Petroleum Engineers

THERMALRECOVERY46-5The convection heat transfer coefficient, h, Btuihr-sqft-“F, can be calculated thus ‘* :h=0.75v,o~6/ril10~4, . . . . . , . . . . . . . (3)where v,+ is the wind velocity, miihr. The radiation heattransfer coefficient, I, normally can be neglected.If the pipe is bare, that is, uninsulated, then J-,~ =rinandU,i=h. . . . . . . . . . . . . . . . . . (4)If the steam is superheated, T, will vary along the lineas heat is being lost to the atmosphere. When the pipeis long, it needs to be broken up into segments and theheat loss calculated segment by segment. In each segment,Ts* =T,$, -Qr,lwsc,s, . . . . . . . . . . (5)whereT.vl ,Ts2 = steam temperatures at the beginning andthe end of the segment, “F,QrI = heat loss along the segment, Btulhr,w,~ = mass rate of steam, lbm/hr, andC,, = heat capacity of steam, Btu/lbm-“F.If the steam is saturated, the heat loss will cause reductionin steam quality.I,2 =f;, -Qr,lwsLs, . . . . . . . . . . . . .(6)where f,i and fs2 equal the steam quality at the beginningand the end of the pipe segment, fraction, and L,is the latent heat of steam, Btu/lbm.Wellbore Heat LossesIn most of the steam injection projects, saturated steamat a certain quality is injected into the formation. Here,we assume a more general case in which the steam firstenters the wellbore as superheated steam, becomes saturatedwith a gradually diminishing quality, and is furthercooled after its complete condensation into hot water.Superheated Steam. Assume that when the depth D is0, the temperature of the steam is T, and varies withtime. Also assume that a linear geothermal gradient existsso thatTf=gGD+ T,,,,, . . . . . . (7)where 7” is the temperature of the formation. Supposeone starts with the temperature of the steam at a depthD r , and desires to calculate the temperature at depth Dlwith the length of the depth interval AD= 02 -D 1 . Sincethe formation temperature at D is g G D , + T,Y,, Ramey ‘sequation for the gas case I9 becomesT(D2,r)=gcDz+T,,-gcA-AB+[T(D,,t)-gcD,A is defined asandA= w~C~[khf+rtiUdit)l2sr,i Urikhf1B=- 778c,,wherekhf =rtr =ur, =-T,,+gGA+AB]e-hDJA.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (8). . . . . . . . . . . . (9). . . . . . . . . . . . . . . . . . . . . . . . . . . .(lO)thermal conductivity of the formation,Btu/D-ft-“F,inside radius of the tubing, ft,overall heat transfer coefficient for theannular space between inside of thetubing and outside of the casing basedon rti, Btu/D-ft-“F,f(r) = transient heat conduction time function forearth, dimensionless, shown in Fig.46.5,c, = heat capacity of steam, Btu/lbm-“F,gc = geothermal gradient, “F/ft, andT.m = surface temperature, OF.For t>7days,2Jatf(t)=lnp -0.29, . . . . . . . . . . .r cowhere 1y is the thermal diffusivity, sq ft/D, and rcO is theoutside radius of casing, ft.Saturated Steam. When the steam is saturated, the wellboreheat loss will cause changes in the steam qualitywhereas the steam temperature, T, , is kept constant. IfTABLE 46.6--MECHANISMS CONTRIBUTING TO STEAM RECOVERYSteam injectron pressure, psigHot waterflood recovery (Includes viscosity reduction and swelling)Recovery from gas driveExtra recovery from steam distillationRecovery improvements from solventlextractton effectsTotal recovery by steamRecovery(% Initial 011 In Place)Torpedo Sandstone Torpedo SandstoneCoreCore37OAPI Crude12 2OAPI Crude800 (52OOF) 84 (327OF) 800 (52OOF) 84 (327°F)71.0 68.7 68.7 66.03.0 3.0 3.0 3.018.9 15.6 9.3 4.94.7 4.6 3.0 3.797.6 91 .9 84.0 77.6