Bulletin of the Tomsk Order of the October Revolution and Order of the Red Banner of Labor Polytechnic Institute named after S. M. Kirov

Volume 287 1977

Determination of the Skin Effect of Oil Exploration Wells from Inflow Rates under Steady-State Conditions

L. A. Pukhlyakov

(Presented by the Department of Fossil Fuels)

For a long time there existed the opinion that, in the process of drilling, a thin layer of clayey rocks is formed around the walls of wells; among American authors this layer was called the skin [6]. In the domestic literature this layer is called a clay cake. Later, however, it was established that through the largest pores the clay mud penetrates into the formation over considerable distances. This penetration is of particular interest when, because of withdrawal of fluid from the formation, the reservoir pressure proves to be reduced. Thus, in the thirties and forties, when rotary drilling was being introduced in our country, catastrophic losses of clay mud occurred when producing formations were penetrated in wells being drilled. At the same time the flow of oil into neighboring producing wells ceased. This occurred as a result of the clay contamination of the formations.

To estimate the degree of alteration of the formation due to clay contamination, M. Hawkins [5] proposed using the following formula:

\[ S=\left(\frac{k_{\text{nz}}}{k_{\text{gl}}}-1\right)\ln\frac{R_{\text{gl}}}{r_{\text{sk}}}, \tag{1} \]

where \(S\) is the skin effect, i.e., the effect of the entire clay-contaminated zone (a dimensionless quantity); \(k_{\text{gl}}\) is the permeability of the clay-contaminated zone in darcies or millidarcies; \(k_{\text{nz}}\) is the permeability of the uncontaminated zone in the same units; \(R_{\text{gl}}\) is the radius of the clay-contaminated zone in cm; and \(r_{\text{sk}}\) is the radius of the well before the casing string is run—one half of the bit diameter in cm.

Most authors, for example K. Getlin [1], B. A. Lysov [2], and others, recommend using the results of well testing under unsteady-state conditions to determine the skin effect. For this purpose one may also use the results of well testing under steady-state conditions.

The method set forth here is based on a new formula for determining the radius of influence of a well:

\[ \frac{R^{2}}{\ln R-\ln (r_{\text{sk}}+y+r_{\text{ot}})} = \frac{2V_{1}}{\pi H m \beta \Delta P_{s}}, \tag{2} \]

where \(R\) is the radius of influence of the well in cm; \(r_{\text{sk}}\) is the radius of the well before the casing string is run, in cm; \(r_{\text{ot}}\) is the radius of influence of the holes, or one half of the average distance between neighboring holes in the filter

wellbore in cm, \(y\) is the depth of the channel at the opening in cm, \(V_1\) is the volume of fluid produced from the formation during the well test in the first regime, in \(\text{cm}^3\), \(H\) is the formation thickness in cm, \(m\) is the formation porosity as a fraction of unity, \(\beta\) is the compressibility of the oil in \(1/\text{at}\), and \(\Delta P_s\) is the drawdown on the formation at the outer boundary of the zone of influence of the openings in the first regime. Methods for determining each of these parameters are set out in articles [3, 4] and are not given here.

After determining the radius of influence of the well in the first regime, the piezoconductivity of the formation is determined, and then the radii of its influence in the other regimes. But now the calculation is carried out by the formula

\[ R_2 = 2.246 \chi t, \tag{3} \]

where \(\chi\) is the piezoconductivity of the formation in \(\text{cm}^2/\text{s}\), and \(t\) is the total operating time of the well during its test, in s.

Then, in accordance with the methods mentioned, the effective permeabilities of the formation in the various regimes \(k_1, k_2\), etc., are determined, as well as the permeability in the un-mudded part of the formation \(k_{\mathrm{nz}}\) and, from the core, the permeability of the formation in the mudded part \(k_{\mathrm{gl}}\). The data obtained are substituted into the formula

\[ G_{\mathrm{gl}} = \frac{\Sigma G_1 (k_{\mathrm{nz}} - k_1)} {k_{\mathrm{nz}} - k_{\mathrm{gl}}}, \tag{4} \]

where \(G_{\mathrm{gl}}\) is the geometric characteristic of the mudded zone in \(1/\text{cm}\), and \(\Sigma G_1\) is the sum of the geometric characteristics in the first regime in the same units.

