A unified equivalent-resistance framework for smart-well inflow-control technologies in reservoir–wellbore coupled simulation

1 Introduction

Long horizontal wells have become one of the most widely adopted development technologies for improving reservoir contact and enhancing hydrocarbon recovery in heterogeneous reservoirs. Compared with conventional vertical wells, horizontal wells provide a larger drainage area and can significantly improve well productivity (Joshi, 1991; Dikken, 1990; Babu and Odeh, 1989; Economides et al., 2013; Deutsch and Journel, 1998; Zhang et al., 2022). However, due to permeability heterogeneity, pressure losses along the wellbore, and the well-known heel-toe effect, fluid inflow is often unevenly distributed along the horizontal section (Holmes et al., 1998; Jiang, 2007; Zhou et al., 2013). High-permeability intervals tend to experience excessive influx and premature water breakthrough, while low-permeability intervals remain underutilized, resulting in reduced sweep efficiency and lower ultimate recovery (Muskat and Wyckoff, 1935; Chaperon, 1986; Dake, 1978). In reservoirs with strong bottom-water support, these effects become even more pronounced, making inflow control a critical component of completion design (Ahmed, 2010; Craft et al., 1991; Lake, 1989).

To improve inflow distribution and delay water production, various flow-control devices (FCDs) have been developed and applied in advanced and intelligent completion systems. Among them, inflow control devices (ICDs), autonomous inflow control devices (AICDs), and inflow control valves (ICVs) represent three important categories of downhole flow-control technologies (Al-Khelaiwi and Davies, 2007; Aadnoy and Hareland, 2009; Li et al., 2011; Birchenko et al., 2010; Youngs et al., 2009; Zhao et al., 2024). ICDs introduce an additional pressure drop along the wellbore through nozzles, channels, or restriction elements, thereby redistributing inflow and mitigating heel-toe effects (Pinilla et al., 2022). AICDs further enhance inflow control by generating different flow resistances for different fluid phases, allowing the device to autonomously restrict unwanted water or gas production after breakthrough (Aakre et al., 2013; Mathiesen et al., 2014; Aakre et al., 2014; Kais et al., 2016; Nugraha et al., 2016; Elverhøy et al., 2018). In contrast, ICVs provide active flow control through adjustable valve openings and can be operated from the surface to optimize production performance during the well life cycle (Yeten et al., 2002; Brouwer and Jansen, 2004; Sarma et al., 2006; Van Essen et al., 2009; Al-Ghareeb, 2009; Zhang et al., 2020; Wang et al., 2016). Field applications and simulation studies have demonstrated that these technologies can improve inflow uniformity, delay unwanted-fluid breakthrough, and increase oil recovery under suitable reservoir conditions (Elfeel et al., 2018; Broni-Bediako et al., 2019; Li G. et al., 2022).

Existing studies have developed effective pressure-drop models for individual flow-control devices (Yang et al., 2019; Li C. et al., 2022). ICDs are generally represented by fixed hydraulic resistance, AICDs by fluid-dependent resistance, and ICVs by valve-opening-dependent resistance (Jansen et al., 2009; Sarma et al., 2008; Addiego-Guevara et al., 2008; da Cruz Schaefer and Sampaio, 2020; Taghavi et al., 2024). These formulations can describe the behavior of each device, but they differ in mathematical form, parameter definition, and calibration method (Birchenko, 2010; Zhang et al., 2023; Cui et al., 2020; Dong and Zhang, 2024; Cerquera et al., 2022; Yang et al., 2023).

Consequently, previous comparisons of ICDs, AICDs, and ICVs are not always performed on a consistent numerical basis (Ahdeema et al., 2024). Changing the device type often requires changing not only the pressure-loss relationship but also its implementation and coupling with the well model. The resulting performance differences may therefore reflect both the intrinsic device mechanisms and the adopted modeling methods (Saltelli et al., 2008; Sobol, 2001). The key limitation of existing approaches is thus not their inability to simulate individual devices, but the lack of a common representation that allows different devices to be compared while keeping the reservoir model, wellbore equations, operating constraints, and numerical procedure unchanged.

To address this limitation, this study proposes a unified equivalent-resistance framework. ICDs, AICDs, and ICVs are represented as different constitutive forms of the same localized resistance element in a multi-segment well model. When the device type is changed, only the resistance law and its update rule are modified, while the reservoir–wellbore coupling structure remains unchanged. This formulation separates device-specific behavior from numerical implementation and provides a consistent basis for objective performance comparison.

