89 ENT®RNOS

WELL FRESSURE BEHAVIOR FOR A VERTICAL

WELL IN A GAS CONDENSATE NATURALLY FRACTURED RESERVOIR

Freddy Humberto Escobar', Humberto García Rocha², luán Mauricio Suaza³, and José Humberto Cantillo⁴

' Universidad Surcolombiana, e-mail: fescobar@usco.edu.co

² Universidad Surcolombiana, e mail: kinino11@hotmail.com ' Universidad Surcolombiana, e-mail: suaza82@yahoo.es

* Ecopetrol S.A. - ICP, e-mail: jose.cantillo@usco.edu.co

Keywords Capillary number, interfacial tensión, relative permeability, ¡nterporosity flow parameter, storativity coefficient, condénsate saturation

Abstract

The complex behavior exhibited by gas condénsate reservoirs due to the existence of a two-phase system: reservoir gas and liquid condénsate and its implications plus the nature of heterogeneities ¡s the subject of the present article which involves handling of reservoir engineering concepts subject to be ¡nterpreted, so that by coupling them with pressure transient analysis using a compositional simulator, we can obtain some patterns which lead to facilítate the understanding of the reservoir's dynamics.

Great volumes of fluids are stored in Naturally Fractured Reservoirs (I\JFR). Simulation of this type of deposits presents great challenges, from not only the geomechanical point of view but also the thermodynamical modeling of the different phases flowing throughout the fracture system.

In this work, we present an attempt to model a gas condénsate formation involving the implications of relative permeabilities to observe their effect on the flow behavior once pressure finally falls below the dewpoint and the effect of the capillary number on the fluid flow phenomena in the near-wellbore región. Interpretation of the pressure test is conducted by the TDS technique.

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Introduction

Gas condénsate reservoirs are truly important to the oil ¡ndustry because of the quality of the recovered oil, and then, its pnce. Barrios et al. (2003), Bnegherbia and Tiab (2002), Fevang and Singh (2000) and Gringarten et al. (2000) have made good contributions to simulation and well test analysis of gas condénsate systems. An inadequate exploitation of these reservoirs cause condénsate formation in the near-wellbore región when the pressure falls below the dewpoint valué which leads to a sharp productivity reduction since the condénsate also reduces relative gas permeability. Retrograde condensation has also an associated problem: the precipitation of the heavier compounds becomes the mixture poorer in these compounds causing a variation of fluid composition and a change in flow parameters. These effects increase the complexity of gas condénsate well test interpretation. Additionally, the fractured nature of the reservoir contributes to reservoir characterization and forecasting to be a challenging milestone to the oil industry. Dealing with these systems requires representative reservoir model construction to accurately handle fracture-matrix systems and their interaction. In this work we extended the work of Muñoz et al. (2006) to naturally fractured occurringformations.

Modeling

To perform the simulation experiments Suaza and García (2006) employed a compositional commercial Simulator to study the behavior of a vertical gas condénsate well producing at constant rate in the center of a circular naturally fractured reservoir which main input data are given in table 1. A logarithmic radial grid with 100 cells ¡n the i-direction was used to better capture the local details around the well. After a sensitivity análisis, we found that 16 layers ¡n the j-direction was enough for an adequate reservoir-fluid description. Several scenarios were studied with different valúes of gas rate, capillary number, storativity coefficient and ¡nterporosity flow parameters. In all the cases, initial reservoir pressure was set higher than the dewpoint pressure to ensure monophasic flow in región III.

We used a mixture of 14 compounds as reported by Fevang and Singh (2000) and the three-parameter Peng and Robinson equation of state to simúlate phase behavior.

