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Summary Use of multilateral wells for oil and gas production has gained strong momentum in the past 5 years. However, most of the multilateral wells do not deliver hydrocarbon fluids at expected production rates. One of the reasons for this is that the well planners overestimate the productivity of wells by using inaccurate methods for predicting composite-inflow-performance relationship (IPR) of well laterals. A more-accurate method for predicting composite IPR of multilateral wells is highly desirable. This paper fills the gap. Starting from terms familiar to petroleum engineers, a general well model was developed with consideration of reservoir-wellbore crossflow for lateral IPR and coupling of fluid flow from individual laterals to the main wellbore. The model allows different IPRs of laterals and permits crossflow between laterals. Pressure losses in the vertical-, curvic- and horizontal-hole sections are rigorously considered. Oil and gas wells are treated differently. The modified Hagedorn-Brown correlation is used for modeling the flow in the vertical sections, and the Beggs and Brill correlation is used for the curvic and horizontal sections for oil wells. The Cullender and Smith method was used for modeling the flow in gas wells. A computer simulator was developed based on the model for predicting multilateral-well production rate. Case studies have indicated excellent accuracy of the computer model. This work provides petroleum engineers a reliable and user-friendly tool for designing and evaluating multilateral wells. Introduction Although oil production by use of multiple-drainholes was reported in the 1960s (Borisov 1964), popular applications of multilateral wells for producing oil and gas began in the early 1990s (Hardman 1993) after modern horizontal drilling technology was developed. Salas, Clifford and Jenkins (1996) identified eight categories of main potential applications of multilateral wells. Vij, Narasaiah, Walia et al. (1998) provided an overview of the multilateral technology and its limitations. Raghavan and Joshi (1993) presented an analytical solution of well productivity for symmetric horizontal radials defined as horizontal drainholes of equal length kicked off from the same depth in symmetrical directions. The result was an inflow equation (i.e., the effect of wellbore flow from sandface to the common kick-off point was not considered). With a semianalytical solution, Retnanto and Economides (1996) demonstrated the benefits of using symmetrical multilateral wells in low- to medium-permeability reservoirs. Again, only lateral-inflow performance was considered. Larsen (2006) presented closed-form expressions of skin factors and productivity indices of radial-symmetric multilateral wells. Wellbore hydraulics was not considered. Salas, Clifford and Jenkins (1996) presented an IPR model for multilateral wells with the total skin factor lumping the effects of reservoir homogeneity and other factors. Wellbore hydraulics was also neglected. Wolfsteiner, Durlofsky and Aziz (2000) developed a general and sophisticated model for productivity of nonconventional wells in heterogeneous reservoirs. Wellbore hydraulics was not included in the model. Yildiz (2002) presented a similar solution that also neglected the effect of wellbore hydraulics. Yildiz (2005) compared his 3D multilateral-well model with data from an electrolytic model and the Salas, Clifford and Jenkin's (1996) model. Good agreements were observed. Smith, Tweedie and Gallivan (1997) addressed the importance of coupling the effects of fluid flow through perforations and wellbore hydraulics in reservoir simulation for multilateral-well economics evaluation. Permadi, Wibowo and Permadi (1998) investigated the effect of wellbore hydraulics on inflow performance of a stacked dual-lateral well, assuming single-phase flow in the wellbore. Ouyang and Aziz (1998) presented a simplified approach to coupling wellbore hydraulics and reservoir inflow for arbitrary well configurations. Chen, Zhu and Hill (2000) presented another model of multilateral-well deliverability by considering segmented horizontal holes and single-phase liquid flow in the horizontal sections of the well. Kamkom and Zhu (2005) applied Vogel's (1968) two-phase flow correlation to multilateral wells. The absolute open flow (AOF) was determined by use of Babu and Odeh's (1989) horizontal-well IPR model. The wellbore hydraulics was modeled with the correlation of Beggs and Brill (1973). Kamkom and Zhu's model is valid for reservoir pressures being lower than the bubblepoint pressure. Although