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Pressure distribution in a layer at inflow of gas taking into account change of factor of compressibility of gas

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Pirieva M.A., Romashkin S.V., Burmistrov N.A.

Tyumen State Oil and Gas University, Tyumen, Russia


According to the law of Darcy for a radial stream filtration process a fluid in a layer is described logarithmic by dependences:

Р(r) = Р w + qμ/(2πkh )· ln (r /rw ) , (1)

where Pi – initial pressure, P(r) – pressure in a layer on distance r from a wellbore, Рw - pressure in a well, q – rate in wellbore, μ – liquids viscosity, k – permeability of a layer, h –thickness of a layer, r – radius of a contour, rw – well radius.

Formulas (1) are written down for inflow in the well measured on a face of a well, and consequently it take place to any fluid-gas and oil, and their mixes. However, as practically always inflow characteristics are estimated on gaugings of an arriving fluid on a surface settlement dependences put into practice differ. For oil and oil mixes factors of Bo and Bm are usually entered.

For the gas mixes which are strongly liquids, it is accepted to estimate change of an output for wellbore conditions taking into account change of density of gas in a well on the basis of the known equation of a condition for hydrocarbonic gases PV = ZRT , where Р, V, T – pressure, volume and temperature, R - universal gas constant, Z - supercompressibility factor. For gas well equation (1) changing as:

Pwb2 = Pav2+(qsZ Ps T/ P·Tsμ/(2πKh )·ln (r/ rw),(2)

where the data on a well and on a external contour is taken into consideration only, and also some average value Z is applied to all area of drainage such approach, basically, is admissible for practical calculations.

In effect, the problem is reduced to finding Р(r) by summation of differences of pressure on layer sites on radius from a well with r = ri to required ri+1 with pressure Р(r) with updating of value Z on each step:

, . (3)

As a result of the calculation of schedules of pressure executed thus the dependences, resulted on fig. are received. Schedules are constructed in co-ordinates P from lg r more obviously to see those deviations which take place at comparison of the rough accelerated calculation and calculation taking into account change Z from R.


As a whole the resulted calculations show that, applying the specified method of the account of influence of pressure and temperature on change of factor of supercompressibility, layer parameters in 1,5 – 2,0 times different from calculation by simplified techniques turn out.


Fig. Schedules of change of pressure in a layer, constructed with the account ; Changes Z from pressure – (1) and without taking into account – (2)


It is interesting that practically in all books and practical guidances under the analysis and interpretation of display diagrams of pressure similar curvature IC always contacted a nonlinear stream of a filtration of a liquid in a layer, described two-members the equation: , where A and B - the factors of filtrational resistance depending on imperfection of a well, zone geometry of drainage, parameters and properties of gas.

So we received curvature IC is not connected absolutely not with nonlinearity of the law of a filtration.

The computer programs allowing on the personal computer quickly to carry out specified procedures are developed.

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