Corey's correlation including their dependence with not only fluid saturation but also capillary number were used. To match the experimental data the end-point relative permeabilities and the exponents n„ and n_uare employed:

\ⁿ«

k.,. = iC,

V'.:

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The commercial Simulator has the following three models for estimation of the capillary number:

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,yt=> - ^kk'v^AP¡ ' " o L

í,= 0.012

(6)

= 0.15866] ⁰ * ^AP’^)m^ 1 + 0.54653 j^(/* ^AP -^1 (7) [ (t*AP\ ) \ (t*AP\ j ' '

(8)

(9)

k/h,rt *

+ 7.43

(10)

-ln

^,S 2

kjha& i

(<k ),pc

+ 7.43

-In

(11)

^S 2

Simulation Results

Effect of Gas Flow Rate

Gas condénsate saturation for five different gas flow rates was determined and reported ¡n Fig. 1. As the gas rate increases, the dewpoint pressure shows up earlier since the pressure drop is accelerated, in other words, as the flow rate increases the size of región III decreases. Notice the existence of a higher condénsate saturation in the fracture than in the matrix.

Fig. 2 presents the behavior of pressure and pressure derivative for different flow rates. As flow rate increases both curves are shifted upwards since skin factor increases due to the increment of non-Darcy effects ("turbulence"). Curves for gas rate of 13000 Mscf/d presents a better behavior than the one for 14000 Mscf/d where skin is higher. It is observed that as the rate increases the biphasic zone shows up earlier because the dewpoint pressure is reached faster.

Effect of Capillary Number

For this effect, we take into account (1) the effect of condénsate flow and (2) the estimation of the naturally fracture reservoir parameters by using the TDS technique, Engler an Tiab (1996).

Effect of condénsate flow

The well pressure behavior with and without considering capillary number effects is given in Fig. 3. The reader can observe a favorable effect added by the capillary number since a lower pressure drop is registered, and therefore, there will be a lower condénsate saturation. Also, the pressure trend is smoother since well damage is smaller. From 100 hrs the pressure difference between the two curves is practically constant and about 130 psi.

Fig. 4 presents the saturation profile with and without capillary number effects for the same dewpoint pressure. It was concluded that the Nc contributes to a condénsate saturation reduction around the well and reservoir. We observe in Fig. 4 that the condénsate saturation in the matrix suffers revaporization due to the fluid depletion inside the fracture, and then, this is restored from the matrix.

Fig. 5 shows the gas relative permeability, k,₉, curve whether or not capillary number effects are included. A máximum valué, k,₉ = 1, corresponds to the monophasic flow zone (región III) with a length of 1863.2 ft which indicates that the dewpoint pressure is located to 136.8 ft from the well. The capillary number effect increases the gas relative permeability around the well and the reservoir. k,₈ is greater in the matrix than the fracture since fluid movements are restricted by the space.

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The behavior of pressure and pressure derivative including or not capillary number effects is reported in Fig. 6. Only one phase is present during the first radial flow regime and during the matrix-fracture transition dominated period. Once the second radial flow develops the condénsate has reached its critical valué and begins flowing simultaneously with gas. This phenomenon is more evident when capillary effects are excluded since condénsate mobility increases.

Fig. 7 presents the pressure behavior for different Nc's. The lower Nc the higher the reservoir's depletion.

Fig. 8 and 9 indícate that as the capillary number increases, condénsate saturation reduces due to the reduction of interfacial tensión. It causes an increment of the gas relative permeability.

Estimation of Naturally fractured reservoir parameters Synthetic data reported in Fig. 6 were simulated with the following reservoir and fluid information:

q = 1764 B r_w = 0.25 ft c, = 1x10'^J

( = 0.1808 cp h„ = 90 ft í_m = 0.188

B = 2.04 bbl/STB h, = 10ft

Considering Nc effects and applying TDS technique, Engler and Tiab (1996):

7Q.6(/n B h(t*AP')_r2

Where:

<j> =

42.5/;c, (t*'AP { I

l*AP'

t*AP')_rl

:nt©rnos

From Fig. 6, read (t* P'),, = {t* P% =12.11 psi, t„„ = 1,49 hrs, (t* P')„,= 2.95 psi,t_i;

= 0 007 hrs, P_rl = 129.3 psi, t,, = 35.6 hrs, P_r;, - 200.4 psi. kfb.t ⁼ 37.9 md, = 0.071 and, - 2.48x10'were obtained, respeciívely, using Eqs. 6 through 9. Using Eqs. 10 and 11, skin factors of -0.49 and 0 49 were calculated, respectively, from the first and second radial flow regimes.

