Some Data on Reservoir Permeability and the Physical Properties of Oil from the Ozernoye Field in Tomsk Oblast

N. V. Koptyaev, G. N. Chertenkova

(Presented by the scientific seminar of the Department of Fossil Fuels)

Before raising the question of determining the permeability of reservoir Yu-1 at the Ozernoye field, the authors investigated the physical properties of the oil of this field under reservoir conditions. The study was carried out on a UVIPN-2M installation for investigating reservoir oils, equipped with a VVDU-1 high-pressure viscometer. The determination was performed according to the method described by V. N. Mamuna et al. [1]. The results of this study are given in Table 1.

Table 1

Physical properties of the oil from the Ozernoye field, Tomsk Oblast, under reservoir and surface conditions. The oil was taken from well 71 at a reservoir pressure of 263,5 ati and a reservoir temperature of 96°C. Perforation interval 2550–2580 m

Special attention was given by the authors to determining the viscosity of the oil. Initially this parameter was studied for unde-gassed oil at various pressures and temperatures. The results of this study are given in Table 2. Then a study was carried out of this parameter for partially degassed oil. Degassing was performed at pressures first of 50 and then 10 atm, and the viscosity was determined first at 60 and, in the second case, at 12 atm (Table 3).

Table 2

Results of the study of the viscosity of oil from the Ozernoye field in the unde-gassed state

Table 3

Results of the study of the viscosity of oil in the partially degassed state

The composition of the associated gas of the oil of the Ozernoye field was determined by V. F. Kuznetsova, a staff member of the Department of Fuel Technology of the Faculty of Chemistry and Technology. The results of this study are given in Table 4.

In terms of physical properties, the oil of the Ozernoye field differs hardly at all from the oils of other fields in Tomsk Oblast. In particular, its viscosity under reservoir conditions proved to be 0.65 centipoise. For the oil of the Klyuchevskoye field it is 0.8909 centipoise [2], for the oil of the Olenye field, 0.74 centipoise, and for the oil of

Table 4

Results of analysis of the gas released during degassing of oil from the Ozernoye field, in volume percent

for Pervomaiskoye—0.77 c-poise, for oil from Severnoye—0.74 c-poise, for oil from Strezhevoye—0.69 c-poise [3].

In addition to the physical properties of the oil, to determine the permeability of the formation, data obtained in the course of drilling and testing the well were used, namely: the well diameter before running the casing string (bit diameter), 190 mm (hence the calculated well radius \(r\) is 9.5 cm), perforation interval 2550–2580 m, filter length 3000 cm (30 m), number of holes in the filter \(n\), 465, formation pressure \(P_{\text{pl.}}\), 263.5 atm. The magnitudes of the bottom-hole pressures and the corresponding inflows into the well are given in Table 5. The mean radius of the holes in the string \(\lambda\) was taken as equal to 0.5 cm.

The calculation was carried out in accordance with the procedure set forth earlier [4] and consisted of the following:

1. The formation thickness per one hole was determined:

\[ h'=\frac{3000}{465}=6.4516\ \text{cm}; \]

1. The radius of influence of the holes \(S\) was determined. In this case, since the formation thickness per one hole (6.4516 cm) is less than the well diameter (19.0 cm), the calculation is carried out through the area per one hole, i.e., by the formula

\[ S=0.5\sqrt{2\pi r h'}, \tag{1} \]

substituting the corresponding values into which, we obtain

\[ S=0.5\sqrt{2\cdot 3.14\cdot 9.5\cdot 6.4516} =0.5\sqrt{385.0994}=9.812\ \text{cm}. \]

From the data obtained it is evident that, in the case under consideration, the radius of influence of a hole (9.812 cm) is less than the well diameter (19 cm). Thus, to calculate the inflow parameters here it is necessary to use the formula for high perforation density [4, formula 16], which can be written in the following form:

\[ P_{\text{pl}}-P_{\text{zab}} =\frac{Q'\mu}{2\pi k} \left( \frac{1}{\lambda} -\frac{1}{s} -\frac{0.25}{r}\ln\frac{s}{\lambda} +0.0625\frac{s\cdot\lambda}{r^2} -0.0117187\frac{s^2-\lambda^2}{r^3} +\right. \]

\[ \left. +0.0026042\frac{s^3}{r^4} -0.0007935\frac{s^4}{r^5} +0.0002075\frac{s^5}{r^6} -0.0000610\frac{s^6}{r^7} +\frac{1}{h'}\ln\frac{R}{r+s} \right), \tag{2} \]

Table 5

Results of determining the permeability of Horizon Ю-1 sandstone from Well 71 of the Ozernoye Field

where

\(P_{\mathrm{pl}}\) and \(P_{\mathrm{bh}}\) are the reservoir and bottom-hole pressures in ati;

\(Q^1\) is the inflow into the well under reservoir conditions per one opening, in \(\mathrm{cm^3/sec}\);

\(k\) is the reservoir permeability, in darcys;

\(R\) is the radius of influence of the well, which in the case under consideration may be taken as equal to \(10000\ \mathrm{cm}\) (\(100\ \mathrm{m}\)). The remaining parameters are given above.

