Proppant Bank Buildup in a Vertical Fracture Without Fluid Loss
Authors: Schols R.S. , Visser W. 
Published: December 2007

This paper was prepared for the SPE-European Spring Meeting 1974 of the Society of Petroleum Engineers of AIME, held in Amsterdam, the Netherlands, May 29–30, 1974. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by whom the paper is presented. Publication elsewhere after publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon request to the Editor PETROLEUM ENGINEERS JOURNAL is usually granted upon request to the Editor of the appropriate journal provided agreement to give proper credit is made.
Discussion of this paper is invited. Three copies of any discussion should be sent to the Netherland Section of the Society of Petroleum Engineers, P. O. Box 228, The Hague, the Netherlands. Such discussion may be presented at the above meeting and, with the paper, may be considered for publication in one of the two SPE magazines.

Abstract
An experimental and theoretical study has been made of the build-up of a proppant bank in a non-leaking fracture of constant width during a conventional fracturing treatment with a low-viscous fracturing fluid. The results indicate that the build-up of a proppant bank can be considered to take place in proppant bank can be considered to take place in three consecutive phases. During the first phase the bank builds up gradually as a function of time until an equilibrium height H(e) is reached near the well bore and the bank stops-growing at this point as a result of the erosion caused by the increased fluid drag forces on the proppant particles. During the second phase the bank grows only in height until it reaches He over its full length. Finally, in the third phase the bank grows only in length and the injected proppant saltates over the full length of, the bank towards the bank's front where it settles, increasing the length of the bank in the direction of flow. The analytical relations derived for each of these phases in bank build-up have been confirmed by experiments in a transparent model. The observed disturbance of the proppant bank close to the well bore, induced by the jetting effect of the injected proppant slurry, might be a major 'bottle-neck' in obtaining effective fractures. This phenomenon should be investigated extensively. phenomenon should be investigated extensively.

Introduction
Productivity improvement in oil and/or gas wells Productivity improvement in oil and/or gas wells obtained with a conventional hydraulic fracturing treatment depends mainly on fracture length and fracture conductivity. Both length and conductivity are directly related to the efficiency with which a fracture can be filled with proppant material. During a conventional treatment with a low-viscous fracturing fluid the injected proppant material will settle and form a bank at the bottom of the fracture. Only that part of the fracture where a bank is formed contributes to actual fracture length and conductivity, because this part remains open after the fracture is allowed to close. Therefore, knowledge of the dimensions of the bank formed and its rate of build-up is required for a proper hydraulic fracturing design. We have studied proper hydraulic fracturing design. We have studied this both theoretically and experimentally.

2. THEORETICAL DESCRIPTION OF PROPPANTBANK BUILD-UP IN A RECTILINEAR VERTICAL FRACTURE
In the description of a proppant-bank build-up we considered a rectilinear vertical fracture of uniform width and height extending from line well bore into a non-dipping formation. It was assumed that no fluid losses occur through the fracture faces. The proppant material is considered to be of uniforms size and homogeneously suspended in a Newtonian incompressible fracturing fluid with a constant temperature.