The Effect of an Immobile Liquid Saturation on the Non-Darcy Flow Coefficient in Porous Media

1987 ◽  
Vol 2 (04) ◽  
pp. 331-338 ◽  
Author(s):  
R.D. Evans ◽  
C.S. Hudson ◽  
J.E. Greenlee
Keyword(s):  
Porous Media ◽  
Flow Coefficient ◽  
Darcy Flow ◽  
Liquid Saturation

Effect of Heterogeneity on the Non-Darcy Flow Coefficient

1999 ◽  
Vol 2 (03) ◽  
pp. 296-302 ◽  
Author(s):  
Ganesh Narayanaswamy ◽  
Mukul M. Sharma ◽  
G.A. Pope
Keyword(s):  
Experimental Study ◽  
Reynolds Number ◽  
Porous Media ◽  
Pressure Drop ◽  
Characteristic Length ◽  
Flow Coefficient ◽  
Darcy Flow ◽  
Liquid Saturation ◽  
Flow Through ◽  
Heterogeneous Formation

Summary An analytical method for calculating an effective non-Darcy flow coefficient for a heterogeneous formation is presented. The method presented here can be used to calculate an effective non-Darcy flow coefficient for heterogeneous gridblocks in reservoir simulators. Based on this method, it is shown that the non-Darcy flow coefficient of a heterogeneous formation is larger than the non-Darcy flow coefficient of an equivalent homogenous formation. Non-Darcy flow coefficients calculated from gas well data show that non-Darcy flow coefficients obtained from well tests are significantly larger than those predicted from experimental correlations. Permeability heterogeneity is a very likely reason for the differences in non-Darcy flow coefficients often seen between laboratory and field data. Introduction In this paper, we present an analytical method for calculating an effective non-Darcy flow coefficient for a heterogeneous reservoir. The effect of heterogeneity on the non-Darcy flow coefficient is also shown using numerical simulations. Non-Darcy flow coefficients calculated from the analysis of welltest data from a gas condensate field are compared with experimental correlations. Such a comparison allows us to more accurately assess the importance of non-Darcy flow in gas condensate reservoirs. Literature Review As early as 1901, Reynolds observed, in his classical experiments of injecting dye into water flowing through glass tubes, that after some high flowrate, flow rate was no longer proportional to the pressure drop. Forchheimer1 also observed this phenomena and proposed the following quadratic equation to express the relationship between pressure drop and velocity in a porous medium: d P d r = μ k u + β ρ u 2 . ( 1 ) This equation has come to be known asForchheimer's equation. At low Reynolds number (creeping flow conditions), the above equation reduces to Darcy's law. Tek2 developed a generalized Darcy equation in dimensionless form which predicts the pressure drop with good agreement over all ranges of Reynolds numbers. Katz et al.3 attributed the phenomenon of non-Darcy flow to turbulence. Tek et al.4 proposed the following correlation for?: β = 5.5 × 10 9 k 5 / 4 ϕ 3 / 4 . ( 2 ) Gewers and Nichol5 conducted experiments on microvugular carbonate cores to measure the non-Darcy flow coefficient. They also studied the effect of the presence of a second static fluid phase and the effect on plugging due to fines migration. They found that ? decreases and then increases with liquid saturation. Wong6 studied the effect of a mobile liquid saturation on ?. He used distilled water as the liquid phase and water saturated nitrogen as the gas phase on the same cores used by Gewers and Nichol. He plotted ? vs liquid saturation and found that there is an eight-fold increase in ? when the liquid saturation increases from 40% to 70%. He concluded that ? can be approximately calculated from the dry core experiments by using the effective gas permeability. Geertsma7,8 introduced an empirical relationship between ?,k and ? based on a combination of experimental data and dimensional analysis. He noted that the observed departure from Darcy's law was due to the convective acceleration and deceleration of the fluid particles. He also defined a new Reynolds number as ?k??/?, and suggested the following correlation for ? with a constant C (k is in ft 2, ?is in 1/ft). β = C k 0.5 ϕ 5.5 . ( 3 ) For the case of gas flowing through a core with a static liquid phase, he suggested the following correlation: β = C ( k k r g ) 0.5 [ ϕ ( 1 − S w ) ] 5.5 . ( 4 ) Phipps and Khalil9 proposed a method for determining the exponent in a Forchheimer-type equation. Firoozabadi and Katz10 presented are view of the theory of high velocity gas flow through porous media. Evanset al.11 reviewed the various correlations. They conducted an experimental study of the effect of the immobile liquid saturation and suggested a correlation based on dimensional analysis. Nguyen12performed an experimental study of non-Darcy flow through perforations on a synthetic core using air. These experiments showed that non-Darcy flow exists in the convergence zone and the perforation tunnel. Results of this study showed that Darcy flow equations can over predict well productivity by as much as 100%. Jones13 conducted experiments on 355 sandstone and 29 limestone cores. These tests were done for various core types: vuggy limestones, crystalline limestones, and fine grained sandstones. He presented the following correlation: β = 6.15 × 10 10 k − 1.55 . ( 5 ) He also points out that the group ?k? which is the characteristic length used for defining a Reynolds number for porous media, should be proportional to the characteristic length k/ϕ. He developed an approximate multilayer flow model that demonstrates that the departure from the above relation is due to permeability variations. Jones suggested that heterogeneity may be the reason why all correlations involving ? exhibit so much scatter.

