Transient pressure analysis for vertical wells with spherical power-law flow

  • Freddy Humberto Escobar Universidad Surcolombiana
  • Javier-Andrés Martínez Universidad Surcolombiana
  • Luis-Fernando Bonilla Universidad Surcolombiana
Keywords: Pseudoplastic fluid, Consistency, Power-law, Radial flow, Partial completion, Partial penetration, Well tests, Transient pressure


Heavy oil is considered nowadays as one of the unconventional reservoirs of main interest in the oil industry. Some of them display non-Newtonian pseudoplastic behavior which mathematical modeling differs from the conventional case and, therefore, the flow regimes display some particular behaviors.
Fracturing fluids, foams, some fluids for Enhanced Oil Recovery (EOR) and drilling muds can also fall into this category. The spherical/hemispherical flow mainly caused by partial completion/penetration deserves a particular treatment for pseudoplastic flow. A single research for this case was found in the literature to introduce only its mathematical model.

The pressure and pressure derivative behavior of spherical/hemispherical flow behavior of a slightly compressible, non-Newtonian power-law fluid (pseudoplastic) is studied in this work and conventional and Tiab’s Direct Synthesis (TDS) methodologies are extended for well test interpretation purposes. For pseudoplastic spherical/ hemispherical flow, the slope of the pressure derivative is no longer -½, besides it changes with the value of flow behavior index n, which indicates that the interpretation of pressure data for the dealt systems through the use of traditional methods should not be accurate. New Equations are introduced to estimate spherical/ hemispherical permeability and spherical/hemispherical skin factor for the systems under consideration. The Equations were successfully verified by its application to synthetic cases.


Chatas, A.T. (1966). Unsteady spherical flow in petroleum reservoirs. SPE Journal, 6(2), 102-114

Ci-qun, L. (1988). Transient spherical flow of non-newtonian power-law fluids in porous media.

Culham, W.E. (1974). Pressure buildup Equations for spherical flow regime problems. SPE Journal, 14(6), 545-555.

Escobar, F. H., Martínez, J. A. & Montealegre-M., M. (2010). Pressure and pressure derivative analysis for a well in a radial composite reservoir with a non-newtonian/Newtonian interface. CT&F-Ciencia, Tecnología y Futuro, 4(2), 33-42.

Escobar, F.H., Zambrano, A.P, Giraldo, D.V. & Cantillo, J.H. (2011). Pressure and pressure derivative analysis for nonnewtonian pseudoplastic fluids in double-porosity formations. CT&F-Ciencia, Tecnología y Futuro, 4(3), 47-59.

Joseph, J.A. & Koederitz, L.F. (1985). Unsteady-state spherical flow with storage and skin. SPE Journal, 25(6),

Katime-Meindl, I. & Tiab, D. (2001). Analysis of pressure transient test of non-newtonian fluids in infinite reservoir and in the presence of a single linear boundary by the direct synthesis technique. SPE Annual Technical Conference and Exhibition. New Orleans, Louisiana. SPE 71587.

Martínez, J.A., Escobar, F.H. & Cantillo, J.H. (2011). Application f the TDS technique to dilatant non-newtonian/
newtonian fluid composite reservoirs. Ingeniería e Investigación, 31(3), 130-134.

Martínez, J.A., Escobar, F.H. & Montealegre-M., M. (2011). Vertical well pressure and pressure derivative analysis for Bingham fluids in a homogeneous reservoirs. Dyna, 78(166), 21-28.

Moncada, K., Tiab, D., Escobar, F.H., Montealegre-M, M., Chacon, A., Zamora, R.A. & Nese, S.L. (2005). Determination of vertical and horizontal permeabilities for vertical oil and gas wells with partial completion and
partial penetration using pressure and pressure derivative plots without type-curve matching. CT&F-Ciencia,
Tecnología y Futuro, 3(1), 77-95.

Proett, M.A. & Chin, W.C. (1998). New exact spherical flow solution with storage for early-time test interpretation with applications to early-evaluation drillstem and wireline formation testing. SPE Permian Basin Oil and Gas Recovery Conference. Midland, Texas, SPE 39768.

Tiab, D. (1993). Analysis of pressure and pressure derivative without type-curve matching: 1- Skin and wellbore
storage. Journal of Petroleum Science and Engineering, 12(3), 171-181.
How to Cite
Humberto Escobar, F., Martínez, J.-A., & Bonilla, L.-F. (2012). Transient pressure analysis for vertical wells with spherical power-law flow. CT&F - Ciencia, Tecnología Y Futuro, 5(1), 19-36.


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