prediction of critical drawdown pressure for prevention of ...€¦ · existing sand-production...

Prediction of Critical Drawdown Pressure for Prevention of Sand Production in an Oil Well 53

Nigerian Journal of Engineering Science Research (NIJESR). 1(1): 53-64 Copyright@ Department of Mechanical Engineering, Gen. Abdusalami Abubakar College of Engineering, Igbinedion University, Okada, Edo State, Nigeria. ISSN: 2636-7114 Journal Homepage: http://nijesr.iuokada.edu.ng

Prediction of Critical Drawdown Pressure for Prevention of Sand Production in an Oil Well

*1Adingwupu, A.C., 2Oluwafemi, J.,

3Erameh, A.A.,

4Emifoniye, E.U.

1Department of Mechanical Engineering, Igbinedion University, Okada, Nigeria

([email protected]) 2Department of Mechanical Engineering, University of Lagos, Akoka, Nigeria

([email protected]) 3Department of Mechanical Engineering, Igbinedion University, Okada, Nigeria

([email protected]) 4Department of Mechanical Engineering, Igbinedion University, Okada, Nigeria

([email protected])

*Corresponding author: Adingwupu, A.C., [email protected] (+2348035043583)

Key words: Fluidized sand, Porosity, Finite volume, Volumetric flux.

Nomenclature

∇p Pressure gradient C Fluidized solid Concentration Porosity Volumetric flux Mass flow rate t Time Density of the fluidized sand Effective Permeability P Pressure I x- directions and y-direction kinematic viscosity

INTRODUCTION

Sand production is a costly and inevitable phenomenon that occurs whenever the forces on sand particles, induced by fluid flow and/or solution-gas drive, are greater than the strength of the formation so as to lead to the loss of its mechanical integrity. The formation material collapses locally, and the sand fragments are carried into the wellbore where they can block the flow, damage pumps and pipes, and contaminate the produced oil. Sand production creates cavities in the formation that continually

Manuscript History

Received: 07-07-2018

Revised: 12-19-2018

Accepted: 12-23-2018

Published: 12-27-2018

Abstract: This article presents a two dimensional finite volume model for sand production in an oil well for effective reservoir management using a staggered grid formulation for the evolution of controlling field variables such as porosity, fluidized sand concentration and pressure. The model was applied to IHI 10 oil field to determine the field variables applying the field drawdown pressure in the well. From the plot of sand production against drawdown pressure as adopted from the Oando IHI10 well experimental data, it could be seen that sanding occurred from drawdown pressure of 958Psi, which corresponds to the drawdown pressure at which the fluidized solid concentration from the present model became very much pronounced in the oil flow. Hence the present model can be applied to study sand production in oil wells.

Adingwupu et al., (2018). Prediction of Critical Drawdown Pressure for Prevention of Sand Production in an Oil Well. Nigeria Journal of Engineering Science Research. 1(1): 53-64