Based on the proposed framework, a reservoir–wellbore–FCD coupled model is developed to compare ICDs, AICDs, and ICVs under identical reservoir and operating conditions. Sensitivity analyses are conducted to evaluate the effects of device resistance, permeability heterogeneity, and initial water saturation on inflow distribution, water breakthrough, and cumulative oil and water production. The main contributions of this study are as follows.

• A unified equivalent-resistance representation is proposed for ICDs, AICDs, and ICVs, in which fixed, fluid-dependent, and opening-dependent behaviors are expressed as different resistance laws within the same formulation.
• A reservoir–wellbore–device coupled model is developed that allows the device type to be changed without modifying the underlying multi-segment well equations or numerical coupling structure.
• A consistent comparison is performed to isolate the effects of device mechanisms and quantify their responses to resistance level, reservoir heterogeneity, and initial water saturation.

2 Methodology

Figure 1 summarizes the methodological framework of this study, including device-data calibration and cross-validation, unified equivalent-resistance representation and hydraulic normalization, reservoir–wellbore–FCD coupling, and controlled comparative evaluation. The device-specific pressure-drop correlations are retained and incorporated as localized resistance elements within the same multi-segment well formulation. This allows ICDs, AICDs, and ICVs to be compared under identical reservoir, operating, and numerical conditions, thereby distinguishing device-mechanism effects from differences in model implementation.

2.1 Physical model and reservoir flow formulation

Before deriving the governing equations, the physical system is defined as a horizontal well completed in a reservoir with a finite bottom-water zone. This scenario is used to examine the effects of flow-control devices on inflow distribution, water breakthrough, and production performance. The corresponding physical model is shown in Figure 2. The model consists of an oil-bearing zone underlain by a bottom-water zone, with the horizontal well placed in the oil zone above the oil-water contact. Driven by pressure gradients, fluids flow from the reservoir into the wellbore. Reservoir inflow, annular flow, device-induced pressure loss, and tubing flow are then coupled to establish the reservoir-wellbore simulation framework. The horizontal section length is denoted by L _w.

The reservoir is described using an oil-water two-phase black-oil formulation. The phase saturations satisfy S _o + S _w = 1, and capillary pressure is neglected (P _c = P _o − P _w = 0) because the study focuses on macroscopic inflow redistribution and flow-control performance rather than capillary-dominated displacement. Thus, oil and water pressures are assumed identical within each grid block. Field-measured relative permeability curves and oil-water PVT properties are used as model inputs.

The initial reservoir pressure is uniformly set to 11.3 MPa, and the initial water saturation is 20%. A finite bottom-water zone is assigned at the bottom of the model, and closed boundaries are applied at all external faces. These settings define the initial and boundary conditions for the reservoir-wellbore-FCD coupled simulation. The governing equations for oil–water flow are expressed in Equation 1:where p, p _o, and p _w denote reservoir, oil-phase, and water-phase pressures; S _o and S _w are oil and water saturations; φ is porosity; k _x, k _y, and k _z are directional absolute permeabilities; k _ro and k _rw are relative permeabilities; μ _o and μ _w are phase viscosities; B _o and B _w are formation volume factors; Q _o, Q _w, and Q _winj are oil production, water production, and water injection rates, respectively; and Q is the total liquid rate. The variables x, y, z, and t denote spatial coordinates and time. The parameters r, r _w, L, and k _av denote radial distance, wellbore radius, effective well length, and effective near-well permeability. W, L, and h are reservoir dimensions, whereas p ₀, S _w0, and h _w denote initial pressure, initial water saturation, and the bottom-water-zone thickness. Capillary pressure is neglected, i.e., p _w − p _o = 0, and the phase saturations satisfy S _o + S _w = 1.

