PRODUCTION OF OIL AND GAS

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PRODUCTION OF OIL AND GAS
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Units and Conversion

• People in petroleum industry has their own unit
  call oilfield units
• All equation presented including the constants
  are in oilfield units
• Table of conversion btw Oilfield and SI units

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Producing Oil Well

• Introduction
• To understand the process of flow from reservoir
  into the well sandface, a simple expression of
  Darcys Law in radial coordinates can be used
• (1)
• where A2prh
• The equation is general and suggest a number of
  interesting conclusion
• Flow rate is large if pressure gradient,
  permeability and reservoir height are large
• Flow rate is large if viscosity of flowing fluid
  is small
• This expression assumes single-phase fluid
  flowing and saturating the reservoir

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• Transient flow of undersaturated oil
• Diffusivity equ describing the P profile in an
  infinite-acting, radial reservoir, slightly
  compressible and constant viscosity fluid
  (undersaturated oil or water)
• (2)
• Its generalized solution is
• (3)
• where Ei(x) is the exponential integral and x is
  given by
• (4)

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• For x lt 0.01 (large values of time or small
  distance), Ei(x) can be approximate by ln(gx),
  where g is Eulers constant (1.78)
• Therefore at wellbore and shortly after
  production, can be approximated by
• (5)
• (6)
• Using variables in oilfields units and coverting
  natural log to log base 10, results in pressure
  drawdown equation describing the declining
  flowing bottomhole pressure
• (7)

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• Due to long time flow with same wellhead P, Pwf
  is largely constant
• Therefore the above equ which is for constant
  rate, must be adjusted
• Approximation of analytical solution with
  appropriate inner boundary conditions
• (8)
• With t in hours

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Example 1
Using the well reservoir variables in Appendix A,
develop a production rate profile for a year
assuming that no boundary effects emerge. Do
this in increments of 2 months and use a flowing
bottomhole pressure equal to 3500
psi Solution From equ. (8) and substitutions of
the appropriate variables in Appendix A, the well
production rate is given by
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Example (continued)

For t2 months, production rate, q428 STB/day.
Charting every two months will yield,
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• Steady-state well performance
• In a well, within the reservoir (Fig 2), area of
  flow at any distance, r is 2prh, and equ (1)
  becomes
• (9)
• assume q is constant,
• (10)
• and finally
• (11)

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• Logarithmic nature of Equ (11) means the pressure
  drop doubles or triples as radial distance
  increases.
• Thus, near-wellbore region is of extreme
  importance in well production bcoz it is where
  much of pressure drop occurs
• Skin effect concept the steady state pressure
  drop is
• (12)
• Which adds to the pressure drop in the reservoir,
  constant P at boundary (re) when at s.s., pe is
  the radial flow thus equ (11), becomes
• (13)

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• In oilfield units, equation (13) becomes
• (14)
• Two other concepts
• Effective wellbore radius rw, derived from
  rearrangement of equ (14)
• (15)
• In a damage well, e.g. s10, reservoir drains
  into well rw4.5x10-5rw
• Conversely, in stimulated well, e.g s-2 or even
  -6 (for a fractured well), rw7.4rw and 403rw,
  respectively

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• Productivity index, J (production rate/pressure
  difference)
• (16)
• Maximize J by increasing q for a given driving
  force (drawdown) or minimize drawdown for a given
  rate
• Can be accomplished with a decrease of the skin
  effect (thru matrix stimulation and removal of
  near-wellbore damage) or thru superposition of a
  negative skin effect from an induced hydraulic
  fracture
• In very large viscosity reservoir (mgt100cp),
  thermal recovery may be indicated to reduce the
  viscosity

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Example 2
Assume that a well in the reservoir described in
Appendix A has a drainage area equal to 640 acres
(re 2980 ft) and is producing at a steady-state
with an outer boundary (constant) pressure equal
to 5651 psi. Calculate the steady-state
production if the flowing bottomhole pressure is
equal to 4500 psi. Use a skin effect equal to
10. Describe 2 mechanisms to increase the flow
rate by 50. Solution From equ. (14) and
rearrangment
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Example 2 (continued)
To increase production rate by 50, one
possibility is to increase the drawdown by 50
A second possibility is to reduce the skin
effect. In this case
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• Pseudo-steady-state flow
• Steady-state conditions implied a
  constant-pressure outer boundary
• For no-flow boundaries, drainage area can be
  described by natural limits such as faults,
  pichouts, etc, or artificially induced by
  adjoining wells production- pseudo-steady-state
• Pressure at outer boundary is not constant but
  declines at constant rate with time
  (dpe/dt)constant, therefore
• (17)
• at r re, equ (17) becomes
• (18)