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increase in size and eventually become unstable, leading to the collapse of the wellbore as presented in (Hossein et al., 2013). Each year, sanding problems cost the oil industry hundreds of millions of dollars. Hence, it is pertinent to study the mechanics of sand fluidization and develop an efficient computational model that can be used to predict sand production during field operations. Sand production in oil and gas wells can occur if fluid flow exceeds a certain threshold governed by factors such as consistency of the reservoir rock, stress state and the type of completion used around the well. Willson et al., (2002) stated that the amount of solids can be less than a few grams per cubic meter of reservoir fluid, posing only minor problems or a substantial amount over a short period of time, resulting in erosion and in some cases filling and blocking of the wellbore. Prediction of sand production from a formation during fluid recovery (for example, hydrocarbons) is important in evaluating the necessity of sand control in an unconsolidated or poorly-consolidated formation. Such predictions also assist in selecting a particular sand control technique. Two fundamental processes together lead to sand production as presented by Kooijman et al. (1992): (1) rock failure through which cement bonds between grains in a formation are broken and disjoint grains are generated and (2) transport of these disjoint grains by a fluid from the formation into a borehole. Most existing sand-production prediction models concentrate on determining sand production due to rock failure and therefore can only determine the conditions for the onset of sand production. A significant proportion of the world oil and gas reserves is contained in weakly consolidated sandstone reservoirs and hence is prone to sand production as presented by Adeyanjua et al. (2011). Material degradation is a key process leading to sanding. Drilling operations, cyclic effects of shut-in and start-up, operational conditions, reservoir pressure depletion, and strength-weakening effect of water may gradually lead to sandstone degradation around the perforations and boreholes. High pressure gradient due to fluid flow also facilitates the detachment of sand particles. In addition, fluid flow is responsible for the transport and production of cohesionless sand particles or detached sand clumps to the wellbore. Sand production is the cause of many problems in the oil industry and it affects the completion adversely. These problems include, but are not limited to, plugging the perforations or production liner, wellbore instability, failure of sand control completions, collapse of some sections of a horizontal well in unconsolidated formations, environmental effects, additional cost of remedial and clean-up operations, and pipelines and surface facilities erosion as presented by Papamichos and Cerasi (2010), in case the sand gets out of the well. The mechanical prevention of sanding is costly and leads to low productivity/injectivity. Therefore, there is always a cost benefit if sand management and modelling is implemented. In the past decades, a number of approaches have been developed to predict the sand production. In general, these approaches can be categorized into three basic groups: 1) empirical methods, 2) laboratory evaluation, and 3) theoretical modelling including analytical and numerical methods. Empirical methods are quite simple and usually based on the field observations. The correlations between sand production and field data such as log data could be established in the works of Antheunis et al. (1976) and Veeken et al. (1994). Sand production laboratory experiments have been conducted since 1930’s according to Terzaghi, (1936). Bratli and Risnes, (1981) carried out tests on loose sands to study the effect of arching around a cavity. Later on, it was observed that even consolidated reservoirs may experience problems due to sand production. Since then, efforts have been made to simulate and study this phenomenon in laboratories. Jaeger et al. (2007) stated that different types of shear failures may occur around an opening depending on the relative magnitudes of three far-field principal stress components. Hence an appropriate laboratory sanding simulation should be the one which includes the effect of three independent stress components. In practice, this is only possible if the experiment is conducted on cubic samples. In this approach, the stresses represent three principal far-field stresses and the induced stresses around the borehole are not symmetric. This is a more realistic way to simulate sanding as happens in real situations. Only few attempts have been made so far to conduct sanding experiments on cube samples as presented by Kooijman et al. (1992). Younessi et al. (2012) performed several sanding tests on cubes of synthetically made samples.

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The samples prepared based on an established procedure developed in the laboratory, Samples, with a dimension of 100×100×100mm3, were subjected to far-field stresses while increasing the pore pressure inside the cell. Sands were produced from a borehole in the sample centre. The experiment was conducted with anisotropic lateral stress to investigate the effect of stress anisotropy on sand production. By applying uniform lateral stresses, an experiment analogy to TWC was performed for comparison purposes. Comparison of the results of these two experiments demonstrated the importance of considering the intermediate stress component in sanding analysis. There exist many different types of models for predicting sand production. Morital et al. (1989), Rodriguez et al. (1996), Osorio et al. (1997), Li et al. (1990) and Settari, and Mourits, (1998) presented some of these sand prediction models. Although most of these would predict the transient and catastrophic types of sand production rate, some models attempt to predict the rate and quantity of solids that would be produced with the liquids in a continuous mode. The approaches used by these models by quantifying volumetric sand production may be classified into strain-based, erosion-based, and particle-based models as stated by Wan and Wang (2001). In this project, a two dimensional finite volume model of sand production in an oil well will be developed to predict volumetric sand production for effective reservoir management.

MATERIALS AND METHODS

VOLUMETRIC SAND PRODUCTION MODELING Fig. 1 illustrates the mechanics of sand production around a wellbore with sand grains being dislodged from the oil sand matrix. From a mechanistic point of view, sand production emerges as a result of an instability occurring in a viscous fluid saturated porous medium that undergoes mechanical deformation in the presence of fluid fluxes. This condition can be described within a three-phase system as stated in Adeyanju and Oyekunle (2010) in which are solid (s), fluid (f), and fluidized solid (fs) interaction. Despite the non-homogeneous structure of the porous medium, it is still possible to invoke a continuum theory of mixtures such that all three phases are simultaneously present everywhere to occupy a chosen representative elementary volume (REV), as shown in Fig. 1. Biot (1941) stated that a mathematical description is required to define the physical processes characterized above. The following development is patterned after the work of Vardoulakis et al. (1996), Wan and Wang (2000), Biot (1941).

Fig.1 Continuum Representation of Sand Production near Wellbore (Adeyanju and Oyekunle, 2010)

The following assumptions were made for the formulation of the governing equation: Solid skeleton is deformable and described within infinitesimal strain theory

i. Fluidized particles are particles in suspension that move together with fluid ii. The densities of both solid and fluidized solid phases are equal and constant, = iii. Fluid is incompressible so that its density (ρ) is constant iv. At any instant, both fluid and fluidized particles have the same velocity

MASS BALANCE Mass balance is written for each phase in terms of every parameter and state variable related to it. For the solid phase, mass balance requires that a change in solid porosity with time equal to mass generation during an erosional process as presented by Vardoulakis et al. (1996), Wan and Wang (2000).

