Mathematical Modeling of Preformed Particle Gel Transport in Fractured Geothermal Reservoirs

Abstract

We are developing swellable Preformed Particle Gels (PPG), which can control preferential fluid and heat flow through fracture networks to increase the performance of EGS reservoirs. Part of this development is a mathematical model and numerical simulator to simulate PPG treatments by considering coupled thermal-hydraulic-mechanical effects, and gel swelling kinetics and plugging efficiency, from which an optimized gel treatment design and operation can be achieved. The starting point for our mathematical model is the TOUGH2-CSM formulation and code. The TOUGH2-CSM fluid and heat flow formulation is based on the TOUGH2 one for multiphase, multi-component, and multi-porosity systems, with the latter including the MINC and EDFM models. The TOUGH2-CSM geomechanical formulation is based on the linear theory of elasticity for multi-porosity, non-isothermal media. We modified our formulation to simulate injection of PPG into fractures. We developed an equation of state module for gel-water systems based on a previous TOUGH2 module that handles air and water since PPGs consist mostly of water. We use experimental studies of PPG flow through fractures to obtain the PPG flow formulation. For example, experiments have shown that PPG flow rate is a nonlinear function of pressure gradient; from that, we formulated PPG flow as that of a shear-thinning fluid with a yield stress (Herschel-Bulkley fluid). Injected PPG consists of polymer-based particles that are swollen with water. When injected into a fracture whose walls are permeable, it was found that water leaks off through the fracture walls and a more concentrated PPG is deposited there as a filter cake. In addition, the transverse pressure gradient under which PPG flows can also dehydrate the PPG, resulting in a more concentrated, flowing PPG and a separate flowing water phase. These features of PPG were also incorporated into our model. Our simulator was verified by matching data from these experimental studies. They include PPG injection into an open fracture, which is used to verify our PPG rheology model, and PPG injection into a closed fracture, where the fracture is filled with PPG and leakoff from fracture pressurization causes filter cake to form. Finally, we apply our model to field conditions to ascertain the effect of PPG treatments on energy recovery from an EGS.