Page 232 - Petroleum Production Engineering, A Computer-Assisted Approach

Guo, Boyun / Computer Assited Petroleum Production Engg 0750682701_chap15 Final Proof page 230 22.12.2006 6:14pm

15/230 PRODUCTION ENHANCEMENT
that dominates long-term production performance. This k ¼ qBm : (15:17)
average horizontal permeability can be derived from the 4pH R m R
pseudo-radial flow regime. For vertical wells partially pene- For any types of linear flow, Eqs. (15.2) and (15.5) indicate
trating nonfractured reservoirs, both horizontal and vertical that plotting of the bottom-hole pressure versus the
permeabilities influence long-term production performance. square-root of time data will show a trend with a constant
These permeabilities can usually be derived from the hemi- slope m L , where
spherical flow regime. r ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Flow regimes are usually identified using the diagnostic m L ¼ qB m , (15:18)
0
pressure derivative p defined as H L X L pfc t k y
dDp dDp where H L ¼ h and X L ¼ 2x f for linear flow, and
0
p ¼ ¼ t , (15:7)
d ln (t) dt H L ¼ h Z w and X L ¼ L for pseudo-linear flow, respec-
tively. Then the permeability in the flow plane can be
where t is time and Dp is defined as estimated by
Dp ¼ p i p wf (15:8) 2
m qB
for drawdown tests, where p i and p wf are initial reservoir k y ¼ : (15:19)
pfc t m L H L X L
pressure and flowing bottom-hole pressure, respectively.
For pressure buildup tests, the Dp is defined as If a horizontal well is tested for a time long enough to
detect the pseudo-radial flow, then it is possible to estimate
Dp ¼ p sw p wfe , (15:9)
other directional permeabilities by
where p ws and p wfe are ship-in bottom-hole pressure and k 2
the flowing bottom-hole pressure at the end of flow (before k x ¼ h (15:20)
k y
shut-in), respectively.
For any type of radial flow (e.g., horizontal radial flow, and
vertical radial flow, horizontal pseudo-radial flow), the 2
diagnostic derivative is derived from Eqs. (15.1), (15.3), k z ¼ k yz : (15:21)
and (15.6) as k y
dDp qBm Although k x and k z are not used in well productivity
0
p ¼ ¼ , (15:10) analysis, they provide some insight about reservoir anisot-
d ln (t) 4pkH R
ropy.
where k is the average permeability in the flow plane (k h or Skin Factor. Skin factor is a constant that is used to
k yz ) and adjust the flow equation derived from the ideal condition
p ffiffiffiffiffiffiffiffiffiffiffi
k h ¼ k x k y (homogeneous and isotropic porous media) to suit the
applications in nonideal conditions. It is an empirical fac-
H R is the thickness of the radial flow (h or L). Apparently, tor employed to consider the lumped effects of several
the diagnostic derivative is constant over the radial flow aspects that are not considered in the theoretical basis
0
time regime. The plot of p versus t data should show a when the flow equations were derived. The value of the
trend of straight line parallel to the t-axis. skin factor can be derived from pressure transient test
For linear flow (e.g., flow toward a hydraulic fracture), analysis with Eqs. (15.1), (15.2), (15.3), (15.5), and (15.6).
the diagnostic derivative is derived from Eq. (15.2) as But its value has different meanings depending on flow
s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi regime. A general expression of the skin factor is
dDp qB mt
0
p ¼ ¼ : (15:12) X
d ln (t) 4hx f pfc t k y S ¼ S D þ S Cþu þ S P þ S PS , (15:22)
For pseudo-linear flow (e.g., flow toward a horizontal well), where S D is damage skin during drilling, cementing, well
the diagnostic derivative is derived from Eq. (15.5) as completion, fluid injection, and even oil and gas produc-
s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
dDp qB mt tion. Physically, it is due to plugging of pore space by
0
p ¼ ¼ : (15:13) external or internal solid particles and fluids. This com-
d ln (t) 2L(h z w )
pfc t k y
ponent of skin factor can be removed or averted with well
stimulation operations. The S Cþu is a skin component due
Taking logarithm of Eqs. (15.12) and (15.13) gives
r ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi to partial completion and deviation angle, which make the
1 qB m flow pattern near the wellbore deviate from ideal radial
0
log p ðÞ ¼ log tðÞ þ log (15:14)
2 4hx f pfc t k y flow pattern. This skin component is not removable in
water coning and gas coning systems. The S P is a skin
and component due to the nonideal flow condition around the
r ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1 qB m perforations associated with cased-hole completion. It
0
log p ðÞ ¼ log t ðÞ þ log : (15:15)
2 2L(h z w ) pfc t k y depends on a number of parameters including perforation
density, phase angle, perforation depth, diameter, com-
Equations (15.13) and (15.14) indicate that the signature of pacted zone, and others. This component can be mini-
1
the linear flow regime is the ⁄ 2 slope on the log-log plot of mized with optimized perorating technologies. The SS PS
diagnostic derivative versus time. represents pseudo-skin components due to non–Darcy
Once the flow regimes are identified, permeabilities flow effect, multiphase effect, and flow convergence near
associated with the flow regime can be determined based the wellbore. These components cannot be eliminated.
on slope analyses. For any types of radial flow, Eqs. (15.1), It is essential to know the magnitude of components of
(15.3), and (15.6) indicate that plotting of bottom-hole the skin factor S derived from the pressure transient test
pressure versus time data on a semilog scale will show a data analysis. Commercial software packages are available
trend with a constant slope m R , where for decomposition of the skin factor on the basis of well
qBm completion method. One of the packages is WellFlo (EPS,
m R ¼ : (15:16) 2005).
4pkH R
Then the average permeability in the flow plane (k h or k yz ) Example Problem 15.1 A horizontal wellbore was placed
can be estimated by in a 100-ft thick oil reservoir of 0.23 porosity. Oil formation