Chapter 5 Darcy s Law and Applications

Size: px

Start display at page:

Download "Chapter 5 Darcy s Law and Applications"

Deborah Park
5 years ago
Views:

1 Chater 5 Darcy s La and Alications 4.1 Introdction Darcy' s la q reservoir Note : Time scale is added dn dt

2 4. Darcy s La; Flid Potential K h 1 l h K h l Different Sand Pac Different K

3 The ressre at any oint in the flo ath in fig 4. gh gz g h z Darcy s exerimental la as roved to be indeendent of the direction of flo in the earth s gravitational field. a + g h z hg + gz 4. From Eq.4.1 K dh here K is a const. 4.3

4 + gz Φ d g K gz d g K gz g d K Φ , 1 atm z gz d atm + Φ 4.6, b b b z z z z g d b + Φ Eq4. & Eq4.3 here

5 + gz Φ Φ Φ A b A B B b P P P P B A P P b B b A B A z z g d z z g d z z g d The reason for this Eq4.6 is that flid flo beteen to oints A and B is governed by the difference in otential beteen the oints, not the absolte otentials, i.e.

6 Exeriments erformed ith a variety of different liqids revealed that the la can be generalized as dφ 4.8 here ermeability μ viscosity density of flid K dφ Note : 4.4 g /μ K/g -- > /μ K/g K /μ g

7 4.3 Sign convention Φ 1 Φ Linear flo l 1 l dφ 4.9 Radial flo dφ 4.10 Φ 1 r r Φ

8 4.4 Units: Units Conversion d Φ 3 / / L L L T LT M L M T L d 1 / 1 L L L T L M LT M T L Darcy s eqation or In cgs nits In SI nits m gz + Φ

9 In Darcy nits nits hybrid atm d and c hen nit Darcy Darcy d / 1 /, 1 sec / 1 1

11 Darcy eqation In absolte nits cgs nits sec sec / sec / /, sec / / sec / A q gm oise gm gm dyne gm dyne z l g dyne dz g d d Φ + Φ dz θ

12 Darcy eqation In Darcy nits dz g d + sec sec /, sec / sec / 3 3 A q gm c z l Darcy g atm dz θ

13 Darcy eqation + dz d A q γ θ γ sin d A q, / ft A c ft z l md g g si D bbl q ater γ In field nits or here dz θ

14 Note: In this text 1 Darcy or 1 Darcy 10-8 or 1 Darcy 10-1 m 1 m In other boo 1 Darcy Darcy m 1 Darcy 1 m

15 Conversion of Permeability md and Coefficient of Permeability m/s g 3 8 ft / s c 1 md ft si / ft H 6.4 lb / ft O m c H O 1 lb m lb c ft / s PKCoefficient of Permeability f 3 g g c 1 md m s

16 4.5 Real Gas otential The flid otential fnction Φ d b + gz 4.6 For an incomressible flid consant Φ + gz 4.7 Φ or or M zrt d b + gz zrt RT d + gz b M M b zd f, T For a comressible flid RT z dφ d + gdz M 4.0 d dφ + gdz + gz 4.19

17 4.6 Datm Pressre From eq4.0 dφ d + gdz dψ From eq4.1 q A dφ A dψ 4. Note: Ψ otential is freqently refered to as the datm ressre

18 4.7 Radial Steady State Flid; Well Stimlation Assme 1Steady state Darcy s la for the radial flo of single hase oil 0 e and ressre rofile const. t Reservoir is homogeneos 3Well is erforated across the entire formation thicness. ith time q q A d 4.3 dr For qconst. across any radial area Aπrh π rh d dr d q π rh q r 1 d dr f πh r r q r f ln 4.4 πh r dr at r r e e f q r ln πh r e 4.5

19 In drilling a ell P ellbore >P formation md flo from ellbore to formation md article ssended in the md lg the ore saces Redcing Damage zone r < r < ra sin q S πh 4.6 S sin factor, dim ensionless nmber