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• Equ. (18) is not useful bcoz pe is not known at
  any given time.
• But average reservoir pressure can be obtained
  from periodic pressure buildup tests. It depends
  on drainage area and properties of fluid and rock
• (19)
• Since dV2prhfdr, Equ. (19) becomes
• Expression for p at any point r can be
  substitute from equ (17) and integration results
  in
• (20)

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• Introducing skin effect and incorporating term ¾
  in log expression leads to the inflow
  relationship for a no-flow boundary oil reservoir
• (21)
• This equation is particularly useful bcoz it
  provides relationship btw average reservoir
  pressure and q.

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Example 3
What would be the average reservoir pressure if
the outer boundary pressure is 6000 psi, the
flowing bottomhole pressure is 3000 psi, the
drainage area is 640 acres, and the well radius
is 0.328 ft? What would be the ratio of the flow
rates before (q1) and after (q2) the average
reservoir pressure drops by 1000 psi? Assume
that s0. Solution A ratio of equ. (18) and
(21) results in Drainage area A640, thus
re2980 ft, substitute in the above equ.
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Example 3 (continued)
The flow-rate ratio would be
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• 4.1 Transition to pseudo-steady state from
  infinite acting behavior
• Time at which pseudo-state begins, tpss is given
  by
• (22)
• tDA has a characteristic value that depends on
  the drainage shape. Circle or square tDA0.1
  1x2 rectangle tDA0.3 1x4 rectangle tDA0.8
  off-centered well in irregular patterns have
  large tDA
• If a drainage area can be approximate by a circle
  with equivalent drainage radius re, the equ (22)
  yields
• (23)
• for the onset of pseudo-steady state, tpss is in
  hours, all other variables are in customary
  oilfield units

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• Inflow performance relationship
• All wee equations relate the well production rate
  and the driving force in the reservoir i.e.
  pressure diff between the initial, outer boundary
  or average reservoir pressure and the flowing
  bottomhole pressure
• If pwf is given, production rate can be obtained
  readily
• However pwff (wellhead p) which in turns depends
  on separator or pipeline p, etc.
• Thus, what a well actually produce must be the
  combination of what the reservoir can deliver and
  what the impose wellbore hydraulic would allow
• Then it is useful to present well production rate
  f (pwf) known as inflow performance
  relationship (IPR) curve

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Example 4

• Using well and reservoir data in Appendix A,
  construct transient IPR curves for 1, 6 and 24
  months. Assume zero skin.
• Solution
• Equ. (8) with substituted variables takes the
  form

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• Horizontal well production
• Excellent producers for thin (h lt 50 ft)
  reservoir or thicker reservoirs with good
  vertical permeability, kv
• Relationship mixed s.s. in the horizontal plane
  and pseudo-steady state in the vertical plane is
• (24)
• Where Iani is a measurement of vertical-to-horizon
  tal permeability anistropy and given by
• (25)

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• In equ (24), a is the large half-axis of the
  drainage ellipsoid formed by a horizontal well of
  length L, the expression for the ellipsoid is
• (26)
• For L/2 lt 0.9reH
• The productivity index ratio btw horizontal and
  a vertical well in a specific reservoir may be
  large.
• This productivity index ratio can be
  manifested by an increase in the production rate,
  a decrease in the pressure drawdown, or both

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Example 5
Develop an expression for a vertical well
effective wellbore radius that would result in
equivalent production from a horizontal well.
Estimate the equivalent vertical well skin effect
when L2000 ft, h53 ft, a3065 ft, Iani3 and
reH2980 ft Solution The log expression
inside the large parentheses in Equ. (24) can be
gathered Comparison btw equ. (14) and equ (24)
results in rw 341 ft and s -6.9