Sensitivity of Micellar Flooding Reservoir Heterogeneity

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<p>SOCIETY (N? PETROLEUM ENGINEERS OF AIME</p> <p>;?!%SPE 5808Micellar F!ooding Heterogeneities</p> <p>The</p> <p>Sensitivity to Reservoir</p> <p>of</p> <p>By ,. ., ..</p> <p>C..A..Kossack and H..L. Biltiartz; Wi, . . . . . ..,. .</p> <p>Atlantic Richfield Co.</p> <p>@Copyright 1976 Ameriean Iristitiitg gf,Miniag, Metallurgical,and Petroleum Engineers,Inc. . . .. ..i%IS PI@ER IS SUBJECT TO CORRECTION This paper was prepared for We Itiproved 0i2. Recovery Symposium of the Society of Petroleum. Erig@e~r,~.of AIME, to be held in Tulsa, Okla., March 22-24, 1976. IlluPermission to copyis restricted to an abstract of not more than 300 words. The abstract should contain conspicuous acknowledgstrations may not be copied. Publication elsewhere after ment of.where and by whom the paper is presented. publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon request to the Editor of the appropriate journal provided agreement to give proper credit is made. Three copies of any discussion should be Discussion of this paper is invited. sent to the Society of Petroleum Engineers offiae. Such discussion may be presented at the above meeting and with the paper, may be considered for publication in one of the two SPE magazines.</p> <p>ABSTRACT .. . This paper provides a comparative evaluation of the effect of reservoir heterogeneityon amiscible -tertiary micellar flood. The sensitivityof slug size, preflushvolum-e, surfactant loss, and miscibility saturation of this complex displacement process was evaluated for a homogeneous, randomly heterogeneous, non-communicating layered and partially communicating layered model The five-component, finitereservoir. difference reservoir simulator used for this study is described in detail. The results show that reservoir heterogeneityis a dominant factor, adversely affecting the performance ofmicellar flooding to suchan extent that the process may notbe feasible in many non-homogeneous reservoirs. Inth.e partiall ycommunicatin glayered model reservoir, large volumes of preflush were required; and even after adequate preflushing~ 50 to70 percent of the post waterflood oil in place was unrecoverable. The results indicate References and illustrations at end of paper. thatfor a heterogeneous reservoir the most econornical slug size maybe a very small surfactant slug that displaces only the easily mobilized oil. This work also shows thata reduction in the surfactants adsorption praperties anda micellar fluid that mobilizes oil at low surfactant concentrations will, for a micellar flood with a given slug size, both substantially improve recovery. INTRODUCTION The o~jective ofthis work wasto stud) the effectof reservoir heterogeneityon the performance ofmicellar flooding using a numerical simulator. The four reservoir descriptions used in this study were homogeneous, randomly heterogeneous! noncommunicating layered, and partially comMicellar floods municating layered models. were simulatedto compare the effect of slug size, surfactant loss, and critical slug saturation upon tertiary oil recovery in the four</p> <p>*ifi ..</p> <p>q</p> <p>THE SENSITIVITY 03? MIGELLAR FLOODING TO RESERVOIR HETEROGENEITIES 5 Z i=l</p> <p>sP17 5808 -...-</p> <p>model reservoirs. These sensitivity studies indicate where and under what conditions the mice llar flooding concept might be applicable. The performance prediction of a micellar flood in a complex reservoir requires a numerical simulator that represents the reservoir features, chemical properties, and displacement mechanisms that affect the. flood To simulate this oil recovery performance. process the model described .below accounts f dr the flow of five separate components - -oil, water, surfactant, polymer, and pref lush. In addition, the simulator includes the adsorption of