Pressure Transient Behavior of Non-Newtonian/Newtonian Fluid Composite Reservoirs

1981 ◽  
Vol 21 (02) ◽  
pp. 271-280 ◽  
Author(s):  
O. Lund ◽  
Chi U. Ikoku
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Porous Media ◽  
Newtonian Fluid ◽  
Power Law ◽  
Well Test ◽  
Well Test Analysis ◽  
Partial Differential ◽  
Test Analysis ◽  
Power Law Fluids

Abstract Pressure transient theory of flow of non-Newtonian power-law fluids in porous media is extended to non-Newtonian/Newtonian fluid composite reservoirs. This paper examines application of non-Newtonian and conventional (Newtonian) well test analysis techniques to injectivity and falloff tests in wells where different amounts of non-Newtonian fluids have been injected into the reservoir to displace the in-situ Newtonian fluid (oil and/or water). Early time pressure data can be analyzed by non-Newtonian well test analysis methods. Conventional semilog methods may be used to analyze late time falloff data. The location of the non-Newtonian fluid front can be estimated from well tests using the radius of investigation equation for power-law fluids. An equation for calculating shear rates and apparent viscosities for power-law fluids in reservoirs is presented. An example problem is used to illustrate observations and solution techniques. Introduction Recent studies have proposed new well test analysis techniques for interpreting pressure data obtained during injectivity and falloff testing in reservoirs containing slightly compressible non-Newtonian, power-law fluids. The first papers proposing well test analysis methods for non-Newtonian fluid injection wells were published in 1979. Odeh and Yang1 derived a partial differential equation for flow of power-law fluids through porous media. They used a power-law function relating the viscosity to the shear rate. The power-law viscosity function was coupled with the variable viscosity diffusivity equation and a shear rate relationship proposed by Savins2 to give the new partial differential equation. An approximate analytical solution was obtained. The solution provided new plotting techniques for analyzing injection and falloff test data. The utility of the new methods was demonstrated on field tests. They also derived the steady-state flow equation and an expression for the radius of investigation. Isochronal testing was discussed. McDonald3 presented a numerical study using the power-law flow equation of Odeh and Yang. He presented different numerical techniques of solving the equation and compared results with the analytical results of Odeh and Yang. He found that a finer grid was required for finite difference simulation of power-law fluids than for black-oil fluids. A partial differential equation for radial flow of non-Newtonian power-law fluids through porous media was published by Ikoku and Ramey4,5 in 1979. Coupling the non-Newtonian Darcy's law with the continuity equation, the rigorous partial differential equation was derived:Equation 1

Flow of Non-Newtonian Power-Law Fluids Through Porous Media

1979 ◽  
Vol 19 (03) ◽  
pp. 155-163 ◽  
Author(s):  
A.S. Odeh ◽  
H.T. Yang
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Porous Media ◽  
Test Data ◽  
Power Law ◽  
Newtonian Fluids ◽  
Unsteady State ◽  
Partial Differential ◽  
State Flow ◽  
Power Law Fluids

Abstract The partial differential equation that describes the flow, of non-Newtonian, power-law, slightly compressible fluids in porous media is derived. An approximate solution, in closed form, is developed for the unsteady-state flow behavior and verified by. two different methods. Using the unsteady-state solution, a method for analyzing injection test data is formulated and used to analyze four injection tests. Theoretical results were used to derive steady-state equations of flow, equivalent transient drainage radius, and a method for analyzing isochronal test data. The theoretical fundamentals of the flow, of non-Newtonian power-law fluids in porous media are established. Introduction Non-Newtonian power-law fluids are those that obey the relation = constant. Here, is the viscosity, e is the shear rate at which the viscosity is measured, and n is a constant. Examples of such fluids are polymers. This paper establishes the theoretical foundation of the flow of such fluids in porous media. The partial differential equation describing this flow is derived and solved for unsteady-state flow. In addition, a method for interpreting isochronal tests and an equation for calculating the equivalent transient drainage radius are presented. The unsteady-state flow solution provides a method for interpreting flow tests (such as injection tests).Non-Newtonian power-law fluids are injected into the porous media for mobility control, necessitating a basic porous media for mobility control, necessitating a basic understanding of the flow behavior of such fluids in porous media. Several authors have studied the porous media. Several authors have studied the rheological properties of these fluids using linear flow experiments and standard viscometers. Van Poollen and Jargon presented a theoretical study of these fluids. They described the flow by the partial differential equation used for Newtonian fluids and accounted for the effect of shear rate on viscosity by varying the viscosity as a function of space. They solved the equation numerically using finite difference. The numerical results showed that the pressure behavior vs time differed from that for Newtonian fluids. However, no methods for analyzing flow-test data (such as injection tests) were offered. This probably was because of the lack of analytic solution normally required to understand the relationship among the variables.Recently, injectivity tests were conducted using a polysaccharide polymer (biopolymer). The data showed polysaccharide polymer (biopolymer). The data showed anomalies when analyzed using methods derived for Newtonian fluids. Some of these anomalies appeared to be fractures. However, when the methods of analysis developed here were applied, the anomalies disappeared. Field data for four injectivity tests are reported and used to illustrate our analysis methods. Theoretical Consideration General Consideration The partial differential equation describing the flow of a non-Newtonian, slightly compressible power-law fluid in porous media derived in Appendix A is ..........(1) where the symbols are defined in the nomenclature. JPT P. 155

