Injection period pressure transient behaviour of two-phase water-oil flow: A semi-analytical study


  • Althaf Shafeer Department of Petroleum Engineering, Universiti Teknologi PETRONAS, Persiaran UTP, 32610 Seri Iskandar, Perak, Malaysia Phone: +60102958492; Fax: +6053654082.
  • Lee Jang Hyun Department of Petroleum Engineering, Universiti Teknologi PETRONAS, Persiaran UTP, 32610 Seri Iskandar, Perak, Malaysia Phone: +60102958492; Fax: +6053654082.
  • Tarek Arbi Ganat Department of Petroleum Engineering, Universiti Teknologi PETRONAS, Persiaran UTP, 32610 Seri Iskandar, Perak, Malaysia Phone: +60102958492; Fax: +6053654082.
  • Azeb Demisi Habte Department of Petroleum Engineering, Universiti Teknologi PETRONAS, Persiaran UTP, 32610 Seri Iskandar, Perak, Malaysia Phone: +60102958492; Fax: +6053654082.



injection period, pressure transient behaviour, skin, two-phase, wellbore storage


This paper presents a study on the pressure transient behaviour during the injection period in a vertical well in the presence of wellbore storage and skin effect. The two-phase water-oil radial flow problem is solved using a semi-analytical technique called the Laplace-Transform Finite-Difference method. Moreover, the factors that influence the degree of wellbore storage and skin effect are analysed. The results demonstrated that the effect of wellbore storage on the pressure transient behaviour is significant during the early times. Factors such as compressibility of fluid, effective wellbore volume and endpoint mobility ratio significantly affect the duration of wellbore storage. The impact of the skin during the injection period is significant on the pressure transient behaviour and could last for a longer duration. A substantial effect of skin is observed for a positive skin factor and unfavourable endpoint mobility ratio. In addition, the duration of the effect is directly proportional to the thickness of the skin zone. Hence attention must be given to the parameters that could prolong these effects and included in the solution methods to precisely interpret the injection period pressure transient behaviour for a better estimation of the reservoir and well properties.   


F. J. Kuchuk, M. Onur, and F. Hollaender, Pressure transient formation and well testing: convolution, deconvolution and nonlinear estimation vol. 57: Elsevier, 2010.

H. J. Ramey Jr, "Short-Time Well Test Data Interpretation in the Presence of Skin Effect and Wellbore Storage," presented at SPE 39th Annual California Regional Fall Meeting held In Bakersfield : Journal of Petroleum Technology, 1970.

A. C. Gringarten, D. Bourdet, P. A. Landel, and V. J. Kniazeff, "A Comparison Between Different Skin and Wellbore Storage Type-Curve for Early-Time Transient Analysis," presented at the 54th Annual fall Technical Conference and Exhibition of the Society of Petroleum Engineers of AIME, 1979.

K. Razminia, A. Hashemi, A. Razminia, and D. Baleanu, "Explicit deconvolution of well test data dominated by wellbore storage," in Abstract and Applied Analysis, 2014.

P. Donnez, Essentials of Reservoir Engineering vol. 2. Paris, France: Editions Technip, 2012.

J. Lee, J. B. Rollins, and J. P. Spivey, Pressure Transient Testing vol. 9, 2003.

A. F. Van Everdingen and W. Hurst, "The Application of the Laplace Transformation to Flow Problems in Reservoirs," Petroleum Transactions, AIME, pp. 305-324-B, 1949.

D. G. Hatzignatiou, A. M. M. Peres, and A. C. Reynolds, "Effect of Wellbore Storage on the Analysis of Multiphase Flow Pressure Data," SPE Formation Evaluation, vol. 9, pp. 219-227, 2013.

L. P. Dake, The practice of reservoir engineering (revised edition) vol. 36: Elsevier, 2001.

A. Van Everdingen, "The skin effect and its influence on the productive capacity of a well," Journal of petroleum technology, vol. 5, pp. 171-176, 1953.

P. Liu, W. Li, J. Xia, Y. Jiao, and A. Bie, "Derivation and application of mathematical model for well test analysis with variable skin factor in hydrocarbon reservoirs," AIP Advances, vol. 6, p. 065324, 2016.

M. F. J. Hawkins, "A Note on the Skin Effect," Journal of Petroleum Technology, 1956.

A. D. Habte, "Laplace - Transform Finite Difference and Quasistationary Solution Method for Two - And Three Phase Injection/Falloff test," PhD dissertation, Universiti Teknologi Petronas, Bandar Seri Iskandar, Perak, Malaysia, 2017.

S. Koščak Kolin, T. Kurevija, and D. Grebenar, "Pressure build-up test analysis of the reservoir system with the multiphase flow," Rudarsko-geološko-naftni zbornik, vol. 33, pp. 75-84, 2018.

D. Bourdet, Well Test Analysis : The Use of Advanced Interpretation Models vol. 3, 2002.

A. A. Boughrara, "Injection/Falloff Testing of Vertical and Horizontal Wells," PhD, Petroleum Engineering, University of Tulsa, Tulsa, Oklahoma, U.S.A, 2007.

M. Li, Q. Li, G. Bi, and J. Lin, "A Two-Phase Flow Model for Pressure Transient Analysis of water Injection Well Considering Water Imbibition in Natural Fractured Reservoirs," Mathematical Problems in engineering, 2018.

A. D. Habte and M. Onur, "Laplace - Transform Finite Difference and Quasistationary Solution Method for Water Injection / Falloff Test," SPE Journal, vol. 19, pp. 398-409, 2013.

