Fluid Dynamics of Oil Production by Bakytzhan Zhumagulov, Valentin Monakhov

By Bakytzhan Zhumagulov, Valentin Monakhov

Fluid Dynamics of Oil creation is the right advisor for knowing and construction extra exact oil construction versions. it's devoted to the theoretical and numerical research of fluid dynamic types, and masses realization is paid to the research of the result of the hydrodynamic calculations in line with those types and their use within the predictive estimates of the regulatory means of oil creation. different goods include:

  • A cautious description of over 30 various mathematical types of oil formations
  • Unconventional eventualities, corresponding to versions describing the method of foaming in oil formations and the combo of reservoir move with liquid move in wells.
  • Coverage of extra complicated and multi-dimensional types, together with oil filtration effects and methods
  • Create trustworthy types that hopefully convey the reservoirs movement patterns
  • Learn approximately 30 diversified mathematical versions of oil formations
  • Understand unconventional in addition to complicated and multi-dimensional versions, appropriate for modern day reservoirs
  • Contains numerous types constructed by means of the authors

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0Þ: ð1:50Þ From Laplace Law and equations of state of the fluids we find Fðσ; ρ1 ρ2 Þ  ρ2 ρ 2 1 2 pc ðσÞ 5 0; γ 2 ð1 2 σÞ γ1 σ @F . 0, and have therefore established the existence @σ of the implicit function σ 5 σ1 5 f1 ðρ1 ; ρ2 Þ; ðσ2 5 1 2 σ  f2 Þ. 50) that ρi % const. 50) close to the Muskat-Leverett model. 21), corresponding to the Muskat-Leverett model. Continuing to generalize the above modification of Darcy’s laws, let us present them in the form vi 5 2k0 ðxÞ; rðχi ϕi Þ; i 5 1; 2; ð1:52Þ where ϕi 5 pi 1 ρi gh is the hydraulic pressure head of the phases ðgrh 5 gÞ; k0 5 ðxÞ is the average permeability of the medium to homogeneous fluids and ðμi χi Þ are analogues of relative phase permeabilities k0i ðsÞ.

This is also how the further properties of functions f ðxÞAWp1 ðEÞ should be understood. df Let f ðxÞAWp1 ðEÞ; p $ 1. 2), we obtain ð   df  maxjf 2 f0 j #  dt; that is jf 2 f0 jE # kfx k1;E ; E dt in this case W11 ðEÞCCCðEÞ (W11 ðEÞ fits compactly into CðEÞ). Let now f ðxÞAWp1 ðEÞ; 1p 1 1q 5 1. Then ð x2      df  f ðx2 Þ 2 f ðx1 Þ # 1U dx # k1kq;½x1 ;x2 Š Ukfx kp;E 5 ðx2 2x1 Þ1=q kfx kp;E ; dx x1 ð fx 5 0; xA½0; lŠ\EÞ; 48 Fluid Dynamics of Oil Production Therefore, jf jα;E # kf kð1Þ p;E ; α5 p21 $ 0; p ð2:3Þ and Wp1 ðEÞCCC α ðEÞ.

42) have a unique solution at tA½0; T Š for any finite T . 0. However, the existence of a solution within any arbitrary interval 0 # t # T contradicts the physical implications of the initial model, since it must be the case that when water is injected into injection well ðx 5 0Þ, pure oil cannot indefinitely continue to be recovered from production well ðx 5 XÞ. This paradox makes it difficult to formulate physically acceptable conditions for production wells. Moreover, asymptotics studies suggest that over a period of time these equations produce unrestricted growth of the saturation gradient in production wells.

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