Analytical models & type-curve matching techniques for reservoir characterization using wellbore storage dominated flow regime

Abstract

The applicability of early time data in reservoir characterization is not always considered worthy. Early time data is usually controlled by wellbore storage effect. This effect may last for pseudo-radial flow or even boundary dominated flow. Eliminating this effect is an option for restoring real data. Using the data with this effect is another option that could be used successfully for reservoir characterization.

This paper introduces new techniques for restoring disrupted data by wellbore storage at early time production. The proposed techniques are applicable for reservoirs depleted by horizontal wells and hydraulic fractures. Several analytical models describe early time data, controlled by wellbore storage effect, have been generated for both horizontal wells and horizontal wells intersecting multiple hydraulic fractures. The relationships of the peak points (humps) with the pressure, pressure derivative and production time have been mathematically formulated in this study for different wellbore storage coefficients. For horizontal wells, a complete set of type curves has been included for different wellbore lengths, skin factors and wellbore storage coefficients. Another complete set of type curves has been established for fractured formations based on the number of hydraulic fractures, spacing between fractures, and wellbore storage coefficient.

The study has shown that early radial flow for short to moderate horizontal wells is the most affected by wellbore storage while for long horizontal wells; early linear flow is the most affected flow regime by wellbore storage effect. The study has also emphasized the applicability of early time data for characterizing the formations even though they could be controlled by wellbore storage effect. As a matter of fact, this paper has found out that wellbore storage dominated flow could have remarkable relationships with the other flow regimes might be developed during the entire production times. These relationships can be used to properly describe the formations and quantify some of their characteristics.

Keywords

Reservoir engineering / Reservoir modeling and simulation / Pressure transient analysis / Reservoir characterization / Wellbore storage effect / Skin factor / Reservoir flow regimes / Pressure behaviors

References

[1] R. Agarwal, R. Al-Hussainy, J. Ramey, An investigation of wellbore storage and skin effect in unsteady liquid flow: I analytical treatment, SPE J. 249 (1970) 279-289, http://dx.doi.org/10.2118/2466-PA.

[2] J.H. Ramey, Short-time well test data interpretation in the presence of skin effect and wellbore storage, JPT 22 (1) (1970) 97-104, http://dx.doi.org/10.2118/2336-PA.

[3] R. Earlougher, K. Kersch, J. Ramey, : wellbore effects in injection well testing, JPT 25 (11) (1973) 1244-1250, http://dx.doi.org/10.2118/4371-PA.

[4] R. Raghavan, The effect of producing time on type curve matching, JPT 32 (6) (1980) 1053-1064, http://dx.doi.org/10.2118/6997-PA.

[5] M. Kamal, Effects of wellbore storage and skin on vertical-permeability testing, SPE Form. Eval. 1 (5) (1986) 481-496, http://dx.doi.org/10.2118/13250-PA.

[6] M. Soliman, Analysis of buildup tests with short producing time, SPE Form. Eval. 1 (4) (1986) 363-371, http://dx.doi.org/10.2118/11083-PA.

[7] F. Kuchuk, P. Kirwan, New skin and wellbore storage type curves for partially penetrated wells, SPE Form. Eval. 2 (4) (1987) 546-554, http://dx.doi.org/10.2118/11676-PA.

[8] F. Daviau, G. Mouronval, G. Bourdarot, P. Curutchet, Pressure analysis for horizontal wells, SPE Form. Eval. 3 (4) (1988) 716-724, http://dx.doi.org/10.2118/14251-PA.

[9] E. Ozkan, C. Sarica, M. Haciislamoglu, et al., Effect of conductivity on horizontal-well pressure-behavior, SPE Adv. Technol. Ser. 3 (19) (1995) 85-94, http://dx.doi.org/10.2118/24638-PA.

[10] M. Vasquez-Cruz, R. Camacho-Velasquez, Analysis of short transient tests affected by changing wellbore storage, SPE Reserv. Eval. Eng. 1 (3) (1998) 261-267, http://dx.doi.org/10.2118/36120-PA.

[11] J. Spivey, K. Brown, W. Sawyer, et al., Estimating non-darcy flow coefficient from buildup-test data with wellbore storage, SPE Reserv. Eval. Eng. 7 (4) (2004) 256-269, http://dx.doi.org/10.2118/77484-PA.

[12] Y. Cheng, J. Lee, D. McVay, Fast-fourier-transformation-based deconvolution for interpretation of pressure-transient-test data dominated by wellbore storage, SPE Reserv. Eval. Eng. 8 (3) (2005) 224-239, http://dx.doi.org/10.2118/84471-PA.

[13] D. Ilk, P. Valko, T. Blasingame, Deconvolution of variable-rate reservoir-performance data using B-Splines, SPE Reserv. Eval. Eng. 58 (2) (2006) 582-585, http://dx.doi.org/10.2118/95571-PA.

[14] E. Ozkan, R. Raghavan, Some New Solutions to Solve Problems in Well Test Analysis: Part 2-Computational Considerations and Applications, Society of Petroleum Engineers, 1988 doi:null.

[15] H. Stehfest, Numerical inversion of Laplace transforms, Commun. ACM 13 (1) (1970) 47-49.

[16] R.-S. Nie, Y.-L. Jia, Y. Meng, Y. Wang, J.-M. Yuan, W.-F. Xu, New type curves for modeling productivity of horizontal well with negative skin factors, SPE Reserv. Eng. Eval. 15 (4) (2012) 486-497, http://dx.doi.org/10.2118/163045-PA.