New Transfer Functions for Simulation of Naturally Fractured Reservoirs with Dual Porosity Models
- Pallav Sarma (Stanford University) | Khalid Aziz (Stanford University)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- September 2006
- Document Type
- Journal Paper
- 328 - 340
- 2006. Society of Petroleum Engineers
- 1.2.3 Rock properties, 5.1.5 Geologic Modeling, 5.1 Reservoir Characterisation, 4.1.2 Separation and Treating, 5.8.8 Gas-condensate reservoirs, 5.4.1 Waterflooding, 4.1.5 Processing Equipment, 5.8.6 Naturally Fractured Reservoir, 5.6.4 Drillstem/Well Testing, 5.5 Reservoir Simulation, 5.3.2 Multiphase Flow
- 4 in the last 30 days
- 1,403 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 12.00|
|SPE Non-Member Price:||USD 35.00|
This paper discusses new techniques for the modeling and simulation of naturally fractured reservoirs with dual-porosity models. Most of the existing dual-porosity models idealize matrix-fracture interaction by assuming orthogonal fracture systems (parallelepiped matrix blocks) and pseudo-steady state flow. More importantly, a direct generalization of single-phase flow equations is used to model multiphase flow, which can lead to significant inaccuracies in multiphase flow-behavior predictions. In this work, many of these existing limitations are removed in order to arrive at a transfer function more representative of real reservoirs.
Firstly, combining the differential form of the single-phase transfer function with analytical solutions of the pressure-diffusion equation, an analytical form for a shape factor for transient pressure diffusion is derived to corroborate its time dependence. Further, a pseudosteady shape factor for rhombic fracture systems is also derived and its effect on matrix-fracture mass transfer demonstrated. Finally, a general numerical technique to calculate the shape factor for any arbitrary shape of the matrix block (i.e., nonorthogonal fractures) is proposed. This technique also accounts for both transient and pseudosteady-state pressure behavior. The results were verified against fine-grid single-porosity models and were found to be in excellent agreement.
Secondly, it is shown that the current form of the transfer function used in reservoir simulators does not fully account for the main mechanisms governing multiphase flow. A complete definition of the differential form of the transfer function for two-phase flow is derived and combined with the governing equations for pressure and saturation diffusion to arrive at a modified form of the transfer function for two-phase flow. The new transfer function accurately takes into account pressure diffusion (fluid expansion) and saturation diffusion (imbibition), which are the two main mechanisms driving multiphase matrix-fracture mass transfer. New shape factors for saturation diffusion are defined. It is shown that the prediction of wetting-phase imbibition using the current form of the transfer function can be quite inaccurate, which might have significant consequences from the perspective of reservoir management. Fine-grid single-porosity models are used to verify the validity of the new transfer function. The results from single-block dual-porosity models and the corresponding single-porosity fine-grid models were in good agreement.
A naturally fractured reservoir (NFR) can be defined as a reservoir that contains a connected network of fractures (planar discontinuities) created by natural processes such as diastrophism and volume shrinkage (Ordonez et al. 2001). Fractured petroleum reservoirs represent over 20% of the world's oil and gas reserves (Saidi 1983), but are, however, among the most complicated class of reservoirs. A typical example is the Circle Ridge fractured reservoir located on the Wind River Reservation in Wyoming, U.S.. This reservoir has been in production for more than 50 years but the total oil recovery until now has been less than 15% (www.fracturedreservoirs.com 2000).
It is undeniable that reservoir characterization, modeling, and simulation of naturally fractured reservoirs present unique challenges that differentiate them from conventional, single-porosity reservoirs. Not only do the intrinsic characteristics of the fractures, as well as the matrix, have to be characterized, but the interaction between matrix blocks and surrounding fractures must also be modeled accurately. Further, most of the major NFRs have active aquifers associated with them, or would eventually be subjected to some kind of secondary recovery process such as waterflooding (German 2002), implying that it is essential to have a good understanding of the physics of multiphase flow for such reservoirs. This complexity of naturally fractured reservoirs necessitates the need for their accurate representation from a modeling and simulation perspective, such that production and recovery from such reservoirs be predicted and optimized.
|File Size||2 MB||Number of Pages||13|
Aziz, K. 2001. Fundamentals of Reservoir Simulation. Course notes, PE223.Stanford U.
