A Hybrid Numerical/Analytical Model of a Finite-Conductivity Vertical Fracture Intercepted by a Horizontal Well
- Mohammed Al-Kobaisi (Colorado School of Mines) | Erdal Ozkan (Colorado School of Mines) | Hossein Kazemi (Colorado School of Mines)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- August 2006
- Document Type
- Journal Paper
- 345 - 355
- 2006. Society of Petroleum Engineers
- 5.1.5 Geologic Modeling, 5.3.1 Flow in Porous Media, 1.6.6 Directional Drilling, 5.6.3 Pressure Transient Testing, 5.6.4 Drillstem/Well Testing, 2.2.2 Perforating, 2.5.4 Multistage Fracturing, 3.2.3 Hydraulic Fracturing Design, Implementation and Optimisation, 2.5.2 Fracturing Materials (Fluids, Proppant)
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This paper presents a hybrid numerical/analytical model for the pressure-transient response of a finite-conductivity fracture intercepted by a horizontal well. The model dynamically couples a numerical fracture model with an analytical reservoir model. This approach allows us to include finer details of the fracture characteristics while keeping the computational work manageable. For example, the fracture may have irregular shape, nonuniform width, and variable conductivity, and the well may not intersect the fracture at its geometric center.
In this paper, we use the hybrid model to investigate the effects of fracture properties on the pressure-transient characteristics of a single, finite-conductivity horizontal-well fracture. The single horizontal-well-fracture model can be extended easily to multiply fractured horizontal wells by superposition. The model also can be used to compute the pseudoskin caused by the effects of nonideal fracture geometry, variable conductivity, and flow choking around the wellbore and to investigate the influence of fracture properties on the performance of horizontal wells.
Fracturing horizontal wells is a common practice in tight formations (Moller 1988; Yost and Overbey 1989). Choking of flow around the horizontal well and fracture, however, strongly influences the flow characteristics and reduces the productivity of the fracture (Soliman et al. 1990). Fig. 1 shows the pressure surface on the fracture plane for a square hydraulic fracture intercepted by a horizontal well. The apex of the surface indicates the well intersection, and the increased pressure gradients around the well highlight the choking effect. This aspect of transverse hydraulic fractures emanating from horizontal wells is different from vertical wells. In addition, different fracture geometries may cause horizontal-well-fracture flow regimes that are different from those for vertical-well fractures (Fig. 2). If the fracture is a long rectangle, for example, linear flow dominates the flow convergence in the fracture after a short period of radial flow. Nonrectangular or noncircular fracture geometries may lead to unconventional flow regimes.
The effects of flow-choking, fracture geometry, and variable conductivity in a horizontal-well fracture influence the rate of pressure change until pseudoradial flow is established. As confirmed by our results in this paper, the pseudoskin approach provides a good approximation only for the pressure-transient responses of long, rectangular, horizontal-well fractures beyond the fracture radial-flow period. For the other fracture geometries, the pseudoskin approach is appropriate only after the onset of pseudoradial flow. Therefore, the pseudoskin approach suggested in the literature (Soliman et al. 1990; Raghavan et al. 1997; Chen and Raghavan 1997) to incorporate the flow-choking effect into vertical-well-fracture models (Cinco-Ley et al. 1978; Cinco-Ley and Samaniego 1981; Cinco-Ley and Meng 1988; Ozkan and Raghavan 1991a) should not be extended beyond its suggested application.
The objective of this paper is to present a model that can be used to understand the pressure-transient performance of a single, finite-conductivity horizontal-well fracture without the simplifying assumptions used in the literature (Soliman et al. 1990; Raghavan et al. 1997; Chen and Raghavan 1997; Larsen and Hegre 1991; Larsen and Hegre 1994; Guo and Evans 1993; Horne and Temeng 1995). In this model, the fracture flow is numerically simulated and dynamically coupled with an analytical reservoir-flow solution. Compared with a fully numerical approach, using an analytical solution for reservoir flow reduces the computational work and allows us to concentrate on the details of the fracture flow. For example, the fracture can have an irregular shape because of geological complexities, and conductivity can be variable within the fracture because of nonuniform gel and proppant placement or a nonplanar fracture profile. Although not included in this paper, non-Darcy flow in the fracture aggravated by flow convergence around the wellbore can be considered easily by a simple modification of the transmissibilities in the numerical model. The model presented in this paper is not limited to transverse horizontal-well fractures, either. Because the wellbore is represented as a source term in the fracture grid, several grids may include the wellbore source terms to simulate the appropriate intersection of the wellbore and the fracture plane (Fig. 3). Inherent in the numerical modeling of fracture flow, however, are the gridding, timestepping, and wellbore representation issues.
This paper concentrates on the solution for a single, finite-conductivity, horizontal-well fracture. The procedure for extending the single-fracture solutions to multiply fractured horizontal wells has already been explained in the literature (Raghavan et al. 1997; Chen and Raghavan 1997) and is briefly discussed in Appendix A for completeness.