Revisiting Current Techniques for Analyzing Reservoir Performance: A New Approach for Horizontal-Well Pseudosteady-State Productivity Index

SPE Journal ◽  
2018 ◽  
Vol 24 (01) ◽  
pp. 71-91 ◽  
Author(s):  
Salam Al-Rbeawi
Keyword(s):  
Porous Media ◽  
Pressure Drop ◽  
Transient State ◽  
Darcy Flow ◽  
Analytical Models ◽  
Productivity Index ◽  
Pressure Derivative ◽  
Starting Time ◽  
State Flow ◽  
State Pressure

Summary The objective of this paper is to revisit currently used techniques for analyzing reservoir performance and characterizing the horizontal-well productivity index (PI) in finite-acting oil and gas reservoirs. This paper introduces a new practical and integrated approach for determining the starting time of pseudosteady-state flow and constant-behavior PI. The new approach focuses on the fact that the derivative of PI vanishes to zero when pseudosteady-state flow is developed. At this point, the derivative of transient-state pressure drop and that of pseudosteady-state pressure drop become mathematically identical. This point indicates the starting time of pseudosteady-state flow as well as the constant value of pseudosteady-state PI. The reservoirs of interest in this study are homogeneous and heterogamous, single and dual porous media, undergoing Darcy and non-Darcy flow in the drainage area, and finite-acting, depleted by horizontal wells. The flow in these reservoirs is either single-phase oil flow or single-phase gas flow. Several analytical models are used in this study for describing pressure and pressure-derivative behavior considering different reservoir configurations and wellbore types. These models are developed for heterogeneous and homogeneous formations consisting of single and dual porous media (naturally fractured reservoirs) and experiencing Darcy and non-Darcy flow. Two pressure terms are assembled in these models; the first pressure term represents the time-dependent pressure drop caused by transient-state flow, and the second pressure term represents time-invariant pressure drop controlled by the reservoir boundary. Transient-state PI and pseudosteady-state PI are calculated using the difference between these two pressures assuming constant wellbore flow rate. The analytical models for the pressure derivatives of these two pressure terms are generated. Using the concept that the derivative of constant PI converges to zero, these two pressure derivatives become mathematically equal at a certain production time. This point indicates the starting time of pseudosteady-state flow and the constant behavior of PI. The outcomes of this study are summarized as the following: Understanding pressure, pressure derivative, and PI behavior of bounded reservoirs drained by horizontal wells during transient- and pseudosteady-state production Investigating the effects of different reservoir configurations, wellbore lengths, reservoir homogeneity or heterogeneity, reservoirs as single or dual porous media, and flow pattern in porous media whether it has undergone Darcy or non-Darcy flow Applying the concept of the PI derivative to determine the starting time of pseudosteady-state stabilized PI The novel points in this study are the following: The derivative of the PI can be used to precisely indicate the starting time of pseudosteady-state flow and the constant behavior of PI. The starting time of pseudosteady-state flow determined by the convergence of transient- and pseudosteady-state pressure derivative or by the PI curve is always less than that determined from the curves of total pressure drop and its derivative. Non-Darcy flow may significantly affect the transient-state PI, but pseudosteady-state PI is slightly affected by non-Darcy flow. The starting time of pseudosteady-state flow is not influenced by non-Darcy flow. The convergence of transient- and pseudosteady-state pressure derivatives is affected by reservoir configurations, wellbore lengths, and porous-media characteristics.

scholarly journals A Treatise on Non-Darcy Flow Correlations in Porous Media

2017 ◽  
Vol 08 (04) ◽  
Author(s):  
Vaishali Sharma ◽  
Anirbid Sircar ◽  
Noor Mohammad ◽  
Sannishtha Patel
Keyword(s):  
Porous Media ◽  
Darcy Flow
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