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Power law of filtration and its consequences for low-permeable reservoirs

UDK: 622.276.1/4:558.98.NP
DOI: 10.24887/0028-2448-2020-4-34-37
Key words: non-linear filtration, permeable reservoirs, phase permeability, hydrodynamic simulation
Authors: N.N. Mikhailov (Gubkin University, RF, Moscow; Oil and Gas Research Institute of RAS, RF, Moscow), E.S. Tumanova (VolgogradNIPImorneft Branch of LUKOIL-Engineering LLC in Volgograd, RF, Volgograd), M.V. Zaitsev (Oil and Gas Research Institute of RAS, RF, Moscow)

Nonlinear filtration in low-permeable reservoirs is considered. Low-permeable reservoirs are the most important unconventional source of hydrocarbons, and their development is complicated by filtration anomalies. Existing studies consider non-linear filtration similarly to filtration of a viscoplastic fluid with separation of the initial pressure gradient and determine permeability from Darcy's law. The authors here established a new power law relating the filtration rate to the pressure gradient, which excludes the presence of an initial pressure gradient. Permeability in the power law of filtration does not correspond to Darcy permeability and is not a constant value. Assignment of the reservoir to a low permeability class is based on the values of the absolute permeability, which does not take into account physicochemical interactions during the target phases filtration. Absolute permeability characterizes exclusively the structure of the pore space. Phase permeability accounts for the effects of resistance to the motion of the phases during their physicochemical interaction with the skeleton. The relationship between the phase and absolute permeabilities, assuming the power law of filtration, exists only for fixed values of the pressure gradients. It is shown that within realistic ranges of pressure gradients in low-permeability reservoirs, the phase permeability is not constant but increases with an increasing pressure gradient. It is also shown that classical hydrodynamic models are not applicable for the description of filtration in low-permeability reservoirs. The power law of filtration leads to nonlinearity of the mass conservation equation and to an unconventional form of the piezoelectric conductivity equation. The distinctions of the latter lie in the piezoconductivity coefficient and the nonlinearity of the equation. Agreement with the classical equations is observed only in the particular case of the exponent of 1 in the power law of filtration. Thus, the formal use of commercial simulators to predict the development of deposits with low permeability reservoirs is incorrect.

References

1. Baykov V.A., Galeev R.R., Kolonskikh A.V., Makatrov A.K. et al.,  Nonlinear filtration in low-permeability reservoirs. Analisys and interpretation of laboratory core examination for Priobskoye oilfield (In Russ.), Nauchno-tekhnicheskiy vestnik OAO “NK “Rosneft'”, 2013, no. 2, pp.  8–12.

2. Baykov V.A., Galeev R.R., Kolonskikh A.V. et al., Nonlinear filtration in low-permeability reservoirs. Impact on the technological parameters of the field development (In Russ.), Nauchno-tekhnicheskiy vestnik OAO “NK “Rosneft'”, 2013, no. 2, pp.  17–19.

3. Barenblatt G.I., Entov V.M., Ryzhik V.M., Dvizhenie zhidkostey i gazov v prirodnykh plastakh (Movement of liquids and gases in natural reservoirs), Moscow: Nedra Publ., 1982, 211 p.

4. Li Syuanzhan, Non-linear filtration of water in low permeability reservoirs (In Russ.), Vesti gazovoy nauki, 2015, no. 3 (23), pp. 116–121.

5. Baoquan Z., Linsong C., Chunlan L., Low velocity non-linear flow in ultra-low permeability reservoir, Journal of Petroleum Science and Engineering, 2011, V. 80, pp. 1–6.

6. Fei H., Cheng L.S., Hassan O. et al., Threshold pressure gradient in ultra-low permeability reservoirs, Science and Technology, 2008, V. 26, pp. 1024–1035.

7. Xiong W., Lei Q., Gao S. et al.,  Pseudo threshold pressure gradient to flow for low permeability reservoirs, Petroleum Exploration and Development, 2009, V. 36, pp. 232–236.

8. Mikhaylov N.N., Fizika neftyanogo i gazovogo plasta (Physics of oil and gas reservoir), Moscow: Maks-Press Publ., 2008, 448 p.

9. Levorsen A.I., Geology of petroleum, San Francisco: W. H. Freeman and Company, 1967, 174 p.

10. Wang X., Yang Z., Qi Y., Huang Y., Effect of absorption boundary layer on nonlinear flow in low permeability porous media, Journal of Central South University of Technology, 2011, V. 18, pp. 1299–1303.