the hydraulics in the horizontal branches was considered numerically, this is the first multilateral-well model that considers hydraulics in all the wellbore sections. Ouyang and Huang (2005) history-matched the oil production from a two-lateral well by coupling reservoir inflow and wellbore hydraulics in a numerical simulator. The paper does not describe how the hydraulics in the horizontal wellbore was simulated. In summary, most of the multilateral-well productivity models were derived on the basis of mathematical analyses of fluid flow in the reservoir side, leaving the flow inside the horizontal- and curvic-wellbore sections as a part of the outflow performance of the well. A few studies have considered the wellbore hydraulics in the horizontal section by assuming single-phase flow. Only one study by Kamkom and Zhu (2005) addressed the wellbore hydraulics in the horizontal and curvic sections. However, in reality, multilaterals are not kicked off at the same point (i.e., kick-off points are separated by several vertical sections). The hydraulics in these vertical sections is expected to have more impact on well productivity than the hydraulics in the horizontal sections. This is because the hydrostatic-pressure components that do not exist in the horizontal sections will reduce well deliverability. No literature has been found to address this issue. A more-accurate model considering hydraulics in all the wellbore sections is highly demanded. In this study, we define the upper-most conjunction as the end of inflow system. We have derived a composite-IPR model by rigorously coupling the wellbore hydraulics inside the well sections (i.e., vertical, curvic and horizontal intervals) and the inflow models of all the laterals (lateral IPR). Because the outflow from the upper-most conjunction is a well-known subject, it is excluded from the scope of this paper although a multiphase-outflow model has been incorporated in our computer program. The composite IPR of both multilateral oil and gas wells were developed in this study. Numerical results of these composite-IPR models were compared with that of field wells, and a very good agreement was observed. This paper provides petroleum engineers with a simple and accurate method for predicting and evaluating performance of multilateral wells.
Summary Use of multilateral wells for oil and gas production has gained strong momentum in the past 5 years. However, most of the multilateral wells do not deliver hydrocarbon fluids at expected production rates. One of the reasons for this is that the well planners overestimate the productivity of wells by using inaccurate methods for predicting composite-inflow-performance relationship (IPR) of well laterals. A more-accurate method for predicting composite IPR of multilateral wells is highly desirable. This paper fills the gap. Starting from terms familiar to petroleum engineers, a general well model was developed with consideration of reservoir-wellbore crossflow for lateral IPR and coupling of fluid flow from individual laterals to the main wellbore. The model allows different IPRs of laterals and permits crossflow between laterals. Pressure losses in the vertical-, curvic- and horizontal-hole sections are rigorously considered. Oil and gas wells are treated differently. The modified Hagedorn-Brown correlation is used for modeling the flow in the vertical sections, and the Beggs and Brill correlation is used for the curvic and horizontal sections for oil wells. The Cullender and Smith method was used for modeling the flow in gas wells. A computer simulator was developed based on the model for predicting multilateral-well production rate. Case studies have indicated excellent accuracy of the computer model. This work provides petroleum engineers a reliable and user-friendly tool for designing and evaluating multilateral wells. Introduction Although oil production by use of multiple-drainholes was reported in the 1960s (Borisov 1964), popular applications of multilateral wells for producing oil and gas began in the early 1990s (Hardman 1993) after modern horizontal drilling technology was developed. Salas, Clifford and Jenkins (1996) identified eight categories of main potential applications of multilateral wells. Vij, Narasaiah, Walia et al. (1998) provided an overview of the multilateral technology and its limitations. Raghavan and Joshi (1993) presented an analytical solution of well productivity for symmetric horizontal radials defined as horizontal drainholes of equal length kicked off from the same depth in symmetrical directions. The result was an inflow equation (i.e., the effect of