Abstract
When filter-cake-building additives are used in fracturing fluids, the commonly applied static, 30-minute API filtration test is unsatisfactory, because in a dynamic situation (like fracturing) the formation of a thick filter cake will be inhibited by the shearing forces of the fracturing fluid. A dynamic, filter-cake-controlled, leakoff coefficient that is dependent on the shear rate and shear stress at the fracture face is, therefore, introduced. A test apparatus has been constructed in which the fluid leakoff is measured under conditions of temperature, rate of shear, duration of shear, and fluid-flow pattern as encountered under fracturing conditions. The effects of rock permeability, shear rate, and differential pressure on the permeability, shear rate, and differential pressure on the dynamic leakoff coefficient are presented for various, commonly used fracturing-fluid/fluid-loss-additive combinations.
Introduction
An important parameter in hydraulic fracturing design is the rate at which the fracturing fluid leaks into the formation. This parameter, known as fluid loss, not only determines the development of fracture length and width, but also governs the time required for a fracture to heal after the stimulation treatment has been terminated. The standard leakoff test is a static test, in which the effect of shear rate in the fracture on the viscosity of the fracturing fluid and on the filter-cake buildup is ignored.
Dynamic vs. Static Tests
The three stages in filter-cake buildup arespurt loss during initiation of the filter cake,buildup of filtercake thickness, during which time leakoff is proportional to the square root of time, andlimitation of filter-cake growth by erosion.
In the standard API leakoff test, 1 the fracturing fluid, with or without leakoff additives, is forced through a disk of core material under a pressure differential of 1000 psi [7 MPa), and the flow rate of the filtrate is determined. In such a static test, the third stage-erosion of the filter cake-is absent. In a dynamic situation there is an equilibrium whereby flow along the filter cake limits the filter-cake thickness, and the leakoff rate becomes constant. The duration of each of these stages depends on the type of fluid, the type of additive, the rock permeability, and the test conditions.
The differences between dynamic and static filtration tests are shown in Fig. 1, where the cumulative filtrate volume (measured in some experiments with the dynamic fluid-loss apparatus described below) is expressed as a function of time (Fig. la) and as a function of the square root of time (Fig. ]b), The shear rate at the surface of the disk is either static (O s -1 ), or 109 s -1 or 611 s -1. The curves indicate that the dynamic filtration velocities are higher than those measured in a static test and increase rapidly with increasing shear rate. This is in agreement with the observations made by Hall, who used an axially transfixed cylindrical core sample along which fracturing fluid was pumped, while the filtrate was collected from a bore through the center. Fig. la shows how the lines were drawn to fit the data:
Vc = Vsp + A t + Bt, .........................(1)
where
Vc = cumulative volume per unit area, t = filtration time, Vsp= spurt loss, A = static leakoff component, andB = dynamic leakoff component.
In static leakoff theory, B =0 and then A =2Cw, twice the static leakoff coefficient.-3
Each of the terms in Eq. 1 represents one of the stages in the leakoff process-spurt loss, buildup of filter cake, and erosion of filter cake.
Analysis of the experimental data shows that the spurt loss, Vsp, and the static leakoff component, A, are independent of the shear rate, but the dynamic component, B, varies strongly with the shear rate (see Table 1). This means that, the higher the shear rate, the more the leakoff process is controlled by the third stage. process is controlled by the third stage. One model commonly used is based solely on square-root-of-time behavior with a constant spurt loss. Fig. 1 shows that little accuracy is lost by describing the leakoff with a single square-root-of-time equation:
Vc = VsP + m t,...........................(2)
where the dynamic leakoff coefficient. Cw = 1/2m, depends heavily on shear. and the spurt loss remains the same as in Eq. 1 and independent of the shear rate Table 2 shows that the error in C, that arises as a result of measuring under static conditions can be more than 100%.
SPEJ
P. 629
A simple NMR methodology for evaluating filter cake properties and drilling fluid-induced formation damage