Recent observations inspired a new mechanistic model of gel propagation and dehydration in fractures. Consistent with our experimental results, this model assumed the following:
where ul is the average leakoff rate for that vicinity. The process of transforming an element of mobile gel into concentrated, immobile gel may occur very rapidly. However, for the purposes of our model, this transition does not need to occur in zero time.
The fraction of surface that contacts mobile gel decreases with time as more immobile gel forms (see above figure). Based on area and mass balances, the fractional area covered by concentrated gel at a given time and vicinity is approximated by:
Presumably, as mobile gel in a wormhole dehydrates, a thin layer of concentrated gel forms at the fracture surface. However, this thin layer is continually pushed aside by the leakoff water or mobile gel, and the concentrated gel is added to the accumulation of immobile gel at the sides of the wormhole. Our model works reasonably well when the right side of Eq. 8 is taken to any power between 0.25 and 4.
Combining Eqs. 1 to 5 yields Eq. 6, which is the basis of the new model. The model predicts the leakoff rate (i.e., the rate of gel dehydration) at a given time and distance along the gel-contacted portion of a fracture.
The denominator of Eq. 6 reflects the rate of loss of fracture surface that is contacted by mobile gel (i.e., the wormhole-contact area). For our 24-hr-old Cr(III)-acetate-HPAM gel [0.5% Alcoflood 935, 0.0417% Cr(III) acetate], um has a value around 4 ft/d, which translates to a kgel value around 1 md. The latter value was confirmed from independent experiments. Calculations reveal that after 1 minute of gel contact, at least 50% of the fracture face is covered by concentrated gel rather than fresh gel (see figure above). Within 30 minutes of gel contact, more than 90% of the fracture face is covered by concentrated gel.
At a given distance along a fracture, the new model predicts that the wormhole area diminishes and the wormholes become more widely spaced with time. Consequently, one might expect pressure gradients to develop within the fracture transverse to the direction of flow. However, the compliant nature of the gel (even concentrated gel) mitigates the development of these transverse pressure gradients.