wellbore flow from sandface to the common kick-off point was not considered). With a semianalytical solution, Retnanto and Economides (1996) demonstrated the benefits of using symmetrical multilateral wells in low- to medium-permeability reservoirs. Again, only lateral-inflow performance was considered. Larsen (2006) presented closed-form expressions of skin factors and productivity indices of radial-symmetric multilateral wells. Wellbore hydraulics was not considered. Salas, Clifford and Jenkins (1996) presented an IPR model for multilateral wells with the total skin factor lumping the effects of reservoir homogeneity and other factors. Wellbore hydraulics was also neglected. Wolfsteiner, Durlofsky and Aziz (2000) developed a general and sophisticated model for productivity of nonconventional wells in heterogeneous reservoirs. Wellbore hydraulics was not included in the model. Yildiz (2002) presented a similar solution that also neglected the effect of wellbore hydraulics. Yildiz (2005) compared his 3D multilateral-well model with data from an electrolytic model and the Salas, Clifford and Jenkin's (1996) model. Good agreements were observed. Smith, Tweedie and Gallivan (1997) addressed the importance of coupling the effects of fluid flow through perforations and wellbore hydraulics in reservoir simulation for multilateral-well economics evaluation. Permadi, Wibowo and Permadi (1998) investigated the effect of wellbore hydraulics on inflow performance of a stacked dual-lateral well, assuming single-phase flow in the wellbore. Ouyang and Aziz (1998) presented a simplified approach to coupling wellbore hydraulics and reservoir inflow for arbitrary well configurations. Chen, Zhu and Hill (2000) presented another model of multilateral-well deliverability by considering segmented horizontal holes and single-phase liquid flow in the horizontal sections of the well. Kamkom and Zhu (2005) applied Vogel's (1968) two-phase flow correlation to multilateral wells. The absolute open flow (AOF) was determined by use of Babu and Odeh's (1989) horizontal-well IPR model. The wellbore hydraulics was modeled with the correlation of Beggs and Brill (1973). Kamkom and Zhu's model is valid for reservoir pressures being lower than the bubblepoint pressure. Although the hydraulics in the horizontal branches was considered numerically, this is the first multilateral-well model that considers hydraulics in all the wellbore sections. Ouyang and Huang (2005) history-matched the oil production from a two-lateral well by coupling reservoir inflow and wellbore hydraulics in a numerical simulator. The paper does not describe how the hydraulics in the horizontal wellbore was simulated. In summary, most of the multilateral-well productivity models were derived on the basis of mathematical analyses of fluid flow in the reservoir side, leaving the flow inside the horizontal- and curvic-wellbore sections as a part of the outflow performance of the well. A few studies have considered the wellbore hydraulics in the horizontal section by assuming single-phase flow. Only one study by Kamkom and Zhu (2005) addressed the wellbore hydraulics in the horizontal and curvic sections. However, in reality, multilaterals are not kicked off at the same point (i.e., kick-off points are separated by several vertical sections). The hydraulics in these vertical sections is expected to have more impact on well productivity than the hydraulics in the horizontal sections. This is because the hydrostatic-pressure components that do not exist in the horizontal sections will reduce well deliverability. No literature has been found to address this issue. A more-accurate model considering hydraulics in all the wellbore sections is highly demanded. In this study, we define the upper-most conjunction as the end of inflow system. We have derived a composite-IPR model by rigorously coupling the wellbore hydraulics inside the well sections (i.e., vertical, curvic and horizontal intervals) and the inflow models of all the laterals (lateral IPR). Because the outflow from the upper-most conjunction is a well-known subject, it is excluded from the scope of this paper although a multiphase-outflow model has been incorporated in our computer program. The composite IPR of both multilateral oil and gas wells were developed in this study. Numerical results of these composite-IPR models were compared with that of field wells, and a very good agreement was observed. This paper provides petroleum engineers with a simple and accurate method for predicting and evaluating performance of multilateral wells.
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