Well Test Analysis of Data Dominated by Storage and Skin: Non-Newtonian Power-Law Fluids

1987 ◽  
Vol 2 (04) ◽  
pp. 618-628 ◽  
Author(s):  
S. Vongvuthipornchai ◽  
Rajagopal Raghavan
Keyword(s):  
Power Law ◽  
Well Test ◽  
Well Test Analysis ◽  
Test Analysis ◽  
Power Law Fluids

On the Dynamics and Stability of a Viscoelastic Pipe Conveying a Non-Newtonian Fluid

2009 ◽  
Author(s):  
Vincent O. S. Olunloyo ◽  
Charles A. Osheku ◽  
Sidikat I. Kuye
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Newtonian Fluid ◽  
Elevated Temperatures ◽  
Fluid Velocity ◽  
Flow Induced Vibration ◽  
Partial Differential ◽  
Flow Parameters ◽  
Sea Bed ◽  
Internal Fluid

Flow induced vibration of pipeline and riser systems are strongly dependent on internal fluid flow parameters as well as the mechanical properties of the conveyance vessel. The effect of variability of flow parameters especially at elevated temperatures can lead to instability, buckling and bursting of these systems. In this paper, the effect of high temperature fluid transmission on the vibration and stability of an offshore viscoelastic pipeline conveying a non-Newtonian fluid is investigated analytically. By idealising the viscoelastic pipeline resting on the sea bed as a viscoelastic beam that is resting on an elastic continuum, a non-linear boundary value partial differential equation governing the fluid-structure-soil interaction mechanics is formulated. In particular, formal linearization of the governing partial differential equation, under slight perturbation of the internal fluid velocity and other flow variables revealed their impact, on the natural frequency and stability of the system which can then be computed for design analysis and applications.

Wellbore Storage and Skin Effects During the Transient Flow of Non-Newtonian Power-Law Fluids in Porous Media

1980 ◽  
Vol 20 (01) ◽  
pp. 25-38 ◽  
Author(s):  
Chi U. Ikoku ◽  
Henry J. Ramey
Keyword(s):  
Porous Media ◽  
Power Law ◽  
Transient Flow ◽  
Constant Pressure ◽  
Outer Boundary ◽  
Petroleum Reservoirs ◽  
Storage Effect ◽  
Well Test ◽  
Wellbore Storage ◽  
Power Law Fluids