Barenblatt, G.E., Zheltov, I.P., and Kochina, I.N. 1960. Basic Concepts inthe Theory of Homogeneous Liquids in Fissured Rocks. Journal of AppliedMathematical Mechanics 24: 1286-1303 (in Russian).
Beckner, B.L. 1990. Improved Modeling of Imbibition Matrix/Fracture FluidTransfer in Double Porosity Simulators. PhD dissertation. Stanford, California:Stanford U.
Chang, M. 1993. Deriving the Shape Factor of a Fractured Rock Matrix.Technical Report NIPER-696 (DE93000170). Bartlesville, Oklahoma: NIPER.
Coats, K.H. 1989. ImplicitCompositional Simulation of Single-Porosity and Dual-Porosity Reservoirs.Paper SPE 18427 presented at the SPE Symposium on Reservoir Simulation,Houston, 6-8 February.
Crank, J. 1975. The Mathematics of Diffusion. Second edition. Oxford:Clarendon Press.
GeoQuest. 2000. Eclipse 100 Technical Description 2000A. Schlumberger.
German, E.R. 2002. Water Infiltration in Fractured Porous Media: In-situImaging, Analytical Model, and Numerical Study. PhD dissertation. Stanford,California: Stanford U.
Gilman, J.R. and Kazemi, H. 1983. Improvements in Simulation ofNaturally Fractured Reservoirs. SPEJ 23 (4): 695-707.SPE-10511-PA.
Kazemi, H., Merrill, L.S. Jr., Porterfield, K.L., and Zeman, P.R. 1976. Numerical Simulation of Water-Oil Flowin Naturally Fractured Reservoirs. SPEJ 16 (6): 317-326;Trans., AIME, 261. SPE-5719-PA.
Lim, K.T. and Aziz, K. 1995. Matrix-Fracture Transfer Shape Factors forDual-Porosity Simulators. Journal of Petroleum Science and Engineering13: 169-178
Litvak, B.L. 1985. Simulation and Characterization of Naturally FracturedReservoirs. Paper presented at the Reservoir Characterization TechnicalConference, Dallas.
MathWorks. 1996. Matlab PDE Toolbox User's Guide. The MathWorks Inc.
Ordonez, A., Penuela, G. et al. 2001. Recent Advances in Naturally FracturedReservoir Modeling. CTF 2.
Rossen, R.H. and Shen, E.I. 1987. Simulation of Gas/Oil Drainage andWater/Oil Imbibition in Naturally Fractured Reservoirs. SPERE4 (4): 464-470; Trans., AIME, 287. SPE-16982-PA.
Saidi, A.M. 1983. Simulation ofNaturally Fractured Reservoirs. Paper SPE 12270 presented at the SPEReservoir Simulation Symposium, San Francisco, California, 15-18 November.
Sarma, P. 2003. New Transfer Functions for Simulation of Naturally FracturedReservoirs With Dual-Porosity Models. MS thesis. Stanford, California: StanfordU.
Shaqfeh, E.S.G. 2001. Mathematical and Computational Methods in Engineering.Course notes, ME200B. Stanford U.
Sonier, F., Souillard, P., and Blaskovich, F.T. 1988. Numerical Simulation of NaturallyFractured Reservoirs. SPEREE 3 (4): 1114-1122; Trans.,AIME, 285. SPE-15627-PA.
Thomas, L.K., Dixon, T.N., and Pierson, R.G. 1983. Fractured Reservoir Simulation.SPEJ 23 (2): 42-54. SPE-9305-PA.
Udea, Y., Murata, S., Watanabe, Y., and Funatsu, K. 1989. Investigation of the Shape FactorUsed in the Dual-Porosity Reservoir Simulator. Paper SPE 19469 presented atthe SPE Asia-Pacific Conference , Sydney, Australia, 13-15 September.
Warren, J.E. and Root, P.J. 1963. The Behavior of Naturally FracturedReservoirs. SPEJ 3 (11): 245-255; Trans., AIME,228. SPE-426-PA.
www.fracturedreservoirs.com. 2000. Circle RidgeFractured Reservoir Project. Redmond, Washington: Golder Assocs.