Modeling of the heel-toe effect in a horizontal well with inflow control devices

Khafiz Muradov, Vasily Mihailovich Birchenko, David Roland Davies

Research output: Contribution to conferencePaper

Abstract

The specific inflow rate of a horizontal well normally varies along the well's completion length due to either frictional pressure losses in the well (heel-toe effect) or variation in the well’s specific productivity index and pressure support. Downhole Inflow Control Devices (ICDs) capable of exerting an additional, rate-dependant restriction along the completion can reduce such inflow imbalances. This paper discusses a new method to quantify the pressure losses and inflow distribution along a horizontal well equipped with ICDs producing oil from a homogeneous formation. A new equation with the form of a second order, non-linear Ordinary Differential Equation is derived to describe such a well. Our analysis of the equation provides both a precise numerical solution and an asymptotic solution. Practical engineering requires a compromise between the severity of the heel-toe effect and the reduction in the overall well performance. Hence, we have proposed a dimensionless criterion for estimating the optimal ICD type. Its application is illustrated by a real oil field-based example. Our new model is one of a few attempts to describe the performance and pressure distribution of an advanced (ICD equipped) well. It brings physical understanding of the well’s performance instead of treating it as a black box simulator. The asymptotic analytical solution gives a set of simple equations for the optimal ICD design of horizontal wells with strong heel-toe effects which can be implemented as a simple design sheet for the well completion engineer. The mathematical approach can be further extended to wells with advanced completion, such as those equipped with the groups of inflow devices or Interval Control Valves.
Original languageEnglish
Pages1-13
Number of pages13
Publication statusPublished - Sep 2010
Event12th European Conference on the Mathematics of Oil Recovery 2010 - Oxford, United Kingdom
Duration: 6 Sep 20109 Sep 2010

Conference

Conference12th European Conference on the Mathematics of Oil Recovery 2010
Abbreviated titleECMOR XII
CountryUnited Kingdom
CityOxford
Period6/09/109/09/10

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Horizontal wells
Well completion
Oil fields
Ordinary differential equations
Pressure distribution
Simulators
Productivity
Engineers

Cite this

Muradov, K., Birchenko, V. M., & Davies, D. R. (2010). Modeling of the heel-toe effect in a horizontal well with inflow control devices. 1-13. Paper presented at 12th European Conference on the Mathematics of Oil Recovery 2010, Oxford, United Kingdom.
Muradov, Khafiz ; Birchenko, Vasily Mihailovich ; Davies, David Roland. / Modeling of the heel-toe effect in a horizontal well with inflow control devices. Paper presented at 12th European Conference on the Mathematics of Oil Recovery 2010, Oxford, United Kingdom.13 p.
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Muradov, K, Birchenko, VM & Davies, DR 2010, 'Modeling of the heel-toe effect in a horizontal well with inflow control devices', Paper presented at 12th European Conference on the Mathematics of Oil Recovery 2010, Oxford, United Kingdom, 6/09/10 - 9/09/10 pp. 1-13.

Modeling of the heel-toe effect in a horizontal well with inflow control devices. / Muradov, Khafiz; Birchenko, Vasily Mihailovich; Davies, David Roland.

2010. 1-13 Paper presented at 12th European Conference on the Mathematics of Oil Recovery 2010, Oxford, United Kingdom.

Research output: Contribution to conferencePaper

TY - CONF

T1 - Modeling of the heel-toe effect in a horizontal well with inflow control devices

AU - Muradov, Khafiz

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AU - Davies, David Roland

N1 - Paper no.B043

PY - 2010/9

Y1 - 2010/9

N2 - The specific inflow rate of a horizontal well normally varies along the well's completion length due to either frictional pressure losses in the well (heel-toe effect) or variation in the well’s specific productivity index and pressure support. Downhole Inflow Control Devices (ICDs) capable of exerting an additional, rate-dependant restriction along the completion can reduce such inflow imbalances. This paper discusses a new method to quantify the pressure losses and inflow distribution along a horizontal well equipped with ICDs producing oil from a homogeneous formation. A new equation with the form of a second order, non-linear Ordinary Differential Equation is derived to describe such a well. Our analysis of the equation provides both a precise numerical solution and an asymptotic solution. Practical engineering requires a compromise between the severity of the heel-toe effect and the reduction in the overall well performance. Hence, we have proposed a dimensionless criterion for estimating the optimal ICD type. Its application is illustrated by a real oil field-based example. Our new model is one of a few attempts to describe the performance and pressure distribution of an advanced (ICD equipped) well. It brings physical understanding of the well’s performance instead of treating it as a black box simulator. The asymptotic analytical solution gives a set of simple equations for the optimal ICD design of horizontal wells with strong heel-toe effects which can be implemented as a simple design sheet for the well completion engineer. The mathematical approach can be further extended to wells with advanced completion, such as those equipped with the groups of inflow devices or Interval Control Valves.

AB - The specific inflow rate of a horizontal well normally varies along the well's completion length due to either frictional pressure losses in the well (heel-toe effect) or variation in the well’s specific productivity index and pressure support. Downhole Inflow Control Devices (ICDs) capable of exerting an additional, rate-dependant restriction along the completion can reduce such inflow imbalances. This paper discusses a new method to quantify the pressure losses and inflow distribution along a horizontal well equipped with ICDs producing oil from a homogeneous formation. A new equation with the form of a second order, non-linear Ordinary Differential Equation is derived to describe such a well. Our analysis of the equation provides both a precise numerical solution and an asymptotic solution. Practical engineering requires a compromise between the severity of the heel-toe effect and the reduction in the overall well performance. Hence, we have proposed a dimensionless criterion for estimating the optimal ICD type. Its application is illustrated by a real oil field-based example. Our new model is one of a few attempts to describe the performance and pressure distribution of an advanced (ICD equipped) well. It brings physical understanding of the well’s performance instead of treating it as a black box simulator. The asymptotic analytical solution gives a set of simple equations for the optimal ICD design of horizontal wells with strong heel-toe effects which can be implemented as a simple design sheet for the well completion engineer. The mathematical approach can be further extended to wells with advanced completion, such as those equipped with the groups of inflow devices or Interval Control Valves.

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Muradov K, Birchenko VM, Davies DR. Modeling of the heel-toe effect in a horizontal well with inflow control devices. 2010. Paper presented at 12th European Conference on the Mathematics of Oil Recovery 2010, Oxford, United Kingdom.