A New Technique for Proppant Schedule Design

This study introduces a novel methodology for the design of the proppant pumping schedule for a hydraulic fracture, in which the final proppant distribution along the crack is prescribed. While the design is based on the assumption that the particles have relatively weak impact on the fracture propagation, the validity of this assumption can be tested a posteriori. This makes it possible to relate the proppant velocity to the clear fluid velocity inside the fracture, which is calculated assuming no proppant. Having the history of the clear fluid velocity distribution, the prospective proppant motion can be computed. Volume balance is then used to relate the final concentration at some point inside the fracture to the corresponding input concentration at a specific time instant, which helps to avoid solving an inverse problem. One exceptional feature of the approach lies in the fact that it is applicable to multiple fracture geometries and can be implemented using various hydraulic fracturing simulators. To verify the technique, two fracture geometries are considered Khristianovich-Zheltov-Geertsma-De Klerk (KGD) and pseudo-3D (P3D). It is shown that the developed approach is capable of properly estimating the pumping schedule for both geometries. In particular, the proppant placement along the fracture at the end of the pumping period, calculated according to the adopted proppant transport model, shows close agreement with the design distribution. Comparison with Nolte’s scheduling scheme shows that the latter is not always accurate, and cannot capture the essential differences between the schedules for the fracture geometries considered. Hydraulic fracturing (HF) is a process in which a viscous fluid that is injected into a fracture drives crack propagation. Use of proppant prevents complete closure of the fracture after pumping has stopped and the fluid has leaked off. Despite the fact that many studies have been devoted to proppant transport modelling and investigating the effects of settling, Daneshy (1978), Mobbs and Hammond (2001), Shokir and Al-Quraishi (2007), only a few consider the design of a proppant schedule Crawford (1983), Nolte (1986), Meng and Brown (1987), Gu and Desroches (2003). The appropriate proppant schedule is as important as the correct prediction of the fracture footprint, since it directly affects the proppant distribution inside the fracture, and thus influences the conductivity and the production rate. One of the most common approaches for generating the pumping schedule is a protocol developed by Nolte (1986). This is a very convenient method, as it provides an analytical formula for the schedule for a given efficiency, total pumping time, and a desired (uniform) concentration inside the fracture at the end of the job. The approach is based on the conservation of volume, and the estimation of the total volume of fluid that leaks off during the HF treatment. A power-law type schedule is then suggested and the exponent is calculated based on the proppant volume balance. Not being tied to any fracture geometry, this scheduling approach is considered applicable to multiple fracture geometries, such as PKN or radial. The universality, the consistency with the global balance laws, and the ease of use are possibly the main reasons why this scheduling methodology is commonly used, see e.g. Economides and Nolte (2000), Rahman and Rahman (2010). There is an alternative method, developed in Gu and Desroches (2003), which suggests using an iterative scheme together with an appropriate proppant transport model to solve an inverse problem to generate a pumping schedule. The basis of that procedure is to divide the schedule into intervals and then adjust the input concentration values iteratively based on the results of the forward problem solution using the previous schedule. In principle, this iterative algorithm can yield the most accurate solution, however the accuracy and the required computational resources depend heavily on the complexity of the forward model. It would be desirable to develop a proppant scheduling methodology that is more accurate than Nolte’s method, but less computationally challenging than the iterative procedure described by Gu and Desroches. To facilitate this, the proppant is assumed to have a minor impact on fracture propagation. This allows us to avoid an iterative scheme and lengthy simulations with proppant transport. At the same time, the influence of the fracture geometry and other features that can be built into a HF simulator are taken into account. One of the biggest advantages of the proposed technique is its applicability to various HF simulators, which do not need the ability to model the proppant transport itself, see the examples of such simulators in Adachi et al. (2007), Peirce and Detournay (2008). The paper is organized as follows: Section 2 outlines the procedure for the method; then Sections 3 and 4 illustrate the implementation for KGD and P3D fracture geometries, respectively; and, finally, Section 5 compares different schedules (including Nolte’s schedule) and discusses the applicability and possible extensions of the approach. Idea behind estimation of pumping schedule Assume that the properties of the rock, the fluid and the proppant, as well as the pumping rate are all known and fixed. Before a pumping schedule can be designed, the following target characteristics need to be prescribed by the user: i. the geometry of the hydraulic fracture (HF), which can be interpreted as the type of HF model that is used for the design, such as KGD, radial, PKN, P3D, or a fully planar HF solver. Introduction Peer Reviewed