SOCIXTY OF PETROLEUM ENGINEERS OF AIME6200North Central Expressway =R SPEDallas, Texas I5206

THIS IS A PREPRINT --- SUBJECT TO CORRECTION

Gravity Effects in Miscible Displacement

By

M. C. Miller, Jr. Member AIME, Atlantic Richfield Co., DQlas, Tex.

0 Copyright 1966Ameriesn Institute of Mining, Metallurgical and Petroleum Engineers, Inc.

1531

This paper ?~asprepared for the hlst Annual Fall Meeting of the Society of Petroleum Engineersof AIME, to be held in Dallas, Tex., Oct. 2-5, 1966. Permission to copy is restricted to an abstractof not more than 300 words. illustrationsm~ copied. The abs;;act should contain conspicu-ous acknowledgment of where and by whom the ~aper is m?esented. Publication elsewhere afterpublication in the JOURNAL OF PETROLEUM TECfiO~OGY or-the SOCIETY OF F!ETROLEUMENGINEERS JOURNAL isusually granted upon request to the Editor of the appropriate journal provided agreement to giveproper credit is made.

Discussion of this paper is invited. Three copies of any discussion should be sent to theSociety of Petroleum Engineers office. 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.

ABSTRA13T

Segregation of hydrocarbons and water canseverely reduce the ultimate vertical sweepoutefficiency of mlsclble displacement processeswhen a mobile water phase is present in all orpart of the reservoir. Computer studies haveshown that the decreased miscible sweep result-ing from segregated flow can result in unecon-omic operations in some fields in wh~ch economicoperations were predicted for non-segregatedflow.

Gravity override is enhanced as a resultor segregation, and once the reservoir fluidssegregate, the high rel&tive permeability of th(lighter fluids at the top of the reservoirincreases the gravity override with the resultthat oil irrthe lower portion of the reservoi$is not displaced miscibly.

The shape andrnovement of the oil bankformed.during secondary and tertiary projectscan be paramount to a successful field opera-tion. Results from our computer model studyshow that an oil bank formed ahead of an over-riding miscible fluid is forced down below thesolvent tongue and moved relatively slowlytowara the protiucingwell. The oil bank i.sslowly recovered immiscible at an extremely lowrate by the water injected along with the gas.Thus at the economic limit of the fielclopera-tion, a substantial.amount of the oil displaceaReferences and illustrations at end of paper.

by the miscible fluid early in the reservoirlife is left unswept at abandonment.

Most of the above information has beenobtained from a two-phase flow, two-dimensions:mathematical model, which includes the effectof the segregation of all hydrocarbon fluidsin the presence of a denser, mobile, i~iscib~(water phase present in watered-out systems onthe sweepout behavior of the oil-bank frontand miscible front. This behavior was previ-ously unattainable from our physical [labora-tory] flow models in which miscible fluids wereused.

INTRODUCTION

The miscible slug process and the highpressure gas process are currently employeain our endeavor to maximize the oL1 recoveryfrom reservoirs. Since residual 011 satu-rations of 20 to 50 per cent after gas or wate:floods are common, the additional oil recoverycan be considerable. In the high pressure gasprocessl multiple contact between the injeitedgas and the reservoir oil strips the light end~from the oil uatil a transition fluld is forme{which is misciblewith the reservoir oil.Al$hough pressures in excess of 10,000 psi areusually requ~red for methane to be completelymiscible with crude oil, + miscible flood isachieved by the above mechahism fn the 3)000-to 5,000-psi range. In the miscible slug

GRAVITY EFFECTS IN M~

process, a propane or rich-gas slw which iSmiscible with the reservoir oil is driven by agas which is misctble with the slug but notmiscible with the oil. lower pressures [1,200psi to 3,000WI areusedanda sufficientlylarge slug must be employed In order to preventpremature loss of miscibility by diffusion anddispersion of the slug material.g Injection ofwater along with the gas has been beneficial,and oil recoveries in the 50 to 70 per centrange can be obtained.3 Iackof completecontact between the reservoir oT1 and misciblefluid at the economic limit of a field oper-ation prevents oil recoveries of 100 per cent.

Interpretationand prediction of Lhereservoir performance for miscible processesare difficult as a result of the effects ofviscous fingering1~2~11~12~16 [dynamic in-stability of high mobllf.tyfluids displacinglower mobility fluids], loss of miscibilityfrom diffusion and dispersion of the slugmateria19?16 heterogeneities and

1gravity.1)2) 3>16 me effects of these factorsand their interaction plays a major role in theareal and vertical sweepout performance andthus, ultimately, the economic 0

il-Jq>J. L.i . u . L,LLJJLJULI .