∂ ∂ x k x μ o k ro B o ∂ p ∂ x + ∂ ∂ y k y μ o k ro B o ∂ p ∂ y + ∂ ∂ z k z μ o k ro B o ∂ p ∂ z − Q o = ∂ ∂ t ϕ S o B o ∂ ∂ x k x μ w k rw B w ∂ p ∂ x + ∂ ∂ y k y μ w k rw B w ∂ p ∂ y + ∂ ∂ z k z μ w k rw B w ∂ p ∂ z + Q winj − Q w = ∂ ∂ t ϕ S w B w Q = Q w + Q o r ∂ p o ∂ r r = r w x w , y w , z w , t = Q o μ o 2 π k av k ro L r ∂ p w ∂ r r = r w x w , y w , z w , t = Q w μ w 2 π k av k rw L p w − p o = 0 ∂ p ∂ x x = W = 0 ∂ p ∂ y y = L = 0 ∂ p ∂ z z = h = 0 ∂ p ∂ x x = 0 = 0 ∂ p ∂ y y = 0 = 0 ∂ p ∂ z z = 0 = 0 p 0 = p x , y , z , 0 S w 0 = S w x , y , z , 0 S w 0 z < h w = 1 S o + S w = 1 (1)

2.2 Multi-segment wells and reservoir-wellbore coupling method

The proposed multi-segment well model consists of four layers: reservoir, annulus, flow-control device, and tubing. This structure represents the complete flow path from the reservoir to the wellbore: fluids enter the annulus from reservoir cells, pass through flow-control devices where localized pressure losses occur, and then flow into the tubing.

As shown in Figure 3, the horizontal well is discretized into N _s interconnected segments. Each reservoir cell or completion interval is connected to annulus nodes, and each annulus node is linked to a tubing node through a flow-control device. This hierarchical configuration captures reservoir inflow, annular flow, device-induced pressure loss, and tubing flow within a unified reservoir-wellbore coupling model.

Based on this hierarchical structure, governing equations are established for reservoir inflow, annular flow, flow-control devices, and tubing flow, respectively. The skin factor is neglected because all simulation cases use identical completion conditions and the objective is to evaluate the relative influence of different flow-control devices. The inflow from the formation to the annulus in the i _th section can be calculated using the production-index formulation given in Equation 2.where q_α,i is the flow rate of phase α from the connected reservoir grid block into well segment i; WI_i is the well index of the reservoir–well connection; λ_α,i is the phase mobility; p_r,i and p_w,i are the reservoir-grid pressure and well-segment pressure, respectively; ρ_α,i is the phase density; g is the gravitational acceleration; and z_r,i and z_w,i are the elevations of the reservoir-grid and well-segment pressure points, respectively. In the mobility expression, k_rα,i, μ_α,i, and B_α,i denote the relative permeability, dynamic viscosity, and formation volume factor of phase α, respectively. When the two pressures are evaluated at the same reference depth, the gravitational correction term is omitted.

q α , i = W I i λ α , i p r , i − p w , i − ρ α , i g z r , i − z w , i (2)

The well index, WI is calculated using the Peaceman equation (Peaceman, 1983) in Equation 3.where L _i is the effective completion length of the well within grid block i; k _a and k _b are the principal absolute permeabilities in the plane normal to the well axis; r _e,i is the Peaceman equivalent well-block radius; r _w is the physical wellbore radius; and S _i is the dimensionless skin factor. The geometric mean k _a, k _b accounts for permeability anisotropy in the plane perpendicular to the well segment. For a horizontal well oriented along the x-direction, k _a = k _y, k _b = k _z, and L _i = L _x,i.

W I i = 2 π L i k a k b ln r e , i r w + S i (3)

The formulas for calculating the equivalent radius for nonsquare grids with anisotropic permeability are given in Equation 4.where r _e,i is the numerical equivalent radius associated with the well-containing grid block; Δa and Δb are the grid dimensions in the two directions normal to the well axis; and ka and kb are the corresponding directional permeabilities. The equivalent radius is a numerical matching radius used to relate the grid-block pressure to the near-well radial-flow solution and should not be interpreted as a physical drainage radius. For a horizontal well oriented along the x-direction, Δa = Δy, Δb = Δz, k _a = k _y, and k _b = k _z.

r e , i = 0.28 k b k a Δ a 2 + k a k b Δ b 2 1 / 2 k b k a 1 / 4 + k a k b 1 / 4 (4)

The phase mobility is calculated using Equation 5.where k _rα, μ _α, and B _α represent relative permeability, viscosity, and formation volume factor of phase α, respectively. Field-measured relative permeability curves and PVT data are used in the simulation. Gravity effects are included in the reservoir governing equations through the phase potential term.