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Thus, for the solid phase;

(1)

For the fluid phase [( )]

[( )]

(2)

For the fluidized solid phase, solid particles generated from sand erosion enter into the fluid phase and become fluidized solid moving at the same velocity as the fluid phase. Mass balance requires that,

(3)

Adding equations (2) and (3), we get

(4)

Furthermore, subtracting equation (1) from (4) leads to the continuity equation for the mixture, i.e.

(5)

Equations (1), (2), and (5) constitute the set of mass balance equations with five unknowns, namely; c, , and to be determined. We need two more equations to make the solution of the problem determinate. These will be obtained from constitutive laws describing fluid flow and mass generation.

CONSTITUTIVE LAW FOR FLUID FLOW Due to the complexity of flow in porous media, a semi-empirical Darcy’s law is used rather than the equations of fluid momentum balance. Darcy’s law establishes the relation between pressure gradient and specific discharge as shown in Ataie-Ashtiani et al. (2010) or volumetric flux. Thus,

∇ (6)

The effective permeability can be related to porosity via the Kozeny-Carman equation, i.e,

( ) (7)

Equation (7) describes the dependence of permeability in terms of changing porosity in the eroded region. Furthermore, the viscosity of the fluidized sand and fluid phases can be related to the kinematic viscosity η of the fluid using averaging of the mixture of phases as in Bear (1979), i.e. ( ) (8)

( ) ( ) (9)

CONSTITUTIVE LAW FOR MASS GENERATION Another equation is needed for describing sand erosion, which can be assumed to be driven by the discharge of fluidized particles. Furthermore, it is clear that the erosion rate is higher initially in intact regions where porosity is small. However, the erosional process is more lasting due to the sand matrix being strong as found in Wan and Wang (2000). This suggests that the functional form of mass generation can be generally written as

( ) √ (10)

Where, λ, having the dimension of inverse of length has to be determined experimentally. By combining the mass balance, and the constitutive laws for fluid and sand erosion equations, we finally arrive at the following equations. Expanding equation (2) we have that

(11)

From equation (5), equation (10) reduces to,

(12)

From Equations (9) and Equation (1), we get

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( ) √ (13)

From Equations (6), (7) and (8), we have

( ) ∇ (14)

Where is a constant for each direction i. For a 2 dimensional system, equations (5), (12), (13) and (14) can be rewritten as

(15)

(16)

( ) √

(17)

where,

( )

(18)

( )

(19)

Substituting Equation (18) and Equation (19) into Equation (15)-(17) gives the two dimensional set of equation for a volumetric sand production model.

(20)

(21)

(

)

( ) [(

)

(

)

] (22)

where,

( ) (23)

The field parameters to be determine from these three sets of governing equations are the fluid pressure the Fluidized solid concentration and the porosity

NUMERICAL SOLUTION USING FINITE VOLUME METHOD From Equation (21), we have

Integrating over the control volume

∫ ∫

( )

∫ ∫

∫ ∫

∫ ∫

(24)

Assuming equal area in all faces, dx=dy we have for each term,

∫ ∫

( )

( ) (

) (25)

∫ ∫

(

) (26)

∫ ∫

∫ [

( ) ( )( )]

(27)

∫ ∫

∫ [

( ) ( )( )]

(28)

For fully implicit scheme, evaluating quantities in the new time step, the equation above can be combined to give

( ) (

) (

)

( ) ( )( )

( ) ( )(

) (29)

The final equation can be written as;

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(30)

where,

(

)

(31)

( ) ( ) (32)

( ) ( ) (33)

( ) ( ) (34)

( ) ( ) (35)

(36)

(

) (37)

From Equation (21),

(38)

∫ (

)

∫ (

)

(39)

This gives,

(

) (

) (

) (

) (40)

( )

( )

( )

( )

(41)

(42)

Substituting the SIMPLE algorithm in Equation (42) into Equation (41),

( )

( )

( )

( )

(43)

Rearranging we have,

(44)

where, ( ) ( ) ( ) ( ) (45)

( )

(46)

( )

(47)

( )

(48)

( )

(49)

( )

( )

( )

( )

(50)

And for the faces are given in Table 1

Table 1 Coefficient for the Faces

Face West East North South

( )

( )

( )

( )

From Equation (21)

(

)

( ) [(

)