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Al-Kobaisi, M. 2005. Pressure-TransientResponse of a Finite-Conductivity Fracture Intercepted by a Horizontal Well. MSthesis, Colorado School of Mines, Golden, Colorado.
Chen, C.C. and Raghavan, R. 1997. A Multiply-Fractured Horizontal Wellin a Rectangular Drainage Region. SPEJ 2 (4): 455-465.SPE-37072-PA.
Cinco-Ley, H. and Meng, H.Z. 1988. Pressure Transient Analysis of WellsWith Finite Conductivity Fractures in Double Porosity Reservoirs. Paper SPE18172 presented at the SPE Annual Technical Conference and Exhibition, Houston,2-5 October.
Cinco-Ley, H. and Samaniego-V., F. 1981.Transient Pressure Analysis forFractured Wells. JPT 33 (9): 1749-1766.SPE-7490-PA.
Cinco-Ley, H., Samaniego-V., F., andDominguez, N. 1978. TransientPressure Behavior of a Well With a Finite-Conductivity Vertical Fracture.SPEJ 18 (4): 253-264. SPE-6014-PA.
Guo, G. and Evans, R.D. 1993. Pressure-Transient Behavior andInflow Performance of Horizontal Wells Intersecting Discrete Fractures.Paper SPE 26446 presented at the SPE Annual Technical Conference andExhibition, Houston, 3-6 October.
Horne, R.N. and Temeng, K.O. 1995. Relative Productivities and PressureTransient Modeling of Horizontal Wells With Multiple Fractures. Paper SPE29891 presented at the SPE Middle East Oil Show, Bahrain, 11-14March.
Larsen, L. and Hegre, T.M. 1991. Pressure-Transient Behavior ofHorizontal Wells With Finite-Conductivity Vertical Fractures. Paper SPE22076 presented at the SPE International Arctic Technology Conference,Anchorage, 29-31 May.
Larsen, L. and Hegre, T.M. 1994. Pressure Transient Analysis ofMultifractured Horizontal Wells. Paper SPE 28389 presented at the SPEAnnual Technical Conference and Exhibition, New Orleans, 25-28September.
LePage, W.R. 1961. Complex Variablesand the Laplace Transform for Engineers, 362-372. New York City: DoverPublications Inc.
Moller, A.P. 1988. Horizontal DrillingResults in New Technology. Noroil (December).
Ozkan, E. and Raghavan, R. 1991a. New Solutions for Well-Test-AnalysisProblems: Part 2—Computational Considerations and Applications.SPEFE 6 (3): 369-378. SPE-18616-PA.
Ozkan, E. and Raghavan, R. 1991b. New Solutions for Well-Test-AnalysisProblems: Part 1—Analytical Considerations. SPEFE 6 (3):359-368. SPE-18615-PA.
Raghavan, R., Uraiet, A., and Thomas,G.W. 1978. Vertical FractureHeight: Effect on Transient Flow Behavior. SPEJ 18 (4):265-277. SPE-6016-PA.
Raghavan, R.S., Chen, C.C., and Agarwal,B. 1997. An Analysis of HorizontalWells Intercepted by Multiple Fractures. SPEJ 2 (3): 235-245.SPE-27652-PA.
Rodriguez, F., Horne, R.N., andCinco-Ley, H. 1984a. PartiallyPenetrating Fractures: Pressure Transient Analysis of an Infinite ConductivityFracture. Paper SPE 12743 presented at the SPE California Regional Meeting,Long Beach, California, 11-13 April.
Rodriguez, F., Horne, R.N., andCinco-Ley, H. 1984b. PartiallyPenetrating Fractures: Pressure Transient Analysis of a Finite-ConductivityFracture. Paper SPE 13057 presented at the SPE Annual Technical Conferenceand Exhibition, Houston, 16-19 September.
Roumboutsos, A. and Stewart, G. 1988. A Direct Deconvolution or ConvolutionAlgorithm for Well Test Analysis. Paper SPE 18157 presented at the SPEAnnual Technical Conference and Exhibition, Houston, 2-5 October.
Schulte, W.M. 1986. Production From a Fractured Well WithWell Inflow Limited to Part of the Fracture Height. SPEPE 1(3): 333-343. SPE-12882-PA.
Soliman, M.Y., Hunt, J.L., and El Rabaa,A.M. 1990. Fracturing Aspects ofHorizontal Wells. JPT 42 (8): 966-973.SPE-18542-PA.
Stehfest, H. 1970. Numerical Inversion of LaplaceTransforms. Communications ACM 13 (1): 47-49.
Van Poollen, H.K., Breitenback, E.A., andThurnau, D.H. 1968. Treatment ofIndividual Wells and Grids in Reservoir Modeling. SPEJ 8 (4):341-346. SPE-2022-PA.
Yost, A.B. II and Overbey, W.K. Jr. 1989.Production and StimulationAnalysis of Multiple Hydraulic Fracturing of a 2,000-ft Horizontal Well.Paper SPE 19090 presented at the SPE Gas Technology Symposium, Dallas, 7-9June.