λ α , i = k r α μ α B α (5)

The pressure drop between adjacent tubing segments is decomposed into three components: frictional pressure loss, gravitational pressure loss, and acceleration pressure loss. Such a formulation is consistent with the physical description commonly employed in reservoir–wellbore simulations of horizontal wells with flow-control devices, where the total wellbore pressure drop is expressed as the sum of frictional, gravitational, and acceleration effects as given in Equation 6.where Δp _f, Δp _g, and Δp _acc represent the frictional, gravitational, and acceleration pressure losses, respectively.

p t , i − 1 − p t , i = Δ p g , i + Δ p f , i + Δ p a c c , i (6)

The pressure variation along each wellbore segment is calculated using a one-dimensional steady-state momentum balance. Under the homogeneous-flow assumption, the oil–water mixture is treated as an equivalent single fluid with local mixture density ρ _m. The pressure drop between two adjacent FCD can be calculated using Equation 7.where p _i and p _{i + 1} are the pressures at two adjacent wellbore nodes i and i + 1, respectively; z _i and z _{i + 1} are their corresponding elevations; and g is the gravitational acceleration. The variables ρ _m,i and ρ _{m,i + 1} denote the local oil–water mixture densities at the two nodes, while ρ ¯ m , i is the segment-averaged mixture density. F _i is the Darcy friction factor, Li is the length of wellbore segment i, and D _h,i is its hydraulic diameter. The variables qi and qi + 1 are the local volumetric flow rates, A _i and A _{i + 1} are the corresponding flow areas, and v _i = q _i/A _i and v _{i + 1} = q _{i + 1}/A _{i + 1} are the mixture velocities at the segment inlet and outlet, respectively. The segment-averaged velocity is defined as v _i = (v _i + v _{i + 1})/2. The coefficients α_i and α _{i + 1} are the kinetic-energy correction factors at the two nodes and are taken as unity under the homogeneous-flow approximation. The three terms on the right-hand side represent the gravitational, frictional, and acceleration pressure changes, respectively. The factor v ¯ i v ¯ i preserves the direction of the frictional pressure loss when signed flow rates are considered.

p i − p i + 1 = ρ ¯ m , i g z i + 1 − z i + f i L i D h , i ρ ¯ m , i 2 v ¯ i v ¯ i + ρ ¯ m , i 2 α i + 1 v i + 1 2 − α i v i 2 v i = q i A i , v i + 1 = q i + 1 A i + 1 v ¯ i = v i + v i + 1 2 , ρ ¯ m , i = ρ m , i + ρ m , i + 1 2 (7)

Under the homogeneous oil–water flow assumption, the local mixture properties are evaluated from the flowing water fraction f _w. The mixture density is calculated using a volume-fraction-weighted arithmetic average, whereas the mixture viscosity is determined using a logarithmic mixing rule:where f _w is water cut, ρ _w and ρ _o are water density and oil density; μ _o and μ _w are the corresponding phase viscosities; and f _w denotes the local flowing water-volume fraction.

ρ m = f w ρ w + 1 − f w ρ o μ m = μ o 1 − f w μ w f w (8)

In the multi-segment well formulation, the tubing pressure equations are solved simultaneously with the reservoir inflow equations and the local FCD pressure-drop equations. The coupling among reservoir inflow, FCD resistance, and tubing hydraulics is therefore considered. Annular crossflow between adjacent completion intervals is neglected by assuming that the annular compartments are hydraulically isolated by packers, such that fluid entering each interval flows locally through the corresponding FCD into the tubing. This simplification isolates the effects of device resistance and avoids introducing uncertain annular-communication parameters that are unavailable for calibration. Consequently, the present model is primarily applicable to compartmentalized completions and does not represent cases with significant inter-compartment or behind-pipe crossflow.

The pressure drop across the flow-control device provides the hydraulic coupling between the annulus node and the tubing node. This local pressure-loss relation given in Equation 9 constitutes the core interface of the proposed unified equivalent-resistance framework, allowing ICDs, AICDs, and ICVs to be integrated into a common multi-segment well formulation despite their different operating mechanisms:where p _a,i is the annular pressure; p _t,i is the tubing pressure; Δp _d,i is the pressure drop of device.

p a , i − p t , i = Δ p d , i (9)

2.3 Generalized equivalent-resistance model for devices

To represent different flow-control technologies within a common reservoir-wellbore framework, the local device pressure loss is expressed using a generalized equivalent-resistance formulation that depends on flow rate, fluid-state variables, and device-control parameters. This formulation does not unify the internal physical mechanisms of different devices; instead, it provides a common computational interface that separates device-specific pressure-drop laws from the reservoir-wellbore governing equations. Thus, ICDs, AICDs, and ICVs retain their own constitutive relationships while being implemented consistently in the same multi-segment well model. The unified device model is expressed as:where, R _eq,i denotes the equivalent resistance of the flow-control device installed in the ith segment. The vector x_i represents local fluid-state variables, such as water cut, density, viscosity, Reynolds number, and gas fraction. The vector u _i denotes device-control variables, including the valve opening of an ICV, the nozzle diameter of an ICD, or the inlet-size parameter of an AICD. The parameter set θ d , i contains device-specific calibrated coefficients, such as the discharge coefficient C_d of an ICD and the oil–water selectivity parameters of an AICD.