For well 123 of the Oleneg oil field, the following data were obtained: the radius of influence of the well in the first regime is 6979 cm, the geometric characteristic of the plane-radial-flow zone is \(0.0439\ 1/\text{cm}\), the sum of the geometric characteristics for the well as a whole in this regime is \(1.4073\ 1/\text{cm}\), the effective permeability in this regime is 7.691 millidarcies, the permeability in the mudded part of the formation is 6.5 millidarcies, and the permeability in the un-mudded part of the formation is 217.9 millidarcies. Substituting all this into formula (4), we obtain

\[ G_{\mathrm{gl}} = \frac{1.4073 \cdot (217.9 - 7.691)} {217.9 - 6.5} = 1.3994\ 1/\text{cm}. \tag{5} \]

The shortfall of the obtained value from 1.4073 is \(0.0079\ 1/\text{cm}\), which is less than the geometric characteristic of the plane-radial-flow zone (0.0439) by \(0.0360\ 1/\text{cm}\). This value is substituted into the formula for determining the radius of the mudding zone

\[ G_R^{\mathrm{gl}} = \frac{n}{H} \ln \frac{R_{\mathrm{gl}}}{\delta_{\max}}, \tag{6} \]

where \(G_R^{\mathrm{gl}}\) is the geometric characteristic of the mudded part of the plane-radial-flow zone in \(1/\text{cm}\), \(n\) is the number of openings within the well filter (dimensionless), \(H\) is the formation thickness in cm, and \(\delta_{\max}\) is the maximum component of perforation imperfection, equal in the case under consideration to 1800 cm. Substituting these values into formula (6), we obtain

\[ 0.0360 = \frac{120}{3700} \ln \frac{R_{\mathrm{gl}}}{1800}, \tag{7} \]

whence

\[ \ln \frac{R_{\text{cl}}}{1800}=\frac{0.0360\cdot 3700}{120}, \tag{8} \]

Carrying out the corresponding transformations in this expression, we find that, in the case under consideration, the radius of the clayization zone proved to be equal to 5461 cm.

Finally, substituting the value found and the other data given above into Hawkins’ formula, we obtain

\[ S=\left(\frac{217.9}{6.5}-1\right)\frac{5461}{9.5}=(33.5-1)\ln 574.2=206.5. \tag{9} \]

This is the skin effect of well 123 of the Olenye oil field; for well 125 this parameter proved to be equal to 38.0, and for well 129, 393.

REFERENCES

1. K. Gatlin. Drilling and Well Completion (translated from English). Moscow, Gostoptekhizdat, 1963.

2. B. A. Lysov. Some principles and questions of the methodology of hydrodynamic calculations in acid treatment of a formation. Information collection of papers of the Computing Center of Irkutsk State University, issue 4. “Quantitative geological-geometric and oil-field research methods in the Pre-Lena region of the Siberian Platform.” Irkutsk, 1971.

3. L. A. Pukhlyakov. Determination of the permeability of formation Yu-1 of the Olenye oil field from inflows under stabilized regimes. Izvestiya TPI, vol. 288, 1976.

4. L. A. Pukhlyakov. On the hydrodynamic imperfection of wells associated with incomplete perforation. Izvestiya TPI, vol. 281, 1976.

5. M. F. Hawkins. A Note on the Skin Effect. Journal of Petroleum Technology. No. 12, 1956.

6. W. Hurst. Establishment of the Skin Effect and its Impediment to Fluid Flow into a Well Bore. The Petroleum Engineer, Oct. 1953.