A Predictive Model for Viscous Fingering in Compositional WAG Floods
- J.W. Barker (Elf Geoscience Research Centre) | S.C. Evans (Elf Geoscience Research Centre)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Engineering
- Publication Date
- May 1995
- Document Type
- Journal Paper
- 116 - 122
- 1995. Society of Petroleum Engineers
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- 376 since 2007
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We present a predictive model, with no adjustable parameters, for viscousfingering in compositional WAG floods. The model is used to generate pseudofunctions which can be used in a conventional compositional simulator. Themodel is successfully applied to three test cases including one in a simpleheterogeneous reservoir.
Viscous fingering is an instability which occurs when a more mobile (lessviscous) fluid displaces a less mobile (more viscous) fluid in a porous medium.In this study, we have considered viscous fingering in WAG (Water AlternatingGas) floods, in which water and gas are simultaneously injected to displaceoil. The main purpose of injecting water along with the gas is to reduce themobility ratio between the injected fluids and the oil. However, it may not bepossible to stabilise the displacement completely if the mobility of the oil isparticularly low (i.e. if its viscosity is relatively high). Thus, viscousfingering can still occur in WAG floods.
We also focus here on compositional WAG floods, by which we mean cases wherethe phase behaviour of the oil and gas is modelled using multiple hydrocarboncomponents and an equation of state. This is much more general than afirst-contact miscible WAG flood, in which the oil and gas are miscible in allproportions and can be modelled without an equation of state as just twocomponents.
The scale at which viscous fingering occurs is generally much smaller thanthe size of grid blocks used in reservoir simulation, where it is usually notpossible to resolve any fingering explicitly. An empirical model is thus neededto represent the effects of fingering. In this study, we have developed justsuch a model for compositional WAG floods. This model is predictive in thesense that there are no adjustable parameters which must be 'tuned' forparticular cases. The model is an extension of earlier models developed forsimpler cases, as described in the next section.
One of the best known empirical viscous fingering models is that of Todd andLongstaff. Their model applies only to first-contact miscible gas floods (i.e.with no mobile water present), and has an adjustable parameter . Another wellknown model is that of Koval, which also applies only to first-contact misciblegas floods, and which is in fact equivalent to the Todd and Longstaff model interms of fractional flow. Further, Koval's model has no adjustable parameter,and can be used to fix the parameter in the Todd and Longstaff model.
The Todd and Longstaff model, with calculated as a function of the mobility(viscosity) ratio using Koval's formula, has been shown to compare well bothwith experiments and with high resolution simulation.
Blunt and Christie' developed an empirical fingering model for first-contactmiscible WAG floods. Their idea was to apply the Todd and Longstaff model tothe gas (solvent) fractional flow and total hydrocarbon mobility, but using thetotal mobility ratio at the flood front and Koval's model to calculate . Thiswas an improvement on previous studies which had attempted to recalibrateempirically by comparison with detailed simulations. However, the relativepermeabilities for the water and hydrocarbon phases were left unaltered in theBlunt and Christie model.
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