11. Kovalev A.G., Kuznetsov A.M., Baishev A.B. et al., Sopostavlenie velichin pronitsaemosti produktivnykh porod-kollektorov po zhidkosti i gazu (Comparison of permeability values of productive reservoir rocks by liquid and gas), Proceedings of VNIIneft', 2001, V. 125, pp. 61–63.

 

Nonlinear filtration in low-permeable reservoirs is considered. Low-permeable reservoirs are the most important unconventional source of hydrocarbons, and their development is complicated by filtration anomalies. Existing studies consider non-linear filtration similarly to filtration of a viscoplastic fluid with separation of the initial pressure gradient and determine permeability from Darcy's law. The authors here established a new power law relating the filtration rate to the pressure gradient, which excludes the presence of an initial pressure gradient. Permeability in the power law of filtration does not correspond to Darcy permeability and is not a constant value. Assignment of the reservoir to a low permeability class is based on the values of the absolute permeability, which does not take into account physicochemical interactions during the target phases filtration. Absolute permeability characterizes exclusively the structure of the pore space. Phase permeability accounts for the effects of resistance to the motion of the phases during their physicochemical interaction with the skeleton. The relationship between the phase and absolute permeabilities, assuming the power law of filtration, exists only for fixed values of the pressure gradients. It is shown that within realistic ranges of pressure gradients in low-permeability reservoirs, the phase permeability is not constant but increases with an increasing pressure gradient. It is also shown that classical hydrodynamic models are not applicable for the description of filtration in low-permeability reservoirs. The power law of filtration leads to nonlinearity of the mass conservation equation and to an unconventional form of the piezoelectric conductivity equation. The distinctions of the latter lie in the piezoconductivity coefficient and the nonlinearity of the equation. Agreement with the classical equations is observed only in the particular case of the exponent of 1 in the power law of filtration. Thus, the formal use of commercial simulators to predict the development of deposits with low permeability reservoirs is incorrect.

References

1. Baykov V.A., Galeev R.R., Kolonskikh A.V., Makatrov A.K. et al.,  Nonlinear filtration in low-permeability reservoirs. Analisys and interpretation of laboratory core examination for Priobskoye oilfield (In Russ.), Nauchno-tekhnicheskiy vestnik OAO “NK “Rosneft'”, 2013, no. 2, pp.  8–12.

2. Baykov V.A., Galeev R.R., Kolonskikh A.V. et al., Nonlinear filtration in low-permeability reservoirs. Impact on the technological parameters of the field development (In Russ.), Nauchno-tekhnicheskiy vestnik OAO “NK “Rosneft'”, 2013, no. 2, pp.  17–19.

3. Barenblatt G.I., Entov V.M., Ryzhik V.M., Dvizhenie zhidkostey i gazov v prirodnykh plastakh (Movement of liquids and gases in natural reservoirs), Moscow: Nedra Publ., 1982, 211 p.

4. Li Syuanzhan, Non-linear filtration of water in low permeability reservoirs (In Russ.), Vesti gazovoy nauki, 2015, no. 3 (23), pp. 116–121.

5. Baoquan Z., Linsong C., Chunlan L., Low velocity non-linear flow in ultra-low permeability reservoir, Journal of Petroleum Science and Engineering, 2011, V. 80, pp. 1–6.

6. Fei H., Cheng L.S., Hassan O. et al., Threshold pressure gradient in ultra-low permeability reservoirs, Science and Technology, 2008, V. 26, pp. 1024–1035.

7. Xiong W., Lei Q., Gao S. et al.,  Pseudo threshold pressure gradient to flow for low permeability reservoirs, Petroleum Exploration and Development, 2009, V. 36, pp. 232–236.

8. Mikhaylov N.N., Fizika neftyanogo i gazovogo plasta (Physics of oil and gas reservoir), Moscow: Maks-Press Publ., 2008, 448 p.

9. Levorsen A.I., Geology of petroleum, San Francisco: W. H. Freeman and Company, 1967, 174 p.

10. Wang X., Yang Z., Qi Y., Huang Y., Effect of absorption boundary layer on nonlinear flow in low permeability porous media, Journal of Central South University of Technology, 2011, V. 18, pp. 1299–1303.

11. Kovalev A.G., Kuznetsov A.M., Baishev A.B. et al., Sopostavlenie velichin pronitsaemosti produktivnykh porod-kollektorov po zhidkosti i gazu (Comparison of permeability values of productive reservoir rocks by liquid and gas), Proceedings of VNIIneft', 2001, V. 125, pp. 61–63.

 



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