of the truncation error for parameter estimation is needed for the case of mass transfer in dead pore volume