Fractured-Well-Test Design and Analysis in the Presence of Non-Darcy Flow
- J.A. Gil (Colorado School of Mines) | E. Ozkan (Colorado School of Mines) | R. Raghavan (Phillips Petroleum Co.)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- June 2003
- Document Type
- Journal Paper
- 185 - 196
- 2003. Society of Petroleum Engineers
- 5.2.1 Phase Behavior and PVT Measurements, 3.2.3 Hydraulic Fracturing Design, Implementation and Optimisation, 5.3.2 Multiphase Flow, 5.6.4 Drillstem/Well Testing
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The objective of this paper is to discuss the design and analysis of fractured-gas-well tests to account for non-Darcy flow within the fracture. The results and discussions are based on a semianalytical model. Guidelines and correlations are presented to enable engineers to design fractured-well tests whereby the magnitude of non- Darcy flow may be estimated and its effect minimized, if necessary. The effect of non-Darcy flow skin (or rate-dependent skin) is discussed in detail. A method is also presented to analyze fractured- well tests under non-Darcy flow conditions to estimate the non-Darcy flow coefficient, fracture conductivity, and reservoir properties. Unlike the conventional methods, this method does not require two tests at different production rates.
For unfractured vertical wells, it is possible to ascertain conditions for which the effects of non-Darcy flow should be negligibly small. Such information does not exist for fractured wells. Also, in the latter case, we need to contend with multiple flow regimes. Should the effects of non-Darcy flow be ignored, then it has been shown in the literature1-6 that lower estimates of fracture conductivity and/or half-length will result. The conventional recommendation to conduct tests at two different rates to estimate fracture properties (length and conductivity)4,5 is often not a practical proposition. The adverse effect of non-Darcy flow on our ability to analyze tests is further exacerbated by the influence of producing time on buildup analysis.5,6
In this study, we use the semianalytical model discussed in Refs. 4 through 6 to investigate the effect of non-Darcy flow in the fracture. We incorporate the effect of wellbore storage along the lines suggested by Cinco-L. and Sameniego-V.7 It is assumed that for the ranges of the fluid and reservoir properties considered in this study, flow obeys Darcy's law in the reservoir or, as discussed by Wattenbarger and Ramey,2 the effect of non-Darcy flow in the reservoir is negligibly small when compared with that within the fracture. The ranges of the reservoir and fracture properties considered in this work are similar to those used in Refs. 8 and 9 and are summarized in Table 1.
One of the contributions of this work is to improve fractured-well- test design and analysis under non-Darcy flow conditions. We calculated the magnitude of the skin factor caused by non-Darcy flow and determined the ranges of production rate and fracture half-length for which the estimates of fracture conductivity and half-length will be unaffected by non-Darcy flow. We assume that if the pressure drop caused by non-Darcy flow is less than or equal to 10% of the total drawdown, then the effects of non-Darcy flow will be negligibly small. We also present guidelines and correlations that can be used to design fractures in which non-Darcy skin factor (rate-dependent skin) would not exceed this limit. Our calculations may be used to obtain similar information for other limits or to obtain an alternate design of the fracture variables.
Another contribution of this work is to present an analytical technique for fractured-well tests under the effect of fracture non- Darcy flow. This technique requires transient-pressure data during the bilinear- and linear-flow periods. The technique is applicable for the ranges of parameters required by the technique proposed by Guppy et al.,4,5 but unlike their method, our technique does not require multiple tests at different flow rates. As suggested by Lingen, 10 we use sandface flow rates to determine the non-Darcy flow effects; thus, the effect of wellbore storage does not hinder the application of our technique.
We start this communication with the definition of the variables used and the ranges of parameters investigated. We then present the results to delineate the effect of non-Darcy flow in the fracture and to quantify the non-Darcy flow skin. These discussions lead to the guidelines and correlations to design fractures and well tests with acceptable effects of non-Darcy flow. Introduction of the new analytical technique for fractured wells under non-Darcy flow conditions follows. We conclude this presentation with general comments.
Definitions and Ranges of the Data Used
Here, we introduce the system examined, define the variables used in the discussions, and present the ranges of the data investigated.
Let us first define the system investigated in this work. We consider a laterally infinite reservoir of uniform thickness, h, and a vertical well intercepted by a fully penetrating hydraulic fracture. The hydraulic fracture has a height of h, half-length of xf, width of wf, and permeability of kf. A real gas flows in the system, and the reservoir permeability is assumed to be constant and uniform.
Because we deal with real-gas flow, we present our results in terms of pseudopressure, m(p), defined by
where p is the pressure, Z is the gas compressibility factor, and µ is the gas viscosity. The dimensionless pseudopressure is defined, in field units, by
where pi and pwf stand, respectively, for the initial and flowing wellbore pressures; q is the constant surface production rate; and T is the reservoir temperature. In Eq. 2, the dimensionless time, tD, is defined by
for t in hours. The term (µct) in Eq. 3 is the viscosity-compressibility product at initial conditions.
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