A Semianalytical Model for Calculating Pressure Drop Along Horizontal Wells With Stinger Completions
- J.-D. Jansen (Delft U. of Technology)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- June 2003
- Document Type
- Journal Paper
- 138 - 146
- 2003. Society of Petroleum Engineers
- 2 Well Completion, 2.2.2 Perforating, 3.2.2 Downhole intervention and remediation (including wireline and coiled tubing), 3.3.6 Integrated Modeling, 2.3 Completion Monitoring Systems/Intelligent Wells, 5.5 Reservoir Simulation, 5.1 Reservoir Characterisation, 5.3.2 Multiphase Flow
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Pressure drop along horizontal wells causes unequal drawdown along the well, thus reducing the effectiveness of the toe of the well, and increasing the tendency for water and gas coning at the heel. Completions have been proposed to combat this effect using a stinger that extends from the heel into the horizontal section. This reduces the magnitude of the pressure drop over the wellbore, because the well is effectively split into two segments of reduced length. If the stinger also has an intermediate inflow opening, possibly equipped with a remotely controlled inflow control valve, a further reduction in the wellbore pressure drop can be obtained. We present a semianalytical model to compute the flow in stinger completions in a reservoir that may have varying inflow characteristics along the wellbore. The model is capable of handling flow in a looped configuration, which occurs when the stinger has an intermediate inflow point. It combines either numerical integration or analytical integration in terms of Jacobian elliptic functions, with an iterative "shooting" method to solve the two-point boundary value problem for pressure and flow rate along the well. It can be used to rapidly determine the optimal configuration of a stinger completion with intermediate inflow.
Wellbore Pressure Drop. Pressure drop over horizontal oil wells has been identified in various publications as a potential problem. 1-3 The immediate consequence of wellbore pressure drop is an unequal drawdown distribution along the well, as indicated in Fig. 1. Here, the drawdown ?p is defined as the difference between a reference reservoir pressure pR at a large distance from the well and the wellbore pressure p:
where x=a coordinate along the well running from the heel to the toe. The reduced drawdown near the toe reduces the effectiveness of the well and results in a reduced benefit of increasing the well length. Another effect of the uneven drawdown profile is that the well has a much higher tendency for water and gas coning at the heel than at the toe. This may lead to early water or gas breakthrough at the heel, which in turn may drastically reduce oil production and, in the worst case, render the well useless. Various solutions to counteract the effect of wellbore pressure drop have been proposed and implemented, such as a variable perforation density or an "inflow liner" with adjustable inflow restrictions that decrease the inflow resistance from the heel to the toe.4-6
An alternative method to counteract wellbore friction, first proposed by Brekke and Lien6 during the early 1990s, is the use of a stinger to move the point of highest drawdown from the heel toward the toe. Fig. 2 depicts a horizontal well with length Lw completed with a stinger that extends from the packer at the heel into the horizontal section over a length Lst. This reduces the magnitude of the pressure drop over the well, because the well is effectively split in two segments of reduced length. Permadi et al. describe experiments that confirm the concept.7 In the present paper, we consider a special class of stinger completions that have an additional inflow point at the heel to obtain a further reduction in the wellbore pressure drop (see Fig. 2). In practice, the intermediate inflow opening can be created through the use of a sliding sleeve that can be opened or closed through well intervention, or a remotely controlled inflow control valve (ICV). Several of these completions, using sliding sleeves, have been implemented in operations in Gabon and Nigeria over the past years with varying degrees of success. The possibility of using stinger completions with ICVs to achieve an optimally adjusted inflow profile during the entire life of the well has been discussed in Refs. 8 and 9. Here, we will concentrate on the modeling aspects, for which purpose we consider the intermediate inflow opening as a flow restriction with similar characteristics to those of a surface choke.
Modeling of a stinger completion with intermediate inflow requires the computation of wellbore flow in a looped configuration: fluid flowing from the reservoir into the casing-stinger annulus may subsequently flow to either the stinger end or the inflow point at the heel. The no-flow point, somewhere between heel and stinger end, cannot be determined a priori, and the flow direction in the middle part of the annulus is therefore also initially unknown. Conventional wellbore simulators are capable of modeling flow in branched configurations, but not in networks that contain loops and therefore require solving of a system of equations to determine the flow directions.
An early approach to integrated modeling of wellbore and reservoir flow was presented by Brekke et al., who used a multiphase pipe network simulator coupled to a multiphase reservoir simulator in an iterative procedure (see Ref. 10). More details on the use of network simulators for wellbore flow simulation were presented in Ref. 11, while at present a network simulator is commercially available that can be used in stand-alone mode to model complicated well configurations (see Ref. 12). These network simulators are capable of modeling flow in stinger completions with looped annulus flow, but, to our knowledge, no results have been published that demonstrate this capability. Alternatively, one could attempt to model stinger completions using a reservoir simulator, because most simulators include a feature to model complex wells with an integrated wellbore model (see e.g., Ref. 13). However, to our knowledge, none of the commercially available simulators can deal with wellbore flow in a loop. Although a workaround solution is possible, this is not a straightforward modelling technique.9 Furthermore, one could use a coupled wellbore and reservoir simulator based on a single-phase analytical reservoir description as presented in Ref. 14. However, also in that case, an adaptation of the program would be required to cope with looped wellbore flow.
Here we present an alternative approach, building on the classic model presented by Dikken in 1990 to model the effects of wellbore pressure drop in horizontal wells.1 The motivation for our model development was the need for a quick stand-alone program with full access to the algorithms and the underlying formulations. The model was used as a precursor to a more detailed analysis with a proprietary reservoir simulator using a time-consuming workaround. 9 Furthermore, the model served to verify a more recently developed feature in the simulator to model flow in looped wellbore configurations in a rigorous fashion.
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