New Type Curves for the Analysis of Pressure Transient Data of Horizontal Wells in Non-Newtonian Fluid Reservoirs

New Type Curves for the Analysis of Pressure Transient Data of Horizontal Wells in Non-Newtonian Fluid Reservoirs.

ABSTRACT

This novel work is based on the study of Vongvuthipornchai and Raghavan, 1987. In this work a new 3-Dimensional non-linear partial differential equation describing the transient flow of non- Newtonian fluid in porous media is developed for a hypothetical no-flow boundary cuboid reservoir.

The basic assumptions in the mathematical modeling of the differential equations are; permeability anisotropy with directional permeabilities k_s, k_y and k_z , an isothermal, single phase, slightly compressible fluid with steady state viscosity was assumed,

the horizontal well was place in the y- direction perpendicular to the direction of maximum permeabilityk_s. The effects of gravity were neglected and the reservoir fluid was considered to be a non-Newtonian pseudo plastic fluid that obeys the power law model.

The derived equation was discretized using finite difference approach; the system of linear equations obtained from the discretization was solved with the aid of a MATLAB 7.5.0^R code to obtain pressure data.

Type curves involving the log-log plot ofP_wD Vs t_D and t_D × P_wD‘Vs t_D were made  for  cases when there is permeability isotropy and anisotropy of different power law flow index n ranging from 0.1 to 1 for horizontal well length of 600ft, 1000ft and 1200ft.

The developed type curves were validated by considering a Newtonian case and using Tiab Direct synthesis (TDS) technique to analyze the radial flow regime for the determination of average permeability as well as the procedure presented in Vongvuthipornchai and Raghavan,

INTRODUCTION

OVERVIEW AND PROBLEM DEFINITION

Although recent studies on the steady and unsteady state flow of non-Newtonian fluid in porous media have brought about new well test analysis for non-Newtonian injection and falloff testing.

These methods of analysis have been generally applied to vertical wells for the design and operation of enhanced oil recovery projects.

Despite these wide applications, current trends in the industry indicate increasing application of horizontal wells in enhanced oil recovery operations with the use of non-Newtonian fluids such as polymer and micellar solutions.

However, the proper understanding and analysis of horizontal well pressure data in non- Newtonian fluid reservoirs such as heavy oil reservoirs will aid in the characterization of heavy oil reservoirs in the nearest future.

The motivation for this work which is the first of its kind is to adequately model new 3- Dimensional equations that would explicitly describe the flow of Non-Newtonian reservoir fluids into horizontal wells;

the new diffusivity equation will thus help in adequately evaluating heavy oil reservoirs in terms of, permeability, power-law flow index and mobility using obtained type curves.

The idea behind the use of horizontal well is to increase reservoir area contact .For example, in 1978 Esso Resources Canada drilled a horizontal well at the Cold Lake Leming pilot to field test thermally aided gravity drainage.

Newtonian fluids in porous media. The diffusivity equation is solved numerically in dimensionless terms with the aid of finite difference approach for a no-flow boundary condition.

REFERENCES

Adam T.Bourgoyne Jr.,Keith K. Millheim, Martin E. Chenevert, F.S. Young Jr: ‘Applied Drilling Engineering’ first printing Society of Petroleum Engineers Richardson TX,1986

Odeh and H. T. Yang: ‘Flow of Non-Newtonian Power-Law Fluids through Porous Media’ April, 1979 (SPE 7150)

Alpheus O. Igbokoyi and Djebbar Tiab, SPE, U. of Oklahoma: ‘New Type Curves for the Analysis of Pressure Transient Data Dominated by Skin and Wellbore Storage-Non-Newtonian Fluid’ April, 2007. (SPE 106997)

Aziz S. Odeh and D.K Babu: Transient Flow behavior of Horizontal Wells: Pressure Drawdown and Buildup Analysis. SPE Formation Evaluation, March 1990.

Aziz, K and Settari, A.: Petroleum Reservoir Simulation, Applied Science Publishers Ltd., London (1979) 69-92.

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