surfactant and polymer, permeability re duction, generation of miscibility, and the mixing of miscible fluids. THE MODEL Previous finite -difference siinulator development, omitting stream tube models and incompressible models, in the field of miscible flooding has been very limited due to numerical dispersion dissipating the small surfactant slug. The basic models in this field are not suited for micellar flooding but were designed for solvent and polymer floods. Todd and Longstaffl and Bondor, Hirasaki and Thom2 have developed four-component, miscible flood mode 1s for the simulation of solvent and ptilymer displacement, - re spec tively. These two papers describe methods to simulate many of the important features in a miscible flood and a mobility controlled flood, such as the flow of miscible fluids, the mixing of miscible fluids, adsorption, residual resistance (permeability reduction), arid non Newtonian effects. A numerical model approximating a system of five nonlinear partial differential equations, each representing conservation of fluids, is assumed to describe two-phase, multi -component compressible flow in rese r voirs unclergoing water external micella r flooding. These equations, obtained by combining Da rc ys law with continuity, are represented explicitly for the ith component in Eq.1. Bi k kri pi</p> <p>It is also required</p> <p>that</p> <p>S = 1 and the i</p> <p>usual capillary pressure relationship be expressed as a linear function of the aqueous saturation.</p> <p>?2 -pl=p</p> <p>.c2-~</p> <p>sac/</p> <p>(2)</p> <p>The development and loss of miscibilityy, permeability reduction, and surfactant 10Ss are handled by placing auxiliary constraints on the system of equations and are satisfied explicitly to the pressure solution. The .imulator solves the pressure equation implicitly using either Gaussian elimination or the strongly implicit procedure. The saturations are then calculated explicitly following the standard IMPES (implicit pres p sure, explicit sat~. dtiOIi) rocedure. The model contains an explicit calculation in which the surfactant and polymer are removed from the flow to simulate loss of chemicals. The rat~s of reaction for the polymer adsorption and surfactant loss are assumed to be infinite (an instantaneous reaction) until the predetermined quantity of the component has been either lost or adsorbed; at that time the rate becomes 2eroi The surfactant loss rnechahism can include true chemical adsorption, and pre cipitation when in contact with multivalent ions or the 10Ss of effectiveness when mixed with a high salii~iity brine. The 10Ss is assumed known and inputted to the simulator in terms of pounds of s urfactant 10Ss per acre -foot of reservoir. Once a grid block has lost its specified amount of surfactant, no additional 10Ss is calculated for that cell, To maintain a material balance, lost surfac tant and adsorbed polymer saturations become preflush brine saturation. The amount of surfactant 10Ss is modeled as a function of preflush eff icienc yj see Fig. 1, where preflush efficiency</p> <p>=[[</p> <p>saturation of preflush brine</p> <p>V*[.</p> <p>wei</p> <p>Vli 1</p> <p>+q j=:(q</p> <p>1/</p> <p>BiSi) 1 (1)</p> <p>i=l,2,3,4,5</p> <p>saturation of preflush brine</p> <p>saturation + of reser voir brine</p> <p>1..</p> <p>I</p> <p>1</p> <p>(3)</p> <p>,,</p> <p>SPE 5808</p> <p>C, A.</p> <p>Kossack</p> <p>and H. L.</p> <p>Bilhartz,</p> <p>Jr.</p> <p>IL7 -..</p> <p>Therefore, in a given cell, at any time, the maximum quantity of surfactant 10Ss allowed is dependent on the pref lush efficiency. No desorption of either component is currently allowed in the model. The miscibility mechanism currently used in this model is a. first order approxi mation to many of the complex transition izone phase relationships that are currently being investigated. 