(

)

] (51)

where,

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( ) (52)

∫ ∫

(

)

∫ ∫ ( )

(

)

∫ ∫ ( )

(

)

(53)

∫ ∫

(

)

(

) (

) (54)

∫ ∫ ( )

(

)

∫ ( )( )

( )( )

(55)

∫ ∫ ( )

(

)

∫ ( )( )

( )( )

(56)

(

) (

) ( )( )

( )( ) ( )( ) (

)( ) (58)

The final equation can be written as

( ) (59)

where,

( )( ) ( )( ) (60)

( )( ) ( )( ) (61)

(

) (62)

(63)

( )( )

( )( ) (64)

The discretised equation was solved using a C++ code of SIMPLE algorithm applying NISUS discretisation scheme.

RESULTS AND DISCUSSION

Finite volume method was used to predict sand production in an oil well for effective reservoir management. The effect of the controlling field variables, such as porosity, fluidized sand concentration, and pressure were investigated for a wellbore subjected to a fluid drawdown pressure, especially during the pumping of crude oil from the well. The model was applied to IHI 10 oil field in order to determine the field variables applying the drawdown pressure in the well. The porosity, which defines the ratio of the volume of void space to the total volume, was observed to be highest at the oil well region as seen in Fig.14-Fig. 19. Fig. 14 shows the porosity at a drawdown pressure of 346Psi and the maximum porosity at that drawdown pressure was seen to be 0.045. The porosity was observed to increase with increase in drawdown pressure with the maximum 0.08 which correspond to the maximum drawdown pressure of 1319Psi as seen in Fig. 19. The pressure distribution of the computational domain due to the effect of the pressure of the crude oil as it flows up the well can be seen in Fig. 2-Fig. 7. As observed, when the drawdown pressure of oil in the well increases, the pressure around the well region also increase in magnitude from the least drawdown pressure studied, 346Psi in figure 2 to the maximum drawdown pressure of the well as in Fig. 7. The fluidised solid concentration which gives the ratio of the fluidized solid volume to that of void space was also seen to exhibit a similar behaviour for the range of the drawdown pressure of the oil studied. It is the field variable that quantifies the volumetric sand production prediction in the oil well. Our interest is to determine the pressure at which its effect becomes much significant inside the oil well. The maximum occurred at the nearest region around the well as seen in Fig. 8 –Fig.13. Since our interest is on the well, Fig. 8 shows the least drawdown pressure of 346Psi and the maximum fluidised solid concentration in the well is 0.00375386 while the maximum fluidised solid concentration at the maximum drawdown pressure of 1399Psi is 0.00692627. However, at drawdown pressure of 958 Psi, its effect became more significant.The critical drawdown pressure is the pressure at which the onset of sand production occurs, and from the model the critical pressure is 958 Psi because at this pressure, solid fluidized concentration was pronounced in the entire wellbore. Table 2 shows the results of compiled well test report datasets: Mar. 2009 – Jan. 2011 obtained from Oando IHI10 oil well experimental data.

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Table 2 Compiled Well Test Report Datasets: Mar. 2009 – Jan. 2011 obtained from Oando IHI10 oil well Experimental Data

Well Test Date Wellhead Pressure (psi)

BHP (psi) Initial Pore Pressure (psi)

Total Drawdown ∆P

(psi)

Sand Production

(kg/d) 27-Mar-09 1841 3409 3755 346 0 9-May-09 1763 3329 3755 426 0

25-May-09 1740 3300 3755 455 0 8-Jun-09 1682 3307 3755 448 0

17-Jun-09 1629 3239 3755 516 0 3-Sep-09 1689 3321 3755 434 0

20-Sep-09 1655 3290 3755 465 0 5-Oct-09 1647 3256 3755 499 0

29-Oct-09 1612 3248 3755 507 0 21-Dec-09 1592 3230 3755 525 0 23-Jan-10 1535 3193 3755 562 0 28-Mar-10 1620 3268 3755 487 0 18-Apr-10 1237 2797 3755 958 0 27-Jul-10 1056 2553 3755 1202 0

31-Aug-10 1227 2771 3755 984 0.36 7-Sep-10 1218 2761 3755 994 0.19

18-Sep-10 1131 2655 3755 110 0.5 5-Oct-10 1095 2597 3755 1158 20 6-Oct-10 1090 2597 3755 1158 20

16-Oct-10 1066 2548 3755 1207 21.8 27-Oct-10 1012 2491 3755 1264 16.14 5-Nov-10 1003 2477 3755 1278 6.21 6-Nov-10 1001 2477 3755 1278 7.83 8-Nov-10 999 2469 3755 1286 12.9

25-Nov-10 970 2436 3755 1319 12.18 2-Jan-11 911 2356 3755 1399 33.9

Applying the drawdown pressures for the various days under review in the developed model, lead to the following contours for the pressure distribution, porosity and fluidized solid concentration distribution respectively around the borehole section adopted for analysis.

