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Steam delivery systems for EOR

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For any steamflood process, no matter how efficient, the major cost is always that of generating the process steam. Whether the product of oilfield steam generators, industrial boilers, or electrical/steam cogeneration plants, steam must be delivered through a network of pipes and through pipes down a wellbore to the oil bearing formation. It is imperative that the unavoidable heat losses in this distribution system be minimized with some type of insulating system. This page discusses the process of delivering steam to a thermal enhanced oil recovery (EOR) project.

Heat loss in surface distribution piping

The basic equation for heat loss is


The rate of heat loss in surface lines is usually calculated at steady-state conditions because transients disappear quickly in surface pipes. Thermal resistance to heat loss for that system is


The terms in Eq. 2 are the coefficients of heat transfer for each of the layers of an insulated pipe as shown in Fig. 1. They are, from left to right: conduction in the laminar layer in contact with the pipe wall; conduction in the scale or other solid coating on the inside pipe wall; conduction in the pipe wall; conduction in the scale or other coating on the outside pipe wall; conduction in the insulation; and convection and radiation from the outer surface of the insulation. Table 1 shows thermal conductivity for various materials. Refer to appropriate textbooks[1][2] for more in depth information.

In the previous calculation, hr is the coefficient of radiant heat transfer for the outermost surface of the system; in this case, it is for the insulation. It is common practice to cover insulation with a thin sheath of bright aluminum, mainly for protection from weather and from mechanical abuse. A side benefit is that the bright surface has low radiant emissitivity that, combined with low surface temperature, results in negligible radiant heat loss, so this term is often ignored. If the pipe is uninsulated, the term applies.

Note that for every system there is an optimum insulation thickness. Adding more insulation above this optimum will not result in more heat savings. This is because there are two competing effects; the rate of heat loss decreases with increasing insulation thickness, but heat loss increases as the exposed surface area increases.

Coefficients of heat transfer

The following are useful in most cases, but the reader should refer to appropriate texts[1][2] for more complicated systems.

Value of hf. For condensing steam, the coefficient is large, and it is generally adequate to use


when flow is turbulent (which is most of the time) and is determined by




Because μs ~ 0.018 cp for typical oilfield steam temperatures, turbulence will prevail at


Value of hpi and hpo. These are seldom known, and the terms are usually ignored for steam distribution lines. Actually, these deposits outside and, if not too thick and firmly attached, inside the pipe are desirable because they result in resistance to heat conduction. If they are present but no values are known, McAdams[1] recommends a value of 48,000 Btu/(ft2 -D-°F).

Value of hfc. McAdams[1] offers the next equation to calculate the coefficient of forced convection at the outer surface of a pipe system in air.


for 1,000 < NRe < 50,000, where


Value of hr. In the following relationship for the coefficient of radiant heat transfer, temperatures must be expressed in °Rankine, which is°F + 460.


Emissitivity, ε, of various materials is listed in Table 1.

Buried lines

A special case of insulated lines is pipes buried in the earth. See Fig. 2. Eq. 2 applies, except for two modifications,[3] which are




Heat loss rate is very high for short-term injection for buried pipes, even in dry soil, so this is not recommended in cyclic steam projects. If the soil contains moisture, the losses are even greater.

Heat loss in wells

Heat loss in wells never reaches a steady-state condition. It begins at a very high rate when the well casing is suddenly heated by initial steam injection, then continually decreases in rate as the surrounding earth is heated. For long term continuous steam injection over a period of years, wellbore heat loss becomes relatively small. Conversely, for intermittent cyclic steam injection, the heat-loss rate will always be relatively high because the surrounding earth is never appreciably heated. Eq. 2 still applies but is complicated by the ambient (earth) temperature increasing with depth because of geothermal gradient and by the "insulation," earth again, having high conductivity and practically infinite thickness. The latter property results in the thermal resistance being time dependent. Fig. 3 is a schematic depiction of typical elements that contribute to the resistance to heat flow which is described by


where the first five terms are similar to those in Eq. 2. The last five terms are the resistances in radiation and convection in the casing annulus, in the casing, in the cement, in the altered earth zone (dried earth because of high temperatures), and in the time dependent loss to the earth. If other resistance zones can be identified, such as coatings in the casing or scale deposits, etc., terms should be added for them. Every system should be analyzed according to the elements included, such as wells with no insulation on the tubing, wells with no tubing at all, or simply injection down the casing. All of the additional terms can be determined with equations previously presented except for the coefficient of heat transfer in the annulus, hrc,an and ftD.

Heat loss is a serious problem in cyclic steam stimulation because the wellbore and surface lines are never heated to steady-state conditions. Fig. 4 shows the results of Eq. 12 for several steam-injection rates in a typical Kern River field producer. It demonstrates that because steam is at a relatively constant temperature heat loss rate, it is a constant and injection should be done at the highest practical rate. Fig. 5 shows the benefit of insulating the casing from contact with steam for short duration injection as in a steam cycle. Conversely, Fig. 6[4] shows that for long-term injection, as in a steamflood injector, and for shallow wells, as encountered in the San Joaquin Valley oil fields, there is no benefit from insulating the casing. Thus, it is possible to drill inexpensive slimhole injectors, completed simply with a tubing string, and not appreciably increase heat loss over the life of a project.

Value of hrc,an. In an air-filled annulus operating under free convection, the coefficient of heat transfer for radiation and convection is given by Willhite.[3]




The Grashof number is


the Prandtl number is


and the temperature function is


The temperatures for use in Eq. 17 are proportional to the fractional thermal resistance between the outer tubing surface, in this case the insulation, Tins, and the casing inner wall, Tci. They can be estimated by




Value of f(tD). This is a function of dimensionless time.