3$4 The switch f rorn immiscible ? two-phase flow to a single phase is achieved through fir st contact miscibility, * which is keyed to the amount of the surfactant slug present at any point. This critical satura tion** of the surfactant is a laboratory measured parameter which varies for different micellar fluids) crude oils, and salinity. Its value represents the lowest concentration that the micellar slug can be diluted to and still be miscible with the oil. Therefore, as long as the micellar saturation at a given point is above the critical saturation, all five components are considered as miscible components of the mixed phase and the capillary pressure Miscibility y, for is set equal to zero. P= 2-1 this study, is not a function of pref lush effi ciency except through adsorption which de creases the iurfactant concentration. If the .surfactant saturation is, less than this critical +aiueDthen miscibility between the aqueous phase (reservoir brine solution, polymer solution, surfactant solution, pref lush s olu tion) and the hydrocarbon phase is assumed lost; i, e. , the flow is immiscible, and p C2-1 is non-zero. Even under this condition all four aqueous components remain miscible Each miscible within the wetting phase. component assumes a fraction of the phase relative permeability equal to its volume . *Iu this paper the word miscible implies a numerical state where all the components in a cell are mobile. No inference is intended concerning the number of phases or occurrence of fluid interfaces. **The critical saturation (expressed as a function of the cells pore volumes Sc is equivalent to the minimum surfactant concentration necessary to achieve misci bility. . . ... ..-. .. . ,</p> <p>fraction in that phase, since the movement of one component through a porous medium is not impeded by the presence of other components in the same phase except for a reduction in the area available for flow. Thus, in the two-phase region, S4 &lt; Sc</p> <p>k</p> <p>r,</p> <p>1</p> <p>=</p> <p>Si rkr aqi=l,3,4,5</p> <p>(Saq)aq (4a) (4b)</p> <p>k 2 For miscible k r.</p> <p>= k 2 flow,</p> <p>(Saq) .</p> <p>S4 ~ Sc (5)</p> <p>= Si for all i.</p> <p>1</p> <p>A mixing parameter model is used to account for the creation of dispersed or mixing zones between miscible components A description of the within a single phase. one -fourth power fluidity mixing rule and the definitions of the effective viscosity are .Yhe mechanism of outlhed in Appendix A. permeability reduction due to polymer and surfactant contacting reservoir rock can be handled by the model, but it will not be discussed here because it was neglected for this work. To complete the mathematical formulation of the model, in::ial and boundary conditions are needed. Initial condition: @j = Ij (x, y, ; ;(o,t) surface normal to u</p> <p>Z, O) =0</p> <p>(6) (7)</p> <p>Boundary Where:</p> <p>condition: u = boundary</p> <p>H, n = unit vector</p> <p>Eqs. 1 through 7 describe completely the flow of fluids under the assumed mechanisms i The se equations with unknowns of pressure and saturation constitute a set of nonlinear differential equations which must be solved numerically. The solution of this mathemat ical model is accomplished by reducing the se difference equations to a single oil phase matrix problem through the use of the IMPES solution technique.</p> <p>THE SENSITIVITY</p> <p>OF MICELLAR</p> <p>FLOODING</p> <p>Numerical</p> <p>Dispersion</p> <p>The discretization error which occurs when the first spatial derivative of a quantity, c, is difference (first order accurate with upstream weighting) has the form5 #6 Ax Z-z ,.,J * ~z c (8) ()</p> <p>This match of dispersion applies in the direction of flow when the frontal velocity is a constant throughout the reservoir; i. e. , it is valid for 1-D and 2-D vertical, crosssectional, homogeneous reservoirs. The analysis can be extended to 2 -D vertical, cross -sectional, heterogeneous reservoirs by making the following assumption: If two-dimensional (cross -sect</p> <p>[1J oj</p> <p>*.L P.. .: 1</p> <p>, height .. . .. .. .. 5*</p> <p>Healy, R. N., Reed, R. L., and Stenmark, D. G,: r!M~tipha se Micro emulsion Systems, Paper SPE 5565, presented at SPE-AIME 50th Annual Fall Meeting, Dallas (Sept. 28 -Oct. 1, 1975). Todd, M. R. , ODell, P. M., and Hirasaki, G, J.: Methods for Increased Accuracy in Numerical lators, Trans. AIME Reservoir (1975) &amp;, Simu515.</p> <p>~</p> <p>porosity, density</p> <p>fraction</p> <p>P A7 w</p> <p>dimensionless</p> <p>time uAt/L, pv 6. Lantz, R. B.: Quantitative Evolution of Numerical Diffusion (Truncation Error), II Sot. Pet. ~. ~. (September, 1971) 315xo. Koonce, K. T. and Blackwell, R. J.: Idealized Behavior of Solvent Banks in Stratified Reservoirs. Sot. Pet. ~: J. (December, 19~5) ~8 -3~0 #Dykstra, H. and Parsons, R. L.: The Prediction of Oil Recovery by Water Flo~di in: Secondary Recovery of Oil in the United States, 2nd Edition, API, New York, New York (1950).</p> <p>the fluidity mixing parameter indicating-the degree of mixing</p> <p>Subscripts 7. aq D e i = aqueous = , standard = effective = 1,2, 3,4,5, brine, oil, preflush component: reservoir polymer, surfactant, . deviation 8.</p> <p>,,</p> <p>i</p> <p>SPE 5808 APPENDIX Fluid Mixing A</p> <p>C. A.</p> <p>Kossack</p> <p>and H. L.</p> <p>Bilhartz,</p> <p>Jr.(1 - W4)</p> <p>155</p> <p>U)4v</p> <p>IJ</p> <p>=</p> <p>V4</p> <p>and Effective</p> <p>Viscosity</p> <p>4</p> <p>1,2,</p> <p>3,4,5 (A-2)</p> <p>A mixing parameter model was used to account for the creation of dispersed or mixing zcnes between miscible components within a single phase. 1 If the dispersed zone completely occupied a cell in the model, then the effective viscosity. of each component was that defined by a one-fourth power fluidity mixing rule as given in Eq. A-1. n</p> <p>where ~ is the one-fourth power fluid mixing rule (Eq. A-1) and @i is the mixing pa -, rameter indicating the degree of mixing. The limiting cases of no mixing and complete mixing correspond to ~i = O and ~i = 1, respectively. The model included the option of specifying separately the degree of mixing for each component (when the components share a dispersed zone). APPENDIX B</p> <p>Assignment of Permeabilities from a Log-Normal Distribution The Dykstra -Parsons8 concept of scaling the rock permeability to a log-normal distribution with a permeability variation parameter measuring the degree of heterogeneity provides an unbiased means of assigning permeability to layers or grid blocks. When the cumulative distribution is plotted on a log-probability scale, the location of the (assumed) straight line is fixed by two parameters, the permeability y at the median kM and at one standard deviation (84. 1) above the mean kD. ~ The slope is commonly called the permeability variation, V; see Fig. B-1. The average value of 0,6 was used for the simulations since most sandstone reservoirs have a macroscopic permeability variation of 0.4 S V ~ u u * o * z ~ w %</p> <p>0.8 -</p> <p>STANDARD MICELLAR FLOOO(O.05) ~ 0.10 CRITICAL SATURATION A 0.02S CRITICAL SATURATION v O.001 CRITICAL SATURATION</p> <p>w G 0.8 =</p> <p>h</p> <p>STANDARD MICELLAR FLOGD (6.13% PV SLUG) ~ 12% PV SLUG A 4% PV SLUG</p> <p>0.6 \ 0.4 -</p> <p>*0.2 :0.2 F= * g I [ I 0.2 0.4 0.6 0.8 1.0 1.2 1.4 PORE VOLUMES OF FLUID INJECTED AFTER PRSFLUSH 7C I 1 1.6 . Fig. -</p> <p>o</p> <p>0</p> <p>o0</p> <p>Fig.</p> <p>to</p> <p>critical</p> <p>Homogeneous ressrvoir slug saturation.-</p> <p>sensitivity</p> <p>1 I I 1 I I I 0.2 0.4 0.6 0.8 1,0 1,2 1.4 1.6 PORE VOLUMES OF FLUID INJECTED AFTER PREFLUSH BA - 2 - Randoml heterogeneous reservoir</p> <p>sensitivity</p> <p>to</p> <p>surfac</p> <p>%ant</p> <p>slug</p> <p>size.</p> <p>1.0*</p> <p>1</p> <p>I</p> <p>1</p> <p>I</p> <p>I</p> <p>I</p> <p>I</p> <p>I</p> <p>1.0r</p> <p>I</p> <p>I</p> <p>I</p> <p>I</p> <p>I...</p>