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

scholarly journals A Mathematical Model for the Analysis of the Pressure Transient Response of Fluid Flow in Fractal Reservoir

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Jin-Zhou Zhao ◽  
Cui-Cui Sheng ◽  
Yong-Ming Li ◽  
Shun-Chu Li
Keyword(s):  
Fluid Flow ◽  
Boundary Conditions ◽  
Outer Boundary ◽  
Practical Significance ◽  
Storage Effect ◽  
Well Test ◽  
Type Curves ◽  
Skin Factor ◽  
Wellbore Storage ◽  
Wellbore Pressure

This study uses similar construction method of solution (SCMS) to solve mathematical models of fluid spherical flow in a fractal reservoir which can avoid the complicated mathematical deduction. The models are presented in three kinds of outer boundary conditions (infinite, constant pressure, and closed). The influence of wellbore storage effect, skin factor, and variable flow rate production is also involved in the inner boundary conditions. The analytical solutions are constructed in the Laplace space and presented in a pattern with one continued fraction—the similar structure of solution. The pattern can bring convenience to well test analysis programming. The mathematical beauty of fractal is that the infinite complexity is formed with relatively simple equations. So the relation of reservoir parameters (wellbore storage effect, the skin factor, fractal dimension, and conductivity index), the formation pressure, and the wellbore pressure can be learnt easily. Type curves of the wellbore pressure and pressure derivative are plotted and analyzed in real domain using the Stehfest numerical invention algorithm. The SCMS and type curves can interpret intuitively transient pressure response of fractal spherical flow reservoir. The results obtained in this study have both theoretical and practical significance in evaluating fluid flow in such a fractal reservoir and embody the convenience of the SCMS.

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

POWER-LAW FLUIDS IN POROUS MEDIA

1987 ◽  
Vol 53 (1-6) ◽  
pp. 3-22 ◽  
Author(s):  
RICHARD PARNAS ◽  
YORAM COHEN
Keyword(s):  
Porous Media ◽  
Power Law ◽  
Power Law Fluids

Internal Heat Transfer to Power-Law Fluid Flows Through Porous Media

2000 ◽  
Author(s):  
B. K. Rao ◽  
J. P. McDevitt ◽  
D. L. Vetter
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Power Law ◽  
Polymer Concentration ◽  
Internal Heat ◽  
Fluid Flows ◽  
Vertical Tube ◽  
Uniform Heat Flux ◽  
Power Law Fluid ◽  
Power Law Fluids

Abstract Heat transfer and pressure drop were measured for flow of aqueous solutions of Carbopol 934 through a vertical tube filled with porous media. The heated stainless steel test section has an inside diameter of 2.25 cm, and is 200 diameters long. The porosity was varied from 0.32 to 0.68 by using uniform spherical glass beads. Uniform heat flux thermal boundary condition was imposed bypassing direct electric current through the tube wall. Over a range of the parameters: 45 < Rea < 7,000, 21 < Pra < 58, 0.62<n (power-law exponent)<0.80, 0.22 < d/D < 0.6, and the polymer concentration from 250 to 500 parts per million, the friction factor data for power-law fluids agreed with the Newtonian predictions. Heat transfer to power-law fluids increases with increasing Rea and Prw and decreasing porosity. A new correlation was proposed for predicting heat transfer to power-law fluid flows through confined porous media.

An Investigation of Wellbore Storage and Skin Effect in Unsteady Liquid Flow: I. Analytical Treatment

1970 ◽  
Vol 10 (03) ◽  
pp. 279-290 ◽  
Author(s):  
Ram G. Agarwal ◽  
Rafi Al-Hussainy ◽  
H.J. Ramey
Keyword(s):  
Skin Effect ◽  
Initial Period ◽  
Outer Boundary ◽  
Well Test ◽  
Time Data ◽  
Wellbore Storage ◽  
Straight Line ◽  
Pan American ◽  
Well Tests ◽  
Short Time

Agarwal, Ram G., Pan American Petroleum Corp. Tulsa, Okla., Pan American Petroleum Corp. Tulsa, Okla., Al-Hussainy, Rafi, Junior Members AIME, Mobil Research and Development Corp., Dallas, Tex., Ramey Jr., H.J., Member AIME, Stanford U. Stanford, Calif. Abstract Due to the cost of extended pressure-drawdownor buildup well tests and the possibility of acquisitionof additional information from well tests, the moderntrend has been toward development of well-testanalysis methods pertinent for short-time data."Short-time" data may be defined as pressureinformation obtained prior to the usual straight-lineportion of a well test. For some time there has been portion of a well test. For some time there has been a general belief that the factors affecting short-timedata are too complex for meaningful interpretations. Among these factors are wellbore storage, variousskin effects such as perforations, partial penetration, fractures of various types, the effect of a finiteformation thickness, and non-Darcy flow. A numberof recent publications have dealt with short-timewell-test analysis. The purpose of this paper isto present a fundamental study of the importance ofwellbore storage with a skin effect to short-timetransient flow. Results indicate that properinterpretations of short-time well-test data can bemade under favorable circumstances. Upon starting a test, well pressures appearcontrolled by wellbore storage entirely, and datacannot be interpreted to yield formation flowcapacity or skin effect. Data can be interpreted toyield the wellbore storage constant, however. Afteran initial period, a transition from wellbore storagecontrol to the usual straight line takes place. Dataobtained during this period can be interpreted toobtain formation flow capacity and skin effect incertain cases. One important result is that thesteady-state skin effect concept is invalid at veryshort times. Another important result is that thetime required to reach the usual straight line isnormally not affected significantly by a finite skineffect. Introduction Many practical factors favor short-duration welltesting. These include loss of revenue during shut-in, costs involved in measuring drawdown or buildupdata for extended periods, and limited availabilityof bottomhole-pressure bombs where it is necessaryto survey large numbers of wells. on the other hand, reservoir engineers are well aware of the desirabilityof running long-duration tests. The result is usuallya compromise, and not necessarily a satisfactoryone. This situation is a common dilemma for thefield engineers who must specify the details of specialwell tests and annual surveys, and interpret theresults. For this reason, much effort has been givento the analysis of short-time tests. The term"short-time" is used herein to indicate eitherdrawdown or buildup tests run for a period of timeinsufficient to reach the usual straight-line portions. Drawdown data taken before the traditional straight-lineportion are ever used in analysis of oil or gas portion are ever used in analysis of oil or gas well performance. Well files often contain well-testdata that were abandoned when it was realized thatthe straight line had not been reached. This situationis particularly odd when it is realized that earlydata are used commonly in other technologies whichemploy similar, or analogous, transient test. It is the objective of this study to investigatetechniques which may be used to interpret informationobtained form well tests at times prior to the normalstraight-line period. THEORY The problem to be considered is the classic oneof flow of a slightly compressible (small pressuregradients) fluid in an ideal radial flow system. Thatis, flow is perfectly radial to a well of radius rwin an isotropic medium, and gravitational forces areneglected. We will consider that the medium isinfinite in extent, since interest is focused on timesshort enough for outer boundary effects not to befelt at the well. SPEJ p. 279

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