Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
SpringerLink
Log in

A New Non-Darcy Flow Model for Low-Velocity Multiphase Flow in Tight Reservoirs

  • Published:
Transport in Porous Media Aims and scope Submit manuscript

Abstract

The pore and pore-throat sizes of shale and tight rock formations are on the order of tens of nanometers. The fluid flow in such small pores is significantly affected by walls of pores and pore-throats. This boundary layer effect on fluid flow in tight rocks has been investigated through laboratory work on capillary tubes. It is observed that low permeability is associated with large boundary layer effect on fluid flow. The experimental results from a single capillary tube are extended to a bundle of tubes and finally to porous media of tight formations. A physics-based, non-Darcy low-velocity flow equation is derived to account for the boundary layer effect of tight reservoirs by adding a non-Darcy coefficient term. This non-Darcy equation describes the fluid flow more accurately for tight oil reservoir with low production rate and low pressure gradient. Both analytical and numerical solutions are obtained for the new non-Darcy flow model. First, a Buckley–Leverett-type analytical solution is derived with this non-Darcy flow equation. Then, a numerical model has been developed for implementing this non-Darcy flow model for accurate simulation of multidimensional porous and fractured tight oil reservoirs. Finally, the numerical studies on an actual field example in China demonstrate the non-negligible effect of boundary layer on fluid flow in tight formations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  • Ahmed, T.: Reservoir Engineering Handbook. Gulf Professional Publishing, Houston (2006)

    Google Scholar 

  • Ahmed, T., McKinney, P.: Advanced Reservoir Engineering. Gulf Professional Publishing, Houston (2011)

    Google Scholar 

  • Aziz, K., Settari, A.: Petroleum Reservoir Simulation. Chapman & Hall, London (1979)

    Google Scholar 

  • Barree, R.D., Conway, M.W.: Beyond Beta Factors: A Complete Model for Darcy, Forchheimer, and Trans-Forchheimer Flow in Porous Media. Presented at SPE Annual Technical Conference and Exhibition, 26–29 September, Houston, TX (2004)

  • Buckley, S.E., Leverett, M.C.: Mechanism of fluid displacement in sands. Trans. AIME 146(01), 107–116 (1942)

    Article  Google Scholar 

  • Carman, P.C.: Fluid flow through granular beds. Chem. Eng. Res. Des. 75, 32–48 (1997)

    Article  Google Scholar 

  • Civan, F.: Implications of alternative macroscopic descriptions illustrated by general balance and continuity equations. J. Porous Media 5(4), 271–282 (2002)

    Article  Google Scholar 

  • Civan, F.: Generalized Darcy’s law by control volume analysis including capillary and orifice effects. J. Can. Petrol. Technol. 47(10), 1–7 (2008)

    Article  Google Scholar 

  • Civan, F.: Comparison of control volume analysis and porous media averaging for formulation of porous media transport. In: Ferreira, J.A., Barbeiro, S., Pena, G., Wheeler, M.F. (eds.) Chapter 2 in Modeling and Simulation in Fluid Dynamics in Porous Media, Series: Springer Proceedings in Mathematics & Statistics, vol. 28, pp. 27–53. Springer, New York, New York (2013)

  • Darcy, H.: Les Fontaines Publiques de la Ville de Dijon. Dalmont, Paris (1856)

    Google Scholar 

  • Ergun, S.: Fluid flow through packed columns. Chem. Eng. Prog. 48, 89–94 (1952)

    Google Scholar 

  • Evans, R.D., Hudson, C.S., Greenlee, J.E.: The effect of an immobile liquid saturation on the non-Darcy flow coefficient in porous media. SPE Prod. Eng. 2(4), 331–338 (1987)

    Article  Google Scholar 

  • Evans, E.V., Evans, R.D.: Influence of an immobile or mobile saturation on non-Darcy compressible flow of real gases in propped fractures. J. Pet. Technol. 40(10), 1343–1351 (1988)

    Article  Google Scholar 

  • Forchheimer, P.: Wasserbewegung durch boden. Z. Ver. Deutsch. 45(1782), 1788 (1901)

    Google Scholar 

  • Gavin, L.: Pre-Darcy flow: a missing piece of the improved oil recovery puzzle? Presented at SPE/DOE Symposium on Improved Oil Recovery, Tulsa, Oklahoma, 17–21 April (2004)

  • Hansbo, S.: Consolidation of clay with special reference to influence of vertical drain. Proc. R. Swed. Geotech. Inst. 18(1), 1–160 (1960)

    Google Scholar 

  • Hansbo, S.: Consolidation equation valid for both Darcian and non-Darcian flow. Géotechnique 51(1), 51–54 (2001)

    Article  Google Scholar 

  • Huang, Y., Yang, Z., He, Y., Wang, X., Luo, Y.: Nonlinear porous flow in low permeability porous media. Mech. Eng. 35(5), 1–8 (2013)

    Google Scholar 

  • Jiang, R., Yang, R., Ma, Y., Zhuang, Y., Li, L.: Nonlinear percolation theory and numerical simulation in low permeability reservoirs. Chin. J. Hydrodyn. 26(4), 444–452 (2011)

    Google Scholar 

  • Liu, H.H.: Non-Darcian flow in low-permeability media: key issues related to geological disposal of high-level nuclear waste in shale formations. Hydrogeol. J. 22(7), 1525–1534 (2014)

    Article  Google Scholar 

  • Liu, H.H., Lai, B., Chen, J.: Unconventional spontaneous imbibition into Shale matrix: theory and a methodology to determine relevant parameters. Transp. Porous Media 111(1), 41–57 (2015)