Abstract A model recently presented by Ikoku and Ramey for non-Newtonian power-law flow in porous media was extended to flow in finite circular reservoirs. A constant flow rate was stipulated at the wellbore, and two boundary conditions were considered: no-flow outer boundary and constant-pressure outer boundary. The results were used to derive a new expression for the stabilization time for power-law flow in porous media.Wellbore storage and skin effects always distort the transient pressure behavior of wells in petroleum reservoirs. It is important to investigate the consequences of these phenomena and be able to interpret real well test information. This paper considers the effects of skin and wellbore storage on the transient flow of non-Newtonian power-law fluids in petroleum reservoirs. petroleum reservoirs. A new numerical wellbore storage simulator was used to study the effects of skin and wellbore storage during the transient flow of power-law fluids in infinitely large and finite circular reservoirs. Results are presented both in tabular form and as log-log graphs of dimensionless pressures vs dimensionless times. The log-log graphs may be used in a type-Curve matching procedure to analyze short-time well test data.The early period is dominated by wellbore storage effect. A new expression was obtained for the duration of wellbore storage effect when skin exists for infinitely large reservoirs. This criterion is not valid for finite circular reservoirs with no-flow outer boundary or constant-pressure outer boundary. Results indicate that there is no apparent end of wellbore storage effect for the no-flow outer boundary condition for the values of external radius presented. New relationships were derived for skin presented. New relationships were derived for skin factor and "effective well radius" for power-law flow. Introduction Many papers in the petroleum engineering, chemical engineering, and rheology literature have addressed the subject of non-Newtonian flow in porous media. These studies have represented non-Newtonian flow with power-law models. Most of the results are similar. The main differences in the final expressions lie in the type of power-law model used.In the basic papers on the transient flow of non-Newtonian power-law fluids in porous media, wellbore storage effect was not considered. Ikoku and Ramey and Odeh and Yang presented techniques for calculating the skin factor from injection well test data. However, wellbore storage and skin effects always distort the transient pressure behavior of wells in petroleum reservoirs. It is important to investigate the consequences of these phenomena to be able to interpret real well test information properly.The flow geometries of interest to petroleum engineers in well test analysis usually involve bounded reservoirs. In most cases, a constant flow rate is stipulated at the well along with one of these outer boundary conditions: no flow across the outer boundary, or constant pressure at the outer boundary. Reservoirs with rectangular and other polygonal shapes often are encountered. Transient polygonal shapes often are encountered. Transient pressure behavior for these shapes may be obtained pressure behavior for these shapes may be obtained by applying the principle of superposition in space to the solutions of the infinitely large reservoir cases.In this paper we seek solutions for constant-rate injection into finite circular reservoirs with no-flow and constant-pressure outer boundaries. SPEJ P. 25

Well Test Analysis for Two-Phase Flow of Non-Newtonian Power-Law and Newtonian Fluids

1984 ◽  
Vol 106 (2) ◽  
pp. 295-305 ◽  
Author(s):  
C. S. Gencer ◽  
C. U. Ikoku
Keyword(s):  
Power Law ◽  
Two Phase Flow ◽  
Newtonian Fluids ◽  
Phase Flow ◽  
Well Test ◽  
Finite Radius ◽  
Well Test Analysis ◽  
Two Phase ◽  
Power Law Fluids ◽  
Rock Compressibility

Analysis of injectivity and falloff test data is considered during two-phase flow of non-Newtonian and Newtonian fluids. The non-Newtonian fluids considered are power-law fluids. Two sets of relative permeability data representing preferentially water wet and oil wet systems are considered. The conditions under which saturation gradients develop are thoroughly investigated. The effects of finite radius skin region and rock compressibility on pressure response are also investigated. During two-phase flow of power-law and Newtonian fluids, saturation gradients do not develop under most practical conditions. Injectivity and falloff data can be analyzed using available techniques with appropriate definitions of dimensionless variables for two-phase flow. When saturation gradients exist, the response of this transition region is not interpretable by available methods.

scholarly journals Determination of well-drainage area for power-law fluids by transient pressure analysis

2012 ◽  
Vol 5 (1) ◽  
pp. 45-56 ◽  
Author(s):  
Freddy-Humberto Escobar ◽  
Laura-Jimena Vega ◽  
Luis-Fernando Bonilla
Keyword(s):  
Power Law ◽  
Oil Recovery ◽  
Heavy Oil ◽  
Drainage Area ◽  
Well Test ◽  
Transient Pressure ◽  
Well Test Analysis ◽  
Pressure Derivative ◽  
Oil Companies ◽  
Power Law Fluids

Since conventional oil is almost depleted, oil companies are focusing their efforts on exploiting heavy oil reserves. A modern and practical technique using the pressure and pressure derivative, log-log plot for estimating the well-drainage area in closed and constant-pressure reservoirs, drained by a vertical well is presented by considering a non-Newtonian flow model for describing the fluid behavior. Several synthetic examples were presented for demonstration and verification purposes.Such fluids as heavy oil, fracturing fluids, some fluids used for Enhanced Oil Recovery (EOR) and drilling muds can behave as either Power-law or Bingham, usually referred to as the non-Newtonian fluids. Currently, there is no way to estimate the well-drainage area from conventional well test analysis when a non-Newtonian fluid is dealt with; therefore, none of the commercial well test interpretation package can estimate this parameter (drainage area).

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