Fig.2 Contour of Pressure Distribution on 27-Mar-09 (drawdown pressure 346Psi)

Fig.3 Contour of Pressure Distribution on 25-May-09 (drawdown pressure 455Psi)

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Fig.4 Contour of pressure distribution on 21-Dec-09 (drawdown pressure 525Psi

Fig.5 Contour of pressure distribution on 18-Apr-10 (drawdown pressure 958Psi

Fig.6 Contour of pressure distribution on 7-Sep-10 (drawdown pressure 994Psi

Fig.7 Contour of pressure distribution on 2-Jan-11 (drawdown pressure 1399Psi

Fig.8 Contour of fluidised solid concentration on 27-Mar-09 (drawdown pressure 346Psi

Fig.9 Contour of fluidised solid concentration on 25- May-09 (drawdown pressure 455Psi)

Fig.10 Contour of fluidised solid concentration on 21-Dec-09 (drawdown pressure 525Psi

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Fig.11 Contour of fluidised solid concentration on 18-Apr-10 (drawdown pressure 958Psi


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Fig.12 Contour of fluidised solid concentration on 7-Sep-10 (drawdown pressure 994Psi

Fig.13 Contour of fluidised solid concentration on 2-Jan-11 (drawdown pressure 1399Psi

Fig.14 Contour of porosity distribution on 27-Mar-09 (drawdown pressure 346Psi

Fig.15 Contour of porosity distribution on 25-May-09 (drawdown pressure 455Psi

Fig.16 Contour of porosity distribution on 21-Dec-09 (drawdown pressure 525Psi

Fig.17 Contour of porosity distribution on 18-Apr-10 (drawdown pressure 958Psi

Fig.18 Contour of porosity distribution on 7-Sep-10 (drawdown pressure 994Psi

Fig.19 Contour of porosity distribution on 2-Jan-11 (drawdown pressure 1399Psi

Fig.20. Plot of sand production per day as obtained from the Oando IHI10 well experimental data and

fluidised solid concentration of the wellbore against drawdown pressure

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CONCLUSION The model presented in this article was used to study the fluidised solid concentration and the porosity of IHI 10 oil well production reservoir. It was seen from the results presented that increase in drawdown pressure increased both the porosity and the fluidised solid concentration in the wellbore. From the plot of sand production against drawdown pressure as adopted from the Oando IHI10 well experimental data as well as the maximum fluidised solid concentration of the oil in the well bore, it could be seen from Figure 20 that sanding occurred from drawdown pressure of 958Psi which is very close to the drawdown pressure at which the fluidised solid concentration from the present model (938Psi) became very much pronounced in the oil flow and hence could be regarded as the critical pressure for the operating condition of the IHI 10 well bore.

CONFLICT OF INTEREST There is no conflict of interest associated with this work.

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Papamichos, E.P. Cerasi, J.F. Steneb, T. (2010). Sand production rate under multiphase flow and water breakthrough,‖ in Proceedings of the 44th U.S. Rock Mechanics Symposium and the 5th US/Canada Rock Mechanics Symposium, Salt Lake City, Utah. Vardoulakis, I., Stavropoulou, M., Papanastasiou, P. (1996). Hydro-Mechanical Aspects of Sand Production Problem. Transport in Porous Media. 22: 225-244 Veeceen C.A.M, Wahleiter. J.P., Keedy. C. R. (1994). Experimental modelling of casing deformation in a compacting reservoir. SPE/SRM 28090. In: Proc. Eurock’94. Delft. Netherlands: 497—506. Wan, R.G., Wang, J., (2001) Analysis of sand production in unconsolidated oil sand using a coupled erosional-stress-deformation model. Proceedings of the Canadian International Petroleum Conference 2001, Calgary, Alberta, Canada Willson S. M., Z. A. Moschovidis, J. R (2002).. Cameron, and I. D. Palmer, ―New model for predicting the rate of sand production,‖ in SPE/ISRM Rock Mechanics Conference, Irving, Tex, USA, 152–160 Younessi, A., Rasouli V., Wu B. (2012a), Numerical simulation of sanding under different stress regimes, the 46th US Rock Mechanics / Geomechanics Symposium held in Chicago: 24-27

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