Δ p d , i = R eq , i x i , u i , θ d , i q d , i q d , i d ∈ ICD , AICD , ICV (10)

For ICDs, a quadratic pressure-drop model is used to describe local inertial losses, with pressure drop proportional to the square of flow rate. This formulation is widely applied to nozzle- and restriction-type ICDs and effectively represents their hydraulic behavior under typical operating conditions. The expression is given in Equations 11, 12: where Δp _ICD is the pressure drop generated by the ICD, R_ICD is the corresponding equivalent resistance coefficient, q is the local flow rate through the device, C_d is the discharge coefficient, A is the nozzle cross-sectional area, and ρ_m is the mixture density calculated by Equation 8.

Δ p I C D = R I C D q q (11)

R I C D = ρ m 2 C d A 2 (12)

AICDs differ from conventional ICDs because their hydraulic resistance varies with produced-fluid properties. As water cut increases, the device generates additional pressure loss, restricting water inflow while maintaining lower resistance to oil production. Therefore, AICD pressure drop depends on flow rate, device geometry, mixture density, viscosity, and water cut. To describe these effects, the classical quadratic pressure-drop form was extended by including dimensionless nozzle-diameter and viscosity terms, mixture density, and a water-cut selectivity factor. The calibrated model is expressed as:where Δp is the AICD pressure drop, q is the flow rate, D is the nozzle diameter, ρ _m and μ _m (Equation 8) are the mixture density and mixture viscosity, respectively, f _w is the water-cut fraction, and C, z, y, K _w, β, and K _m are calibration parameters. D _ref and μ _ref are reference values used for nondimensionalization.

Δ p = C D r e f D z ρ m μ r e f μ m y 1 + K w f w β + K m f w 1 − f w q q (13)

The term K _w f _w ^β represents the monotonic water-cut-dependent selectivity, whereas the additional transition term K _m f _w (1-f _w) captures the nonlinear response in the intermediate water-cut range. This term vanishes under single-phase oil and single-phase water conditions and mainly acts in the oil-water mixed-flow regime, which is consistent with the observed larger deviations at intermediate water cuts.

Comparing Equation 13 with the generalized equivalent-resistance formulation introduced in Equation 10, the equivalent resistance of the AICD can be identified in Equation 14:

R A I C D = C D r e f D z ρ m μ r e f μ m y 1 + K w f w β + K m f w 1 − f w (14)

Unlike ICDs and AICDs, an ICV actively controls flow by adjusting valve opening, which changes the effective flow area and hydraulic resistance. A smaller opening reduces flow capacity and increases local pressure drop, whereas a larger opening has the opposite effect. Within the unified equivalent-resistance framework, the ICV is therefore represented as an opening-dependent resistance element.

To describe this behavior, a saturation-type opening function is used to relate valve opening to the effective hydraulic area A _e. Here, A _e represents the combined effects of geometric opening, discharge coefficient, and local contraction losses. The local pressure drop is then calculated using the classical orifice-flow relationship. The calculation formula for A _e is given in Equation 15:where A_e(s) denotes the effective hydraulic flow area of the valve, A ∞ is the asymptotic effective flow area under fully open conditions m², s is the valve opening (mm), and s₅₀ is the characteristic opening corresponding to (A_e = A ∞/2). The parameter s₅₀ determines the opening level at which the transition from rapid area growth to saturation occurs.

A e s = A ∞ s m s m + s 50 m (15)

The pressure-drop equations for the ICV are given in Equation 16.where Δp denotes the pressure drop generated by the ICV, ρ is the mixture-fluid density, q is the local flow rate through the valve, and R_ICV is the equivalent resistance factor representing the hydraulic resistance imposed by the valve-opening setting.

