The simulator is based on an elastic fracture opening equation, a power-law fluid flow equation, and a proppant transport equation. The fluid indices are empirical functions of the proppant concentration and temperature. The finite element method is applied to carry out the calculation. Simulated results show that the fracture grows initially without proppant. As pumping continues, proppant screens out at the fracture tip arresting further fracture growth, and thereafter the fracture width becomes wider and the net borehole pressure increases rapidly as proppant concentration inside the fracture increases. In general, the fracture opening width increases with decrease of rock modulus and fluid leakoff rate, but the relationship is not linear. The distribution of proppant inside the fracture affects significantly the size and the opening width of the fracture.
The frac-pack technique has been successfully applied to under-consolidated and high permeability reservoirs to control sand production and to improve fracture conductivity for many years. The technique is evolved from the phenomenon of tip-screen-out (TSO) which is often observed in hydraulic fracturing of a high permeability rock formation. The phenomenon and a general discussion of the frac-pack treatment can be found in a survey paper by Ellis (1998) and in technical papers by Smith et al (1994, 1987). Papers by Wong et al (1993), Roodhart et al (1993), and Hannah et al (1993) presented a comprehensive review on the design, execution, and evaluation of the frac-pack treatment in the field. The frac-pack treatment and its application to horizontal wells was discussed by Abass et al (1993) from the view point of rock mechanics. An attempt was also made to model the frac-pack phenomenon for estimating the fracture dimensions by Fan and Economides (1995).
A true 3-D frac-pack simulator is presented in the following paragraphs. The simulator is based on an elastic fracture opening equation, a power-law fluid flow equation, and a proppant transport equation. The fluid indices are empirical functions of the proppant concentration and temperature. A summary of governing equations is presented in Section 2. A discussion of the simulated results is presented in Section 3. The frac and pack process is demonstrated and discussed in reference to a set of simulated results. Simulated results have shown that the distribution of proppant inside the fracture is not uniform, and the distribution affects significantly the size and the opening width of the fracture. Since the final shape and size of the fracture is determined at the time when fracture tip screen-out occurs, it is shown that the size and the opening width of the fracture can be controlled by alternating the pumping schedule. A set of calculated results is also compared and discussed with the field data presented by Hannah et al (1993). The agreement between the calculated and observed results is remarkably good.