20 Eq4.5 and Eq4.6 q re Pe Pf ln + πh r S 4.7 In field nit, Eq4.7 is P P q Bo re 141. ln S 4.8 h r e f + 3 q oil rate STB / D h PI P P ressre dradon r e f e Bo ln + S r PI rodctivity index of a ell a direct measre of the ell erformance

21 The varios methods of stimlation a Removal of sin S - Determination of sins - ressre bild test - If S>0, acid treatment - Hydrochloric acid if formation limestone - Md acid if formation is sandstone b Increasing the effective ermeability a hydralic fractring - sandstone b fractre-acidising - carbonate reservoir c Viscosity redction μ o high PI lo The T stimlation o Steam Soaing fig

22 d Redction of the oil formation volme e factor Bo Bo RB/STB can be minimized by choosing the correct srface searator,or combination of searator. e Redction in the ratio re/r - it is seldom considered as a means of ell stimlation f Increasing the ell enetration h

23 4.8 To-Phase Flo:Effective and Relative Permeabilities Darcy eqation In Single hase flo d g d 6 dz in Darcy γ sinθ in nits field nits To-hase flo---oil and ater or oil and gas, or gas and ater --- > Effective ermeability in Darcy eqation Effective ermeability f flid satration effevtive < absolte o, : effective ermeability

24 S S or connate residal or oil irredcible satration ater satration and ro S r S o S S Normalized crve Shae of crves Wettability of roc srface

25 Alternative manner of normalizing the effective ermeability S S o c o K K ro r S S o o o S S S S S S c c 4.3 In the dislacement of one immiscible flid by another r ro K K r ro Note : r f s, h h caillary & gravity forces

26 4.9 The Mechanics of Slementary Recovery --Slementary recovery by dislacing the hydrocarbons toards the rodcing ell ith some injected flid. injected flid --ater becase - - availability - - lo cost - - high secific gravity --Mobility of any flid λ λ * r /μ Relative mobility r /μ --Water dislaces oil

27 -- Water dislaces oil Ideal or iston-lie dislacement Interface ater front Injecting ell Prodcing ell Water zone Water zone Oil zone λ r r S 1 S or ' r The favorable tye of dislacement ' r ' ro o ' ro M 1 and ' r iston lie dislacement here M end oint mobility ratio endoint relative ermeabilities const. Oil recovered ater injected in a linear reservoir bloc

28 Non-ideal dislacement Injecting ell Prodcing ell Non ideal Oil Common recovered M dislacement > or 1 6 ater injected

29 Mobility Control Mobility ratio M Mobility Mobility of of the the dislacing dislaced flid flid ' rd ' ro d o Where d in rd is dislacing flid Mobility control to redce M olymer olymers, flooding sch as increase olysaccharide, d are dissolved in the injection ater

30 combstion sit in injection steam injection ater hot temeratre the g increa by redced drastically be can of order crdes viscos very For decrease method Thermal o o d o sin 1000 ~ heating on oil the of ansive crde the of distillation control mobility effects side tertiary some ith rocesses ery re Secondary method Thermal ex 3 1 cov

31 Tertiary flooding recovering the oil remaining in the reservoir after a conventional secondary recovery roject. After secondary recovery traing of oil drolets becase of srface tension ro After secondary recovery To dislace the oil ith a flid hich is solble in it So A Sor S So. B A Sor To flood ith a flid hich is miscible or artially miscible ith the oil Eliminating srface tension

32 Gas Petrolem Liqid LPG flooding LPG Miscible oil from H C light extracting control mobility C t A t oil CO flooding dioxide Carbone o ro.. 3..,,. 1 tan flooding solton Micellar flooding t Srfac

Fluid Dynamics. Type of Flows Continuity Equation Bernoulli Equation Steady Flow Energy Equation Applications of Bernoulli Equation

Fluid Dynamics. Type of Flows Continuity Equation Bernoulli Equation Steady Flow Energy Equation Applications of Bernoulli Equation Tye of Flows Continity Eqation Bernolli Eqation Steady Flow Energy Eqation Alications of Bernolli Eqation Flid Dynamics Streamlines Lines having the direction of the flid velocity Flids cannot cross a