Δ p = ρ q q 2 A e s 2 = R ICV q q (16)

Based on the unified framework of this article, the calculation formula for the equivalent resistance factor is obtained in Equation 17:

R ICV = ρ 2 A e s 2 (17)

Here, A _e(s) represents the effective hydraulic flow area of the valve, which differs from the physical opening area. It can be regarded as an equivalent parameter that converts the valve opening condition into hydraulic resistance within the proposed equivalent-resistance framework. The pressure-drop relationship is derived from the conventional incompressible orifice-flow equation, whereas the opening-dependent effective-area function is introduced in this study as a bounded phenomenological representation of the nonlinear ICV opening characteristic.

Although ICDs, AICDs, and ICVs operate through different mechanisms, they all influence the reservoir-wellbore system by generating localized pressure loss between the annulus and tubing. This pressure loss represents their common hydraulic effect at the coupling level, not a shared internal mechanism. Therefore, equivalent resistance provides a device-independent quantity that can be consistently incorporated into the multi-segment well equations.

The proposed framework retains the device-specific models by expressing each pressure-drop law as an equivalent-resistance relationship: fixed or geometry-dependent resistance for ICDs, fluid-responsive resistance for AICDs, and opening-dependent controllable resistance for ICVs. Their physical differences are preserved through the dependence of R _eq on device parameters, fluid properties, and control variables.

When the device type is changed, only the corresponding resistance relationship is replaced, while the reservoir equations, wellbore formulation, coupling structure, and numerical solution procedure remain unchanged. This improves implementation consistency and enables controlled comparison under identical reservoir and operating conditions.

2.4 Coupled nonlinear solution strategy

At each time step, reservoir flow, annular flow, device pressure loss, and tubing flow are assembled into a fully coupled nonlinear system and solved simultaneously. The state vector includes reservoir pressure, water saturation, annulus and tubing pressures, segment flow rates, and device flow rates. The system enforces reservoir mass conservation, wellbore hydraulics, and device pressure-drop relations, coupled through pressure and flow continuity. In residual form, it is given in Equation 18:

F z k + 1 = F r e s F w e l l F d e v = 0 (18)

The coupled reservoir-wellbore simulations were performed using a self-developed MATLAB-based reservoir simulator. The coupled nonlinear system was solved with a fully implicit formulation and the Newton-Raphson method, which simultaneously resolves reservoir flow, wellbore flow, and device responses. This improves stability under strongly nonlinear conditions, such as autonomous resistance enhancement in AICDs or rapid ICV opening adjustments. Automatic differentiation was used to construct the Jacobian matrix and ensure accurate derivative evaluation. The Jacobian includes coupling terms from reservoir flow, annular flow, wellbore flow, and device pressure-drop equations, as illustrated in Figure 4.

Because of the strong nonlinear coupling among reservoir flow, wellbore flow, and flow-control-device responses, the discretized governing equations are solved using the Newton–Raphson method. Let R_(x) denote the residual vector of the coupled system. The nonlinear problem can be written as given in Equation 19:

R x = 0 (19)

At the kth Newton iteration, a first-order Taylor expansion of the residual vector about the current iterate x ^k yieldswhere δ x is the increment of the primary variables and J is the Jacobian matrix defined as J = ∂ R ∂ x

R x k + δ x ≈ R x k + J δ x (20)

Since the converged solution satisfies:substituting Equation 20 into Equation 21 gives yields Equation 22.which leads to the Newton correction equation in Equation 23:

R x k + 1 = 0 (21)

R x k + J δ x = 0 (22)

J δ x = − R (23)

3 Results and discussion

Based on the unified equivalent-resistance framework and the reservoir–wellbore–flow-control-device coupled model developed in Section 2, the resistance parameters of ICDs, AICDs, and ICVs were first calibrated using data compiled from the literature and subsequently incorporated into the multi-segment well model to establish a unified simulation platform. On this basis, the water-control performance of different flow-control technologies was comparatively evaluated. Sensitivity analyses were further conducted to systematically investigate the effects of key factors, including the initial additional pressure-drop level, reservoir heterogeneity, and initial water saturation, on inflow uniformity, water-breakthrough behavior, cumulative oil production, and cumulative water production.

3.1 Calibration and validation of device models within the unified resistance framework

This section reports the calibration and cross-validation of the ICD, AICD, and ICV pressure-drop models using compiled literature data. Although the devices have different hydraulic mechanisms, their pressure losses are implemented through a common equivalent-resistance interface while retaining device-specific correlations. Model performance was evaluated using stratified five-fold cross-validation, and accuracy was quantified by RMSE, MAE, MAPE, and R ². The data used can be