Consi dering Nceffects valúes oflt’P¹),, = 12.84 psí and (t*?¹),, = 54 psi were read and Eq. 6 !ed to estimations of k_h, = 35.7 and B.5 md, respectively. Other parameters obtained from the pressure and pressure derivative plot of Fig, 6 are t,, = 0,007 hrs, P„ = 129.3 psi, t„_w = 1.44 hr, and = 3,14 psi, = 35.6 hrs, P_t; = 232.4 psi. -■ 0.071 and 0.011 were estimated from the first and second radial flow, respectively, by using Eq.

7. Eq. 8 allowed an estimation of = 2.73x10^; only for the first radial flow. For the second radial flow the condénsate rate is unknown then Eq. 8 does not apply here. From the application of Eq. 10, a skin factor oí -0 7G was estimated. Notice that skin factorfrom the second radial ftow should not be estimated from Eq. 11 since neither condénsate viscosity nor condénsate flow rate are known. All we can say is that a sharp reduction in flow capacity is virtuaily seen for the increase in both the pressure derivative and the pressure drop valué.

Observa in table 2 that the valúes obtained from the TDS technique agree well with the input ones. Notice how the naturally fractured reservoir parameters and permeabiíity are affected when Nc effeets are excluded.

Varíation of and

Fig. 10 was generated for 0.02 0.2 when Nc effecí are considered. There, we can appreciate that as increases, it is easier to see the early radial flow regime. This causes a reduction of the transition zone until it fully disappears as approaches the unity It ¡s difficult to see the condénsate formation since it takes place at the end of second radial flow regime atabout 30 hrs.

In Fig. 11 we observe the behaviorof the pressure derivative for 3E-6 5E-7, The smallerthe value_F the longer the eariy radial flow line. Condénsate formation occurs at the end of the transition dominated flow for = 5E-7, 7E-7 and 1E-6, and it takes ptace during the second radial flow period for valúes of 2E-6 and 3E-6, at about 20 hrs, Unrier Nc effeets it is difficult to distinguish the single phase and two phase zones.

Conclusions

1. Liquid formation in gas condénsate naturally fractured condénsate occurs in more quantity in the fracture -because of the higher pressure drop- tlian in the matrix. Consíderíng the Nc effeets a significant reduction in condensare saturation will occur with a consequent incrementof gas relative permeabiíity.

2. The higher the capillary number, the lower the condensare saturation and the higher the gas relative permeabiíity due to a reduction of interfacial tensión which impiies a better preferenca for gas flow in the reservoir. Condénsate formation is so smali that it is not rellected in the pressure derivative curve. Also, pressure drop is positively affected since it is lower than the case of exefuding capillary number effeets.

3. TDS technique was usedto estímate reservoir parameters. We found that the capillary number effeets alter the estimation of the naturally fractured reservoir parameters and the estimation of effective permeabiíity and skin factor because an extra pressure drop and an increase in the pressure derivative curve take place. Estimation of these parameters, although possible, should not be performed because condénsate rate and viscosity change.

Acknowfedgments

The authors gratefully acknowledge the financial support of the Colombian Petroleum Institute, ICR under the mutual agreement Number 008 signed between this institution and Universidad Surcolombiana.

Nomenclatura

B Oil VüJumetric factor

í'r Total compressibility, psi"¹

h Thicktiess, ft

»£ Corey’s exponen! for the gas phase

«o Corey’s exponent for the oil phase

k Permeabiíity, md

kjb_a Condénsate effective permeabiíity in the fracture bula system, md

End-point relative perrncítbilities krjy Relative permeabiíity tnodified by N_í:j of the j* phase in the flow direction

at a previous time level L ürid length in the flow dircelion, ñ

P Pressure, psi

q Condénsate rate, BPD

<ias flow rate, MMscf/d S Saturation

Sj Normalized phase saturation

s	Skin tactor
S_gr	Residual gas saturation
	Residual oil saturation
t	Tune
t*AP’	Pressure derivative, psi
V	Velocity, IVscc
M	Warren and Root’s storativity coeffieient
X	Warren and Root’s interporosity flow parameter