S. E. Buckley and M. C. Leverett, "Mechanism of Fluid Displacement in Sands," presented at 1941 New York meeting, 1941.

A. Kantzas, J. Bryan, and S. Taheri, "Fundamentals of fluid flow in porous media," Pore size distribution, 2012.

U. Taura, P. Mahzari, M. Sohrabi, and S. A. Farzaneh, "A New Methodology for Improved Estimation of Two-Phase Relative Permeability Functions for Heavy Oil Displacement Involving Compositional Effects and Instability," in SPE Heavy Oil Conference and Exhibition, 2016.

B. Kayode, "Accuracy of water break-through time prediction," ed: Google Patents, 2019.

P. Bhardwaj, R. Manchanda, J. Hwang, P. Cardiff, and M. Sharma, "A New Reservoir Scale Model for Fracture Propagation and Stress Reorientation in Injection Wells," in 50th US Rock Mechanics/Geomechanics Symposium, 2016.

W. T. Hauss, "A Numerical Simulation Study on the Characteristics of a Variable Wellbore Storage Pressure Transient Response," Master of Science, Petroleum engineering, Texas Tech University, 1988.

Y. Li, X. Li, S. Teng, F. Wang, and D. Xu, "A new changing wellbore storage model for pressure oscillation in pressure buildup test," Journal of Natural Gas Science and Engineering, vol. 19, pp. 350-357, 2014.

H. Stehfest, "Algorithm 368: Numerical inversion of Laplace transforms [D5]," Communications of the ACM, vol. 13, pp. 47-49, 1970.

A. Bouaffane and K. Talbi, "Thermal study of fluid flow inside an annular pipe filled with porous media under local thermal non-equilibrium condition," Journal of Mechanical Engineering and Sciences, vol. 13, pp. 4880-4897, 2019.

F. H. Escobar, J. M. Navarrete, and H. D. Losada, "Evaluation of pressure derivative algorithms for well-test analysis," in SPE International Thermal Operations and Heavy Oil Symposium and Western Regional Meeting, 2004.

F. H. E. Macualo, E. R. Borrego, and N. T. A. Olaya, "Analysis of Pressure And Pressure Derivative Interference Tests Under Linear And Spherical Flow Conditions," Revista DYNA, vol. 85, 2018.

D. Bourdet, J. Ayoub, and Y. Pirard, "Use of Pressure Derivative in Well Test Interpretation," SPE Formation Evaluation, vol. 4, pp. 293-302, 1989.

S. GeoQuest, "Eclipse technical description manual," ed: Schlumberger Geo-Quest, Houston, TX, 2001.

J. R. Fanchi, "Principles of Applied Reservoir Simulation," ed: Gulf Professional Publishing, 2018.

T. T. Mohd, N. A. Bakar, N. Awang, and A. Talib, "Aqueous foams stabilized with silica nanoparticle and alpha olefin sulfonates surfactant," Journal of Mechanical Engineering and Sciences, vol. 12, pp. 3759-3770, 2018.

A. U. Chaudhry, "Oil Well Testing Handbook," Advanced TWPSOM Petroleum Systems, Inc. Houston, Texas, 2004.

B. Guo, K. Sun, and A. Ghalambor, Well productivity handbook: Elsevier, 2014.

A. Satter and G. M. Iqbal, Reservoir Engineering: The fundamentals, simulation, and management of conventional and unconventional recoveries: Gulf Professional Publishing, 2015.

(11 January, 2020). Fekete Reference Materials: General Concepts; Reservoir Fluid Properties. Available:

C. H. Whitson and M. R. Brulé, Phase behavior: Henry L. Doherty Memorial Fund of AIME, Society of Petroleum Engineers, 2000.

M. M. Salehi, P. Omidvar, and F. Naeimi, "Salinity of injection water and its impact on oil recovery absolute permeability, residual oil saturation, interfacial tension and capillary pressure," Egyptian journal of petroleum, vol. 26, pp. 301-312, 2017.

A. Bahadori, Fluid phase behavior for conventional and unconventional oil and gas reservoirs: Gulf Professional Publishing, 2016.

H. Zhuang, Dynamic well testing in petroleum exploration and development: Newnes, 2012.

M. A. Al-Marhoun, "The Oil Compressibility below Bubble Point Pressure Revisited-Formulations and Estimations," in SPE Middle East Oil and Gas Show and Conference, 2009.

"The Effect of Wellbore Storage on Surface Data," 2012.

M. Y. Alklih, B. Ghosh, and E. W. Al-Shalabi, "Tight Reservoir Stimulation for Improved Water Injection-A Novel Technique," in IPTC 2014: International Petroleum Technology Conference, 2014.

W. Ziyi, "Study on the change of porosity and permeability of sandstone reservoir after water flooding," IOSR Journal of Engineering (IOSRJEN), vol. 06, pp. 35-40, 2016.

T. Ahmed and P. McKinney, Advanced reservoir engineering– 4th Edition: Elsevier, 2011.

D. McClatchie, T. Garner, and J. Yurkanin, "Injection well stimulation: putting away more for less in California waterfloods," in SPE Annual Technical Conference and Exhibition, 2004.

Z. Wu and H. Liu, "Investigation of hot-water flooding after steam injection to improve oil recovery in thin heavy-oil reservoir," Journal of Petroleum Exploration and Production Technology, vol. 9, pp. 1547-1554, 2019.




How to Cite

A. Shafeer, L. J. Hyun, T. A. Ganat, and A. D. Habte, “Injection period pressure transient behaviour of two-phase water-oil flow: A semi-analytical study”, J. Mech. Eng. Sci., vol. 14, no. 2, pp. 6719–6733, Jun. 2020.