Fracture-Injection-Test Interpretation: Leakoff Coefficient vs. Permeability
- M.J. Mayerhofer (Union Pacific Resources) | M.J. Economides (Texas A&M U.)
- Document ID
- Society of Petroleum Engineers
- SPE Production & Facilities
- Publication Date
- November 1997
- Document Type
- Journal Paper
- 231 - 236
- 1997. Society of Petroleum Engineers
- 5.2 Reservoir Fluid Dynamics, 5.6.3 Pressure Transient Testing, 4.1.2 Separation and Treating, 5.6.4 Drillstem/Well Testing, 1.10.1 Drill string components and drilling tools (tubulars, jars, subs, stabilisers, reamers, etc), 2.5.2 Fracturing Materials (Fluids, Proppant), 3.2.3 Hydraulic Fracturing Design, Implementation and Optimisation, 3 Production and Well Operations
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Determining the leakoff coefficient from a minifracture pressure decline has become a relatively common industrial procedure. A main assumption of the method, which is often referred to as the Nolte analysis, is a constant leakoff coefficient. Frequently there is no constant leakoff coefficient. The definition of the coefficient is based on a constant pressure differential and a prescribed mode of leakoff. In contrast, the analysis for fracture-pressure decline, introduced by Mayerhofer et al.,10 couples unsteady-state linear flow from the fracture with a varying skin effect at the fracture face, and superposes the leakoff history on the pressure decline. This guarantees a correct rate convolution to account for pressure-dependent fluid loss. The reservoir permeability, fracture-face resistance, and leakoff area can be determined. A comparison of the two methods and their relationship is presented in this paper, using real field cases. We show that the use of modern well-testing log-log diagnostic plots to determine fracture closure pressure is superior to drawing a straight line on a G-function plot or a square-root-of-time plot.
In a series of seminal publications, Nolte1-4 introduced a methodology for determining the fracture leakoff coefficient from injection tests. The technique has been widely used, and the determined leakoff coefficient has been incorporated in fracture treatment design procedures.
The original technique is based on material balance, and it presumes a mode of leakoff into the formation with the fluid loss dependent on the square root of time. Using this assumption, Castillo5 introduced a specialized plot where a time-dependent G function forms a straight line with the pressure decline. The straight line is drawn from the independently obtained closure pressure and encompasses all previous pressure points that fall on the straight line. The slope of this straight line is related directly to the leakoff coefficient. The method of analysis and example applications are presented in Refs. 3 and 6.
The Nolte analysis and the Castillo specialized plot are exactly equivalent to the Horner construction in pressure-transient analysis. In a similar manner, the Horner analysis also presumes a mode of fluid flow (infinite acting radial flow). A specialized (semilogarithmic) straight line leads to the sought variables (permeability and skin). Yet, investigators of pressure-transient analysis recognized early on that the pressure record of a test rarely, if ever, reflects solely infinite acting behavior at all. To account for the different phenomena, only one of which would lead to a Horner plot, the log-log diagnostic plot of pressure and pressure derivative vs. time is considered the essential first step in modern pressure-transient analysis. In the absence of the characteristic response for radial flow, manifested by a flattening derivative curve, no Horner plot can be constructed.
There is no analog in the Nolte analysis for a pattern-recognition exercise, and several attempts have been undertaken to account for deviations7 such as stress sensitivity (i.e., pressure-transient effects) changing fracture area, dominance (or lack thereof) of the filter cake, and reservoir fluid compressibility. Rules of thumb and approximations have been introduced in attempts to account for the fact that the "assumptions of the basic analysis are seldom met in practice."7
Nolte et al.,7 in their latest publication, postulated that the filter cake either completely dominates the leakoff or has a negligible effect. For the case of total reservoir control (filtrate invaded plus reservoir) they provided numerical simulations of the pressure history. To determine the slope on the Castillo G plot,5 they proposed a common reference point at ?pw/?ps+3/4, where ?pw is the net pressure during closing and ?ps is the net pressure immediately after shut-in. This slope was referred to as m3/4. Then the factor kc was used to correct the m3/4 slope. According to Nolte et al.,7 this correction was rarely needed because reservoir control is generally ineffective and, thus, of no practical interest.
The Mayerhofer et al. Method
Mayerhofer and Economides9 and Mayerhofer et al.10 have presented a model that accounts for the filter-cake and reservoir response, allowing for the superposition of the injection history, filter-cake deposition, and associated rate convolution. Their solution is10
The normalized resistance, RD, is simply given by9
Although Eq. 1 may appear complex, it is in fact relatively easy to track as outlined in detail in Ref. 10.
Central to the method is the use of log-log diagnosis, a standard tool in pressure-transient analysis. A successful addendum is the use of the rate-normalized plot (RNP), also a standard in pressure-transient analysis, which allows the detection of trends by deducing rate-transient effects.
Mayerhofer et al.10 have shown in a series of simulations that reservoir dominance would be manifested by a half-slope straight line on the log-log RNP and RNP-derivative plots, whereas filter-cake dominance would appear on the RNP derivative as an increasing trend but of decreasing slope approaching the half-slope straight line. The larger the fracture-face resistance, the more pronounced its dominance on the pressure decline and the steeper the slope of the derivative plot would be.
Interestingly, Nolte's presumption1-4 of the leakoff rate depending on the square root of time but with the filter cake dominating does not form a half-slope straight line. Only reservoir dominance, i.e., linear flow from an infinite conductivity fracture into the reservoir, would result in a half-slope straight line on the log-log diagnostic plot.
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