Page 96 - Petroleum Production Engineering, A Computer-Assisted Approach

Guo, Boyun / Computer Assited Petroleum Production Engg 0750682701_chap07 Final Proof page 88 3.1.2007 8:47pm Compositor Name: SJoearun

7/88 PETROLEUM PRODUCTION ENGINEERING FUNDAMENTALS
7.1 Introduction Oil viscosity (m o ): 1.5 cp
With the knowledge of Nodal analysis, it is possible to Producing GLR (GLR): 300 scf/bbl
forecast well production, that is, future production rate Gas-specific gravity (g g ): 0.7 air ¼ 1
and cumulative production of oil and gas. Combined with Flowing tubing head 800 psia
information of oil and gas prices, the results of a produc- pressure (p hf ):
tion forecast can be used for field economics analyses. Flowing tubing head 150 8F
A production forecast is performed on the basis of temperature (T hf ):
principle of material balance. The remaining oil and gas in Flowing temperature at 180 8F
the reservoir determine future inflow performance relation- tubing shoe (T wf ):
ship (IPR) and, therefore, production rates of wells. Water cut: 10%
Production rates are predicted using IPR (see Chapter 3) Interfacial tension (s): 30 dynes/cm
and tubing performance relationship (TPR) (see Chapter 4) Specific gravity of water (g w ): 1.05
in the future times. Cumulative productions are predicted
by integrations of future production rates.
A complete production forecast should be carried out
in different flow periods identified on the basis of flow Solution To solve Example Problem 7.1, the spreadsheet
regimes and drive mechanisms. For a volumetric oil program TransientProductionForecast.xls was used to
reservoir, these periods include the following: perform Nodal analysis for each month. Operating
points are shown in Fig. 7.1. The production forecast
. Transient flow period result is shown in Table 7.1, which also includes
. Pseudo–steady one-phase flow period calculated cumulative production at the end of each
. Pseudo–steady two-phase flow period month. The data in Table 7.1 are plotted in Fig. 7.2.
7.2 Oil Production during Transient Flow Period
7.3 Oil Production during Pseudo–Steady
The production rate during the transient flow period can Flow Period
be predicted by Nodal analysis using transient IPR and
steady flow TPR. IPR model for oil wells is given by It is generally believed that oil production during a pseudo–
Eq. (3.2), that is, steady-state flow period is due to fluid expansion in under-
saturated oil reservoirs and solution-gas drive in saturated
kh( p i p wf ) oil reservoirs. An undersaturated oil reservoir becomes a
q ¼ : (7:1) saturated oil reservoir when the reservoir pressure drops to
k
162:6B o m o log t þ log fm o c t r 2 3:23 þ 0:87S
w below the oil bubble-point pressure. Single-phase flow
dominates in undersaturated oil reservoirs and two-phase
Equation 7.1 can be used for generating IPR curves for flow prevails in saturated oil reservoirs. Different math-
future time t before any reservoir boundary is reached by ematical models have been used for time projection in
the pressure wave from the wellbore. After all reservoir production forecast for these two types of reservoirs, or
boundaries are reached, either pseudo–steady-state flow or the same reservoir at different stages of development
steady-state flow should prevail depending on the types of based on reservoir pressure. IPR changes over time due to
reservoir boundaries. The time required for the pressure the changes in gas saturation and fluid properties.
wave to reach a circular reservoir boundary can be with
fmc t r 2
t pss 1,200 e .
k 7.3.1 Oil Production During Single-Phase Flow Period
The same TPR is usually used in the transient flow period Following a transient flow period and a transition time, oil
assuming fluid properties remain the same in the well over reservoirs continue to deliver oil through single-phase flow
the period. Depending on the producing gas–liquid ratio under a pseudo–steady-state flow condition. The IPR
(GLR), the TPR model can be chosen from simple ones changes with time because of the decline in reservoir pres-
such as Poettmann–Carpenter and sophisticated ones such sure, while the TPR may be considered constant because
as the modified Hagedorn–Brown. It is essential to validate fluid properties do not significantly vary above the bubble-
the selected TPR model based on measured data such as
flow gradient survey from local wells. point pressure. The TPR model can be chosen from simple
ones such as Poettmann–Carpenter and sophisticated ones
such as the modified Hagedorn–Brown. The IPR model is
Example Problem 7.1 Suppose a reservoir can produce
oil under transient flow for the next 6 months. Predict oil given by Eq. (3.7), in Chapter 3, that is,
production rate and cumulative oil production over the kh( p p wf )
p
6 months using the following data: q ¼ : (7:2)
1 4A
141:2B o m o 2 ln gC A r 2 þ S
w
The driving mechanism above the bubble-point pressure
Reservoir porosity (f): 0.2 is essentially the oil expansion because oil is slightly
Effective horizontal 10 md compressible. The isothermal compressibility is defined as
permeability (k): 1 @V
Pay zone thickness (h): 50 ft c ¼ , (7:3)
Reservoir pressure ( p i ): 5,500 psia V @p
Oil formation volume 1.2 rb/stb where V is the volume of reservoir fluid and p is pressure.
factor (B o ): The isothermal compressibility c is small and essentially
Total reservoir 0.000013 psi 1 constant for a given oil reservoir. The value of c can be
compressibility (c t ): measured experimentally. By separating variables, integra-
Wellbore radius (r w ): 0.328 ft tion of Eq. (7.3) from the initial reservoir pressure p i to the
Skin factor (S ): 0 current average-reservoir pressure p results in
p
Well depth (H): 10,000 ft
Tubing inner diameter (d ): 2.441 V c(p i p) p
Oil gravity (API): 30 API ¼ e , (7:4)
V i