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Lecture：Proppant flow in the wellbore and its distribution between perforations

Lecturer：Egor Dontsov Chief Scientist,Professor

Time: 9:00-10:30 am, Jan. 6^th(Saturday), 2024

Venue: A536, Minglilou Building

Bio：Egor Dontsov is a scientist with over ten years of academic and industrial experience. Prior to joining ResFrac, Egor worked at W.D. Von Gonten Laboratories, the University of Houston as Assistant Professor in the Department of Civil and Environmental Engineering, and the University of British Columbia as Postdoctoral Research and Teaching Fellow in the Mathematics Department. He earned his Ph.D. degree in Civil Engineering at the University of Minnesota and Bachelor’s degree with honors in Physics at Novosibirsk State University. Egor’s primary expertise area lies in theoretical and numerical modeling of hydraulic fracturing, proppant transport, and geomechanics. He has written and been exposed to the development of several academic and commercial simulators of hydraulic fracturing, proppant transport, and reservoir flow. Egor served as a reviewer for dozens of journals and several scientific proposals within and outside of the US, invited multiple times to give keynote lectures and seminars, as well as participated in organization of minisymposia at international conferences and workshops. Egor has published over fifty peer reviewed papers and received several awards, including Outstanding Technical Editor Service Award from SPE Journal in 2018, N.G.W. Cook award, as well as Best Dissertation award from University of Minnesota to name a few.

Abstract：This report presents a model to simulate behavior of particle-laden slurry in a horizontal perforated wellbore with the goal of quantifying fluid and particle distribution between the perforations. There are two primary phenomena that influence the result. The first one is the non-uniform particle distribution within the wellbore’s cross-section and how it changes along the flow. The second phenomenon is related to the ability of particles to turn from the wellbore to a perforation. Consequently, the paper considers both of these phenomena independently at first, and then they are combined to address the whole problem of flow in a perforated wellbore. A mathematical model for calculating the particle and velocity profiles within the wellbore is developed. The model is calibrated against available laboratory data for various flow velocities, particle diameters, pipe diameters, and particle volume fractions. It predicts a steady-state solution for the particle and velocity profiles, as well as it captures the transition in time from a given state to the steady-state solution. The key dimensionless parameter that quantifies the latter solution is identified and is called dimensionless gravity. When it is small, the particles are fully suspended and the solution is uniform. At the same time, when the aforementioned parameter is large, then the solution is strongly non-uniform and resembles a flowing bed state. A mathematical model for the problem of particle turning is developed and is calibrated against available experimental and computational data. The key parameter affecting the result is called turning efficiency. When the efficiency is close to one, then most of the particles that follow the fluid streamlines going into the perforation are able enter the hole. At the same time, zero efficiency corresponds to the case of no particles entering the perforation. Solutions for the both sub-problems are combined to develop a model for the perforated wellbore. Results are compared (not calibrated) to a series of laboratory and field scale experiments for perforated wellbores. Comparison with the available computational results is presented as well. In addition, the comparison is presented in view of the parametric space defined by the dimensionless gravity and turning efficiency. Such a description allows to explain seemingly contradictory results observed in different tests and also allows to highlight parameters for which perforation orientation plays a significant role.

Organizer and Sponsor：

School of Civil Engineering and Geomatics, SWPU

Institute of Science and Technology Development, SWPU