Wormhole growth and interaction in a large sand pack

Cold production is a non-thermal process in which sand is intentionally produced with oil in order to enhance oil recovery. In order to develop a full numerical model using a reservoir simulator, of the cold production process, it is necessary to know the effect of producing large quantities of sand on the overall permeability of the formation. A pressure depletion experiment was performed in order to simulate the production of sand, oil and gas into perforations in a well and within the formation during the cold production process. A numerical simulation of the flow of oil and gas into the orifices before sand production was used to calculate the pressure gradient at the orifices. A significant interference effect was observed during wormhole growth in the sand pack saturated with live oil with two vertically aligned orifices at one end. A sand-filled channel (wormhole) 36 cm in length by 17 cm in diameter developed from the top orifice, whereas only a small sand-filled cavity developed from the bottom orifice. The calculated pressure gradient at the top orifice at the onset of sand production (7.5 MPa/m) was slightly higher than at the bottom orifice (7.1 MPa/m). The growth of the top wormhole decreased the pressure gradient at the bottom orifice and therefore prevented the growth of a bottom wormhole. The experiment suggests that wormholes do not develop from each perforation in a well. ow of oil and gas at the surface of a stationary wormhole, similar in size to the top wormhole, was modeled numerically for two different boundaries: (1) a 30-cm diameter, 80-cm long sand pack, and (2) an 80-cm oil sand hemisphere. The calculated pressure gradients at the surface of the wormhole within the 80-cm sand hemisphere were one order of magnitude larger than the pressure gradients at the surface of the wormhole within the sand pack. These simulations suggest that the diameter of wormholes in the field is significantly greater than 17 cm. The wormhole was composed of a central channel of loose sand surrounded by concentric tensile failure bands. These tensile failure bands likely weaken the sand at the surface of the wormhole and allow it to be produced more easily. This weakening effect would explain the lower pressure gradients calculated at the surface of the wormhole compared to the critical pressure gradient for sand production predicted by Bratli and Risnes [SPE J. (April 1981) 236].