Well 71 of the Ozernoye field was tested under several operating regimes. In the first of these (choke diameter \(4\ \mathrm{mm}\)), the bottom-hole pressure was \(252.7\ \mathrm{ati}\), and the total inflow into the well under surface conditions was \(58.0\ \mathrm{m^3/day}\). To determine the magnitude of the inflow under reservoir conditions per one opening, the formula used is

\[ Q'=\frac{Q\cdot b\cdot 1000000}{n86400}, \tag{3} \]

where

\(Q\) is the total inflow into the well under surface conditions in \(\mathrm{m^3/day}\) (different for different regimes);

\(b\) is the oil formation volume factor, which in the case under consideration proved to be equal to \(1.246\) (Table 1);

\(n\) is the number of openings in the filter (in this case 465);

\(1000000\) is the coefficient expressing the number of \(\mathrm{cm^3}\) in \(\mathrm{m^3}\);

\(86400\) is the coefficient expressing the number of seconds in a day. Substituting the above values into formula (3), we find that the inflow into the well per one opening that is of interest to us, under the first regime, was expressed by the relation

\[ Q'_1=\frac{58.0\cdot 1.246\cdot 1000000}{465\cdot 86400} =1.798784\ \mathrm{cm^3/sec}. \]

Calculating in an analogous manner, we find that under the second regime (choke diameter \(6\ \mathrm{mm}\)) it proved equal to \(2.791217\ \mathrm{cm^3/sec}\), under the third regime (choke diameter \(8\ \mathrm{mm}\))—\(4.199231\ \mathrm{cm^3/sec}\), under the fourth regime (choke diameter \(6\ \mathrm{mm}\))—\(2.6981764\ \mathrm{cm^3/sec}\), and under the fifth regime (choke diameter \(4\ \mathrm{mm}\))—\(1.798784\ \mathrm{cm^3/sec}\) (as under the first regime).

Substituting into expression (2) the quantities pertaining to the first regime, we obtain

\[ 263.5-252.7= \frac{1.7988\cdot 0.65}{2\cdot 3.1416\cdot k_1} \left( \frac{1}{0.5} -\frac{1}{9.812} -\frac{0.25}{9.5}\ln\frac{9.812}{0.5} +0.0625\frac{9.812-0.5}{90.25} -\right. \]

\[ \left. -0.0117187\frac{96.275-0.25}{857.37} +0.0026042\frac{944.65}{8115} -0.0007935\frac{9268.9}{77378} +0.0002075\frac{90947}{735192} -\right. \]

\[ \left. -0.000061\frac{892369}{6983374} +\frac{1}{6.4516}\ln\frac{10000}{9.5+9.812} \right) \]

or, after the corresponding transformations,

\[ 10.8= \frac{1.7988}{9.6666\,k_1} \left( 2.0-0.101916-0.078342+0.006449-0.001312+0.000302- \right. \]

\[ \left. -0.000095+0.000026-0.000008+\frac{6.2496}{6.4516} \right), \]

\[ 10.8=\frac{1.7988}{9.666 k_1}\cdot(1.825104+0.96869), \]

whence the permeability is expressed by the relation

\[ k_1=\frac{1.7988}{9.666\cdot 10.8}\cdot 2.793794=0.048137\ \text{darcy}, \]

or 48.1 millidarcies.

Calculating in an analogous way, we obtain for the second regime 34.3 millidarcies, for the third—33.5 millidarcies, for the fourth—32.9 millidarcies, and for the fifth likewise 32.9 millidarcies (Table 5). The average value of this parameter over all regimes is 36.34 millidarcies.

REFERENCES

1. V. N. Mamuna, G. F. Trebin, B. V. Ulyaninskii. Experimental Study of Reservoir Oils. GOSINTI, 1960.

2. L. A. Pukhlyakov, G. N. Chertenkova. On the viscosity of oil from the Klyuchevskoye field of Tomsk Oblast under reservoir conditions. Izv. TPI, vol. 218, 1971.

3. L. A. Pukhlyakov, G. N. Chertenkova. A new method for increasing the productivity of oil pipelines. Izv. TPI, vol. 217, 1971.

4. L. A. Pukhlyakov. Derivation of the inflow formula for a hydrodynamically imperfect well. Izv. TPI, vol. 201, 1972.