A Novel Integrated Approach to Modelling of Depletion-Induced Change in Full Permeability Tensor of Naturally Fractured Reservoirs

Document Type: Research Paper

Authors

Imam Khomeini International University, Ghazvin, Iran

Abstract

More than half of all hydrocarbon reservoirs are Naturally Fractured Reservoirs (NFRs), in which production forecasting is a complicated function of fluid flow in a fracture-matrix system. Modelling of fluid flow in NFRs is challenging due to formation heterogeneity and anisotropy. Stress sensitivity and depletion effect on already-complex reservoir permeability add to the sophistication. Horizontal permeability anisotropy and stress sensitivity are often ignored or inaccurately taken into account when simulating fluid flow in NFRs. The aim of this paper is to present an integrated approach for evaluating the dynamic and true anisotropic nature of permeability in naturally fractured reservoirs. Among other features, this approach considers the effect of reservoir depletion on reservoir permeability tensor, allowing more realistic production forecasts. In this approach the NFR is discretized into grids for which an analytical model yields full permeability tensors. Then, fluid flow is modelled using the finite-element method to obtain pore-pressure distribution within the reservoir. Next, another analytical model evaluates the change in the aperture of individual fractures as a function of effective stress and rock mechanical properties. The permeability tensor of each grid is then updated based on the apertures obtained for the current time step. The integrated model proceeds according to the next prescribed time increments.

Keywords


[1] Kunkel, J.R., Way, S. C., and McKee, C. R.
(1988). Comparative Evaluation of Selected
Continuum and Discrete-fracture Models:
Creston Study Area, Eastern Washington. US
Nuclear Regulatory Commission.
[2] Schwartz, F.W. and Smith, L. (1988). A
continuum approach for modelling mass
transport in fractured media. Water Resources
Research, 24(8): pp. 1360-1372.
[3] Long, J.C.S., Remer, S., Wilson, C.R. and
Witherspoon, P.A. (1982). Porous media
equivalents for network of discontinuous
fractures. Water Resources Research, 18(3): pp.
645-658.
[4] Therrien, R. and Sudicky, E. (1996). Threedimensional
analysis of variably-saturated flow
and solute transport in discretely-fractured
porous media. Journal of Contaminant
Hydrology, 23(1): pp. 1-44.
[5] Barenblatt, G.I., Zheltov, Y.P. and Kochina,
I.N. (1960). Basic concepts on the theory of
seepage of homogeneous liquids in fissured
rocks. Prikladnaya Matematika i Mekhanika,.
24(5): pp. 852-864.
[6] Chilingarian, G.V., Mazzullo, S.J. and Rieke,
H.H. (1992). Carbonate reservoir
Characterization: A Geologic -Engineering
Analysis. Developments in Petroleum Science, 

ed. G.V. Chilingarian, S.J. Mazzullo, and H.H. Rieke. Vol. 30, Part I., Amsterdam: Elsevier Publ. Co.
[7] Chilingarian, G.V., Mazzullo, S.J. and Rieke, H.H. (1996). Carbonate reservoir Characterization: A Geologic -Engineering Analysis. Developments in Petroleum Science, 44, ed. G.V. Chilingarian, Vol. 44, Part II., Amsterdam: Elsevier Publ. Co.
[8] Bagheri, M.A. and Settari, A.T. (2006). Modelling fluid flow in deformable fractured reservoirs using full tensor permeability, Golden Rocks 2006, The 41st US Symposium on Rock Mechanics (USRMS), American Rock Mechanics Association.
[9] Hughes, R.G. and Blunt, M.J. (2001). Network modelling of multiphase flow in fractures. Advances in Water Resources, 24(3): pp. 409-421.
[10] Long, J.C.S. and Witherspoon, P.A. (1985). The relationship of the degree of interconnection to permeability in fracture networks, Journal of geophysical research, 90(B4): pp. 3087- 3089.
[11] Oda, M. (1985). Permeability tensor for discontinuous rock masses. Geotechnique,. 35(4).
[12] Renard, P. and De Marsily, G. (1997). Calculating equivalent permeability: a review. Advances in Water Resources, 20(5): pp. 253-278.
[13] Lough, M., Lee, S. and Kamath, J. (1998). An efficient boundary integral formulation for flow through fractured porous media. Journal of Computational Physics, 143(2): pp. 462-483.
[14] Snow, D.T. (1968). Rock fracture spacings, openings, and porosities, Journal of Soil Mechanics & Foundations Div.
[15] Snow, D.T. (1969). Anisotropie permeability of fractured media, Water Resources Research,. 5(6): pp. 1273-1289.
[16] Matheron, G., et al. (1987). Conditional simulation of the geometry of fluvio-deltaic reservoirs. in SPE Annual Technical Conference and Exhibition, Society of Petroleum Engineers.
[17] Dagan, G., (1993). Higher-order correction of effective permeability of heterogeneous isotropic formations of lognormal conductivity distribution. Transport in Porous Media, 12(3): pp. 279-290.
[18] elhar, L.W. (1993). Stochastic subsurface hydrology, Prentice Hall PTR.
[19] Cacas, M., et al., (1990). Modelling fracture flow with a stochastic discrete fracture network: Calibration and validation: 1. The flow model, Water Resources Research, 26(3): pp. 479-489.
[20] Durlofsky, L.J. (1991). Numerical calculation of equivalent grid block permeability tensors for heterogeneous porous media, Water resources research, 27( 5): pp. 699-708.
[21] Nakashima, T., Arihara, N. and Sato, K. (2001). Effective permeability estimation for modelling naturally fractured reservoirs. SPE Middle East Oil Show.
[22] Jones, F.O., Jr., (1975). A Laboratory Study of the Effects of Confining Pressure on Fracture Flow and Storage Capacity in Carbonate Rocks.
[23] Buchsteiner, H., Warpinski, N.R. and Economides, M.J. (1993). Stress-Induced Permeability Reduction in Fissured Reservoirs, SPE Paper 26513.
[24] Lorenz, J.C. (1999). Stress-Sensitive Reservoirs. JPT, pp. 61-63.
[25] Abass, H., et al. (2007). Understanding Stress Dependant Permeability of Matrix Natural Fractures and Hydraulic Fractures in Carbonate Formations. in SPE Saudi Arabia Section Technical Symposium, Society of Petroleum Engineers.
[26] Nelson, R. (2001). Geologic Analysis of Naturally Fractured Reservoirs, Elsevier Science.
[27] van Golf-Racht, T.D. (1982). Fundamentals of Fractured Reservoir Engineering, Elsevier Science.
[28] Duan, Y., et al. (2000). Closure Behaviour of Natural Rock Fractures, SPE/AAPG Western Regional Meeting.
[29] Economides, M.J., Hill, A.D. and Ehligh_Economides, C.A. (1993). Petroleum Production Systems., New Jersey, Prentice Hall.
[30] Papadopulos, I.S. (1965). Nonsteady flow to a well in an infinite anisotropic aquifer, in Proceedings of the Dubrovnik Symposium on the Hydrology of Fractured Rocks, International Association of Scientific Hydrology.