## Fluid Flow in 3DEC

3DEC offers a comprehensive set of capabilities for modeling fluid flow and the effect of fluid pressures on rock/soil. It is well known that fluid pressure in rock or soil reduces the effective stress, thereby increasing the probability of failure — either slip on joints or plastic flow of solid material. It is therefore critically important to be able to consider the effect of fluid in mechanical stability analyses.

3DEC offers different levels of sophistication for modeling fluid. The user can simply specify water pressure everywhere in the model and these pressures are used to calculate effective stresses. Effective stresses are then used in the calculations to determine if there is failure of solid material or slip on joints.

A more sophisticated analysis can be done in which fluid flow is calculated based on specified material properties and fluid boundary conditions (pressure or discharge). The fluid flow calculation can be performed on its own (uncoupled) or coupled to mechanical calculations. Fluid flow calculations can be done on the joints and/or the matrix material (blocks between the joints). Fluid pressures are continuous between the joints and the matrix such that “leak-off” from the joints into the matrix can be simulated.

3DEC also offers the ability to model the flow and mechanical effect of proppant. Proppant is assumed to be composed of small particles that are transported in the fluid with the purpose of propping open fractures at the end of injection operations. Proppant flow is calculated by assuming the proppant and fluid is a mixture with some concentration. Proppant concentration changes as a result of advection. If the concentration is high enough, then the proppant will start carrying load and will effectively prop open the host fracture. Other proppant effects considered in 3DEC include gravity-induced settling, bridging and convection. The proppant logic (Detournay et al., 2016) takes into account fluid-mechanical coupling and several effects are represented, such as:

• Pack-formation (when the concentration reaches a given value, the proppant forms a pack, leaving only the fracturing fluid to flow through)
• Bridging (when the proppant stops if the fracture width is small enough, compared to the particle size)
• Proppant convection (when density gradients cause fluid motion in the fluid loaded with proppant)
• Settling (when there is a slip in velocity between slurry and proppant, caused by gravity)
• Viscosity changes as a function of proppant concentration

The following video shows simulation of proppant flowing within a single crack between two blocks (in- and out-of-the plane). Proppant concentration and fluid discharge rates are shown over the course of 40 seconds. The simulation is shown twice in the video.

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