:iMT®RIMOS ⁹²

Greek

A	Change, drop
AP}	Pressure drop of the j^lh phase in the flow dircction, psi
<t>	Porosity
	Viscosity, cp
o	Oil-gas interfacial tensión, dyne/cm

Suffixes

f	Ffacture
fb	Fracture bulk
R	Gas
m	Matrix
min	Minimum
0	Oil
r	Radial, Residual
rl	First radial flow
i-2	Second radial flow
t	Total
w	Well

References

BARRIOS, K„ STEWART, G. and DAVIES, D„ 2003. "A Novel Methodology for the Analysis of Well Test Responses in Gas Condénsate Reservoirs”, paper SPE 81039 presented atthe SPE Latín American and Caribbean Petroleum Engineering Conference held in Port of Spain, Trinidad, West Indies, 27-30 April, 2003.

BENGHERBIA, M. and TIAB, D„ 2002. "Gas-Condensate Well Performance Using Compositional Simulator''. SPE 75531 Presented at the SPE Gas Technology Symposium held ¡n Calgary, Alberta, Cañada, 30 April-2 May, 2002.

ENGLER, T. and TIAB, D., 1996. "Analysis of Pressure and Pressure Derivative withoutType Curve Matching, 4. Naturally Fractured Reservoirs". Journal of Petroleum Science and Engineering 15(1996) p. 127-138.

FEVANG, 0 and SINGH, K., 2000. "Guidelines for Choosing Compositional and Black-Oil Models for Volatile Oil and Gas-Condensate Reservoirs" Paper SPE 63087 Presented at the 2000 SPE Annual Technical Conference and Exhibition held in Dallas, Texas, 1-4 October 2000.

GRINGARTEN, A.C., AL-LAMKI, A., DAUNGKAEW, S„ 2000. "Well Test Analysis in Gas-Condensate Reservoirs", paper SPE 62920 presented at the 2000 SPE Annual Technical Conference and Exhibition held in Dallas, Texas, 1 -4, Oct.. 2000.

KOOL, H„ AZARI, M„ SPE, SOLIMAN, M.Y., PROETT, M.A., IRANI, C.A., and DYBDAHL, B„ 2001. "Testing of Gas Condénsate Reservoirs — Sampling, Test Design and Analysis" SPE 68668 Presented at the SPE Asia Pacific Oil and Gas Conference and Exhibition held in Jakarta, Indonesia, 17-19 April 2001.

SUAZA, I.M. and GARCIA, H„ 2006. "Análisis Del Comportamiento de la Presión y Derivada de Presión para un Pozo Vertical en Yacimientos Naturalmente Fracturados de Gas Condensado". B.S.Thesis. Universidad Surcolombiana.

MUÑOZ, O.F., ESCOBAR, F.H., AVILEZ, H.F., SEPULVEDA, J.A, and CANTILLO, J.H., 2006. "Effect of Non-Darcy Flow and Capillary Number on Well Tests of Gas Condénsate Reservoirs". Paper SPE 100818 prepared for presentaron at the 2006 SPE Asia Pacific Oil & Gas Conference and Exhibition held in Adelaide, Australia, 11-13 September 2006.

Table 1. Input data used ¡n the simulation

Parameter	Valué
Reservoir thickness, ft	100
Reservoir radius, ft	2000
Reservoir depth, ft	15000
Matrix Permeability, md	0.00048
Fracture Permeability, md	30
Matriz porosity, %	18.8
Fracture porosity, %	1.2
Reservoir inicial pressure pressure, psi	5300
Wellbore radius, ft	0.25
Reservoir Temperatura, °F	320

Table 2. Comparison of results

PARAMETER	INPUT VALUES	Includiii" Nc		Excludiim Nc
PARAMETER	INPUT VALUES	From r' radial flow	From 2^nd radial flow	From l^s< radial flow	From 2^n<l radial flow
k/i„ md	30	37.9		35.7	N.C.
to	0.06	0.071		0.071	0.011
X	7x10'⁷	2.48x10'⁷		2.73x10'⁷	N.C.
s	0	-0.49	-0.49	-0.76	N.C.