    Article  Google Scholar 

  • Montillet, A.: Flow through a finite packed bed of spheres: a note on the limit of applicability of the Forchheimer-type equation. J. Fluids Eng. 126(1), 139–143 (2004)

    Article  Google Scholar 

  • Narasimhan, T.N., Witherspoon, P.A.: An integrated finite difference method for analyzing fluid flow in porous media. Water Resour. Res. 12(1), 57–64 (1976)

    Article  Google Scholar 

  • Prada, A., Civan, F.: Modification of Darcy’s law for the threshold pressure gradient. J. Pet. Sci. Eng. 22(4), 237–240 (1999)

    Article  Google Scholar 

  • Pruess, K.: TOUGH2: A General-Purpose Numerical Simulator for Multiphase Fluid and Heat Flow. Lawrence Berkeley Lab, Berkeley (1991)

    Google Scholar 

  • Swartzendruber, D.: Non-Darcy flow behavior in liquid-saturated porous media. J. Geophys. Res. 67(13), 5205–5213 (1962)

    Article  Google Scholar 

  • Wang, C., Wu, Y.S., Xiong, Y., Winterfeld, P.H., Huang., Z.: Geomechanics Coupling Simulation of Fracture Closure and Its Influence on Gas Production in Shale Gas Reservoirs. Presented at SPE Reservoir Simulation Symposium, Houston, Texas, 23–25 February (2015)

  • Wu, Y. S.: MSFLOW: Multiphase Subsurface Flow Model of Oil, Gas and Water in Porous and Fractured Media with Water Shut-Off Capability, DOCUMENTATION and User’s Guide (1998)

  • Wu, Y.S.: Non-Darcy displacement of immiscible fluids in porous media. Water Resour. Res. 37(12), 2943–2950 (2001)

    Article  Google Scholar 

  • Wu, Y.S., Fakcharoenphol P., Zhang R.: Non-Darcy Displacement in Linear Composite and Radial Flow Porous Media. Presented at SPE EUROPEC/EAGE Annual Conference and Exhibition, Barcelona, Spain, 14–17 June (2010)

  • Wu, Y.S., Xiong Y., Kazemi H.: Coupled thermo-hydrological processes in enhanced geothermal systems. In: Pore Scale Phenomena: Frontiers in Energy and Environment, pp. 279–298. World Scientific (2015)

  • Xiong, Y., Fakcharoenphol, P., Winterfeld, P., Zhang, R., Wu, Y.S.: Coupled Geomechanical and Reactive Geochemical Model for Fluid and Heat Flow: Application for Enhanced Geothermal Reservoir. Presented at SPE Reservoir Characterization and Simulation Conference and Exhibition, SPE, Abu Dhabi, UAE, 16–18 September (2013)

  • Xiong, Y.: Development of a compositional model fully coupled with geomechanics and its application to tight oil reservoir simulation. Ph.D. dissertation, Colorado School of Mines (2015)

  • Xu, S., Yue, X.: Experimental research on nonlinear flow characteristics at low velocity. J. China Univ. Pet. (Ed. Nat. Sci.) 5, 014 (2007)

    Google Scholar 

  • Zeng, B., Cheng, L., Li, C.: Low velocity non-linear flow in ultra-low permeability reservoir. J. Pet. Sci. Eng. 80(1), 1–6 (2011)

    Article  Google Scholar 

  • Zhang, R., Wu, Y.S., Fakcharoenphol, P.: Non-Darcy displacement in linear composite and radial aquifer during \(\text{ CO }_{2}\) sequestration. Int. J. Oil Gas Coal Technol. 7(3), 244–262 (2014)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Colorado School of Mines, Golden, CO, USA

    Yi Xiong & Yu-shu Wu

  2. China Petroleum & Chemical Corp (SINOPEC), Beijing, China

    Jinbiao Yu & Hongxia Sun

  3. RIPED of PetroChina, Beijing, China

    Jiangru Yuan

  4. China University of Petroleum (East China), Qingdao, China

    Zhaoqin Huang

Authors
  1. Yi Xiong
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jinbiao Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hongxia Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jiangru Yuan
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Zhaoqin Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Yu-shu Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yi Xiong.

Appendix: Experimental Setup and Procedure

Appendix: Experimental Setup and Procedure

The experimental method and setup is the same as the work of Xu and Yue (2007), and the experimental apparatus is shown in Fig. 13.

Fig. 13
figure 13

Experimental setup. Modified according to Xu and Yue (2007)

Full size image

It consists of three parts, driving force system, filtering system and measurement system. They are separated by the dash lines in the sketch of experimental setup as shown in Fig. 13. Pressurized nitrogen gas is used as the driving force. It is filtered in the gas filtering system and reaches to liquid tank to drive the deionized water in the tank. The moving deionized water is also filtered and reaches to the small capillary tube. The flow rate of capillary tube is measured by observing the change of liquid level in liquid measurement tube and recording the corresponding time. The liquid level is magnified with microscope and transferred to the graphic display in the computer. With the measured flow rate and pressure gradient along the tube, the thickness of boundary flow can be calculated.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Xiong, Y., Yu, J., Sun, H. et al. A New Non-Darcy Flow Model for Low-Velocity Multiphase Flow in Tight Reservoirs. Transp Porous Med 117, 367–383 (2017). https://doi.org/10.1007/s11242-017-0838-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11242-017-0838-8

Keywords

Search

Navigation