[Cartesian Coordinates], incompressible flow

F

of water, oil, solvent, and gas where the oil,

1.L kv

geometry, ~sclvent, and gas are completely miscible

kh components in the hydrocarbon phase. Theseequations are:

2.kr~

/

kro [11avolumetric balance[continuitymobility ratio, IvI = _

Bdequation] for the water phase

Pov .@w = - +

a%n-i- l . [11

3. viscous to gravity pressure gradients,@v /lo [2] a volumetric balance [continuity

~

equation] for the hydrocarbon phase

40 viscous to capillary pressure v l q= = -+ash= = 8SW

+ , [2]gradients, T at+V /Lo

we

[3] ~rcys law for the water phase

--+ k krWV*W, . . l l o c [31where: w=-

P~= gravitational constant

k; =[h] Darcys law for the hydrocarbon phase

specific permeability in horizontaldirection

k r(hc)kv = specific permeability in vertical q==. %hcdirection ~hc 7* [4]

k = relative permeability to oilk; = relative permeability to the dis- [5] the water phase potential

placing fluidM= mobflity ratio ZW=pW+pWgh}~~~ [51q = fluid.injection ratev= total linear pore velocity, v = q [6] the hydrocarbon phase potential

A cross-sectional area ~

L= length of system= thickness of system

~hc=%c+ ~hcgh, . . . . . . . [6]

$ = density difference between the in-jected and displaced fluids [7] the volumetric balance for the three

c= interracial tension between the in- components in the hydrocarbon phase

jetted and displaced fluidse= contact eagle hc=l-%v =So+ss+sg=(co

Go = oil viscosityPd = displacing fluid viscosity +c~+cg)shc, . ..... .[7]0= porosity

In the mathematical model, it is not [8] the density of the hydrocarbon phasenecessary to use scaling groups to predict thebehavior for a given field test. However, the

~ h~ = CO(IO+ CsPs+ CgPg, . . .,[81use of dimensionless scaling groups Is usefulIn correlating the results of several fieldtests. The resulting correlation can be used [9] the effective viscosity of thehydro-to estimate the flow behavior for an unknown carbon phase expressed by [KoballO]field and is therefore useful in screeningpotential miscible flood prospects. l/4 114

(~) =Co (bThe effects of geometry and the ratio of ~hc 1%

VISCOUS to gravitypressure gradients were foundto be paramount in the flow behavior as will be 1/4shown later. 1+c~(

IJs)

TWO-DIMENSIONALMATHEMATICAL MODEL WITH CROSSFLm

The two-dimensionalmathematical model +-cemployed in this study is a computer progrm g@40[which solves simultaneouslythe equationsdescribing two-phase, two-dimensional

GRAVITY EFFECTS IN MISCIBLE DISPIACEMEXI!T-.. .-- .- -,- --- -. . .I

[10] and the capillary pressure equation[function of water saturation only]

pc(sw)=Phc -Pa,..... ,...[10

where

c= concentration of component in hydro-carbon phase

= gravitational constant:= heightk= absolute permeability?&r= relative permeability to designated

phaseP = pressures= saturationt= timev . velocity

P = densityF q viscosity@ = porosity@= potentialV= del operator

Subscriptsc = capillaryg = gas

hc = hydrocarbon phaseo . oilrw = relative to waterro = relative to oils = solventw = water

A finite-difference,alternating-dlrection, leap-frog procedure, similar to theprocedure outlined by Couglas, Peaceman andRachford5 and discussed in detail in thedoctoral dissertations of Nielsen6 and Goddin,7was employed to solve the above equatio~s.This method was modified to include the flowbehavior of three contiguous miscible flulds[oil, solvent snd gas] In the hydrocarbon phaseThe effects of diffusion and dispersion betweenthe fluids in the hydrocarbon phase wereIgnored, leading to a sharp interface betweenthe solvent and oil and the gas and solvent.Eqs. 8 and 9 were used to calculate the densttyand viscosity, respectively, of the hydrocarbonphase.

Although the mathematical model is re-stricted to,two-climensfonalflow systems,the effects of gravlty~ capillary pressure,stratification, flow rate, slug size, reservoirlength and thickness, reduced vertical perme-ability, and reservoir fluid pr~pertles can beinvestigated.

The special case of no vertical crossflow[zero vertical permeability] was treated sepaarately ana analyzed for an itiealizedsituationin which there are no relative permeability orcapilla~ pressure effects. These calculations

showfng the effect of gravity overriae in theabsence of vertical counterblow segregationare discussed In the Appendix and are includedfor those who are concezned with funciamentalfluid-flow behavior. Under these idealizedconditions, the predicteilflow behavior can becorrelated by the product of the geometry

J Lratio, + -% v?aoviscous-to-gravity-gradient ratio,J~g AP

. The resulting

product is a viscobs-to-gravity-pressure-drop@v~L

ratio, and has been used as akhgA,OH

correlating group in several papers.1~2>15However, It will be shown in the next sectionthat It is necessary to scale two groups suchas the geometry ratio and viscous-to-gravity-gradient ratio separately when verticalcounterblow segregation occurs leaaing to ahigh relative permeability of the hydrocarbonphase at the top of the reservoir.

PREDICTED PERFORMANCE OF MISCIBLE SLUGPROCESS IN HORIZONTAL RESERVOIRS

The flow behavior of the miscible slugprocess in five horizontal reservoirs was predicted using the two-dimensional, mathe-matical model aescribea above. Since thephysical properties of the reservoir are notprecisely known, [e.g., the ratio of verticalto horizontal permeability may be as high as1.0 or as low as 0.003] several different case:were,run for each reservoir. The velocity[throughputrate] was varied for proposed fi.elftests to determine the injection rates require