By Bakytzhan Zhumagulov, Valentin Monakhov
Fluid Dynamics of Oil creation is the fitting advisor for realizing and construction extra exact oil creation types. it really is devoted to the theoretical and numerical examine of fluid dynamic types, and masses awareness is paid to the research of the result of the hydrodynamic calculations in line with those versions and their use within the predictive estimates of the regulatory means of oil construction. different goods include:
- A cautious description of over 30 assorted mathematical versions of oil formations
- Unconventional eventualities, equivalent to versions describing the method of foaming in oil formations and the mix of reservoir circulation with liquid stream in wells.
- Coverage of extra complicated and multi-dimensional versions, together with oil filtration effects and methods
- Create trustworthy types that hopefully exhibit the reservoirs circulation patterns
- Learn approximately 30 varied mathematical versions of oil formations
- Understand unconventional in addition to complicated and multi-dimensional types, acceptable for modern reservoirs
- Contains a number of versions constructed through the authors
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Additional info for Fluid Dynamics of Oil Production
Sample text
2 The Proposed Mathematical Model Let pH be the bubble point pressure of gas-cut heavy oil whose reduced density is ρ 5 1 at p . pH . The process of gas separation at p , pH is allowed for by considering a special equation of state for the mixed oil and gas flow: & 1; p $ pH ρ 5 ρðpÞ 5 ð1:84Þ δðp 2 pH Þ 1 1 p # pH where δ 5 const. In what follows, let Y 5 Y ðθÞ be the internal energy corresponding to wax crystallization, θ is the equilibrium temperature, m 5 const is porosity and k 5 kðθ; pÞ is permeability.
4 in that it takes into account the fact that residual phase saturations depend on the temperature of the inhomogeneous fluid, which we were able to establish experimentally. The inclusion of this effect enables the model to describe the movement of the boundary between the inhomogeneous fluid and its stationary components (the Stephan problem). 4, the energy balance equation for an inhomogeneous fluid becomes @θ 5 div½λðx; s; θÞrθ 2~ v θ; @t ð1:66Þ where θ is temperature; λ is the thermal diffusivity; s 5 s1 is wetting phase saturation; ~ v 5~ v 1 1~ v 2 is average mixed flow velocity, and ~ v i is the phase flow velocities.
For many formations it may be assumed that λ1 5 3 [143, p. 176] and λ2 5 2 [110, p. 208]. k1 k2 jp0c At these values of λ1 ; aðsÃ Þ 5 ¼ 6 0 and, consequently, aðsÞ k 1k 1 2 s5sà à and k1 ðsÞ, become zero only when s 5 s . To provide a full picture, let us consider the case of one-dimensional flow through homogeneous rock at a specified mixed flow rate v1 1 v2 5 QðtÞ. 28) then becomes equivalent to the Rappoport-Liss equation ! 41), which will satisfy the condition sjt50 5 s0 ðxÞ; xA½0; X; sjx50 5 sà 2 δ; sjx5X 5 sà ; ð1:42Þ where sà # s0 ðxÞ # s0 2 δ; δ .