The radius in the denominator is the radius of the outermost element in contact with the reservoir, which is the heat altered zone in this case. Willhite[3] gives a table of values for f (tD), for tD <100. A reasonable estimate can be derived from


Ramey[4] gives a calculation of f (tD), for tD ≥100.


Because Rh, Tins , Tci , and f (tD) are interrelated by nonlinear expressions, they must be solved by an iterative trial-and-error procedure.[3]


Can = isobaric specific heat of annular fluid, Btu/(lbm-°F) [kJ/kg•K]
Co = isobaric specific heat of oil, Btu/(lbm-°F) [kJ/kg•K]
Cw = isobaric specific heat of water, Btu/(lbm-°F) [kJ/kg•K]
D = depth below surface, ft [m]
E = efficiency
f(tD) = function of dimensionless time defined by Eq. 22
hf = enthalpy of liquid portion of saturated steam, Btu/lbm [kJ/kg]
hfc = forced convection coefficient of heat transfer, Btu/(sq ft-D-°F) [kJ/m2•d•K]
hft = film coefficient of heat transfer, Btu/(sq ft-D-°F) [kJ/m2•d•K]
hpi = film coefficient of heat transfer at pipe inner radius, Btu/(sq ft-D-°F) [kJ/m2•d•K]
hpo = film coefficient of heat transfer at pipe outer radius, Btu/(sq ft-D-°F) [kJ/m2•d•K]
hr = coefficient of radiant heat transfer for the outermost surface, Btu/(sq ft-D-°F) [kJ/m2•d•K]
hrc,an = radiant/convection heat transfer coefficient in well annulus, Btu/(sq ft-D-°F) [kJ/m2•d•K]
iw = cold water equivalent steam injection rate, B/D [m3/d]
n = index of time increment
NGr = Grashof number
NPr = Prandtl number
RTENOTITLE = heat injection rate, Btu/D [kJ/d]
RTENOTITLE = heat loss rate, Btu/D [kJ/d]
RTENOTITLE = heat removed with produced fluids, Btu/D [kJ/d]
RTENOTITLE = volumetric heat injection rate, MMBtu/D/acre-ft [kJ/m3]
r = radius of reservoir, ft [m]
rci = casing internal radius, ft [m]
rco = outer casing radius, ft [m]
re = external radius of heated zone, ft [m]
rh = radius of heated or steam zone, ft [m]
ri = inside pipe radius, ft [m]
rins = insulation external radius, ft [m]
ro = outside pipe radius, ft [m]
rw = radius of well, ft [m]
Rh = overall specific thermal resistance, °F-ft-D/Btu [K•m•d/kJ]
t = time, D [d]
tcD = critical dimensionless time
tD = dimensionless time
T = average temperature in heated reservoir, °F
Ta = air temperature, °F
TA = ambient temperature, °F
Tb = bulk fluid temperature, °F
Tci = temperature of casing wall, °F
To = temperature of outer surface, °F
α = thermal diffusivity of reservoir, ft2/D [m2/d]
αE = thermal diffusivity of earth, ft2/D [m2/d]
αs = thermal diffusivity of surrounding formation, ft2/D [m2/d]
γ = specific gravity
ε = emissivity
εci = radiant emissivity of casing wall
εins = radiant emissivity of insulation outer surface
λ = thermal conductivity, Btu/(ft-D-°F) [kJ/m•d•K]
λa = thermal conductivity of air, Btu/(ft-D-°F) [kJ/m•d•K]
λa,a = thermal conductivity of air in well annulus, Btu/(ft-D-°F) [kJ/m•d•K]
λE = thermal conductivity of unaltered earth, cp [Pa•s]
λEa = thermal conductivity of altered earth, cp [Pa•s]
λins = thermal conductivity of insulation, cp [Pa•s]
λp = thermal conductivity of pipe, cp [Pa•s]
λS = thermal conductivity of surrounding formation, cp [Pa•s]
μ = viscosity, cp [Pa•s]
μa = viscosity of air, cp [Pa•s]
μan = viscosity of well annulus gas, cp [Pa•s]
π = constant pi, 3.141
ρ = density, lbm/ft3 [kg/m3]
ρa,sc = density of air, lbm/ft3 [kg/m 3]
υs = steam specific volume, ft3/lbm [m3/kg]
υw = wind velocity, miles/hr [km/h]


  1. 1.0 1.1 1.2 1.3 McAdams, W.H., Williams, G.C., and Smith, K.A. 1967. Standard Handbook for Mechanical Engineers. In Transmission of Heat by Conduction and Convection, seventh edition. T. Baumeister and L. Marks, eds., Ch. 4, 92. New York City: McGraw-Hill Book Co. Inc.
  2. 2.0 2.1 Rohsenow, W.M. and Hartnett, J.P. 1973. Handbook of Heat Transfer, 3. New York City: McGraw-Hill Book Co. Inc.
  3. 3.0 3.1 3.2 3.3 Willhite, G.P. 1967. Over-all Heat Transfer Coefficients in Steam And Hot Water Injection Wells. J Pet Technol 19 (5): 607-615. SPE-1449-PA.
  4. 4.0 4.1 4.2 Dennis, E.L. 1995. Project Design for Slimhole Steam Injectors in Thermal Recovery Projects as Compared to Conventional Steam Injectors. Presented at the SPE Western Regional Meeting, Bakersfield, California, 8-10 March 1995. SPE-29629-MS.

Noteworthy papers in OnePetro

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See also

Steamflood design

Cyclic steam stimulation design

Steamflood heat management

Thermal recovery by steam injection