Concept of Geometric Factor and Its Practical Application to Estimate Horizontal and Vertical Permeabilities

Abstract

In a probe-type formation test, because of the geometry of the wellbore and the sealing effect of mudcake, the flow pattern is not perfectly spherical. To account for the deviation from spherical flow, several geometric correction factors were proposed for different analysis techniques (Steward and Wittmann 1979;Wilkinson and Hammond 1990;Dussan and Sharma 1992;Goode and Thambynayagam 1992;Proett and Chin 1996). A geometric factor is used in formation rate analysis (FRA) (Kasap et al. 1999), a technique used in analyzing a probe test to estimate formation pressure and permeability. Like other geometric correction factors, the geometric factor is a strong function of permeability anisotropy that is generally unknown before a test. When analyzing the test, we would logically assume an isotropic formation and use the corresponding isotropic geometric factor. Consequently, the FRA-estimated permeability does not represent the true spherical permeability. In contrast, the spherical permeability can be estimated from buildup analysis without prior knowledge of permeability anisotropy. Therefore, there is a discrepancy between the permeability estimates from the two analysis methods. In addition, if considered separately, neither FRA nor buildup analysis can decompose the estimated permeability into its horizontal and vertical components.This paper presents the derived numerical values of several geometric factors. Using these factors, we show that the discrepancy between the permeabilities estimated from FRA and from the conventional buildup analysis is attributable to the permeabilityanisotropy effect. A correct geometric-factor value must be used to estimate permeability correctly. On the basis of the permeabilityanisotropy effect, we present the procedures to estimate horizontal and vertical permeabilities by combining FRA permeability and buildup permeability or by history matching. These procedures are verified with a simulated probe test. Analysis of three actual tests is presented.

A New Technique to Determine Horizontal and Vertical Permeabilities from the Time-Delayed Response of a Vertical Interference Test

“…However, the existing interpretation methods do no take the permeability anisotropy effect into account. The concept of geometric factor and its affecting factors are discussed in Goggin et al (1988); Wilkson and Hammond (1990); Sheng et al (2006); and Sheng (2008).…”

“…Using these input data, the pressure responses with time were generated using Interpret, which had been in the market for years. We had verified the software and used the software in our earlier papers (Liu et al 2004;Sheng et al 2006). From these generated pressure responses, the time delay, t L , and the maximum pressure drop are obtained and are reported in Table 1.…”

“…The simulator, RCISim (Liu et al 2004), was used to simulate the pressure responses. The simulator was used in our earlier publications (Sheng et al 2006;Sheng 2008). In the case with wellbore storage and skin, a typical wellbore storage value associated with the fluid line volume of a wireline testing tool was used, and the skin was assumed to be 5.…”

Upscaling WFT Permeability Data: A Systematic Approach to Analyzing and Integrating Well Test Data From Wireline Formation Testers WFT

“…Calculate the buildup permeability from the spherical buildup equation: using the total compressibility (c t ϭ s w c w ϩ s g c g ϩ c f ) and the two-phase viscosity ( 2-phase ϭ s w w ϩ (1-s w ) g ) 3. Combine the drawdown and buildup data for FRA analysis, assuming the formation is isotropic (k H /k V ϭ1); and use isotropic a geometric factor (G os ) iso corresponding to the ratio of r p /r w , as given by Sheng et al (2004) in Tables 2 to 3. 4. Assume that the buildup-estimated permeability represents the true spherical permeability and correct the geometric factor (G os ) ani for anisotropic formation;…”

“…The buildup analysis is capable of detecting the invasion radius if the radius of investigation is larger than the diameter of the invasion fluid bank. (Sheng et al, 2004) Reservoir heterogeneity and anisotropy impact the horizontal and vertical permeabilities. FRA techniques assume a homogeneous formation for the preliminary estimation of reservoir permeability and then correct it for anisotropy using step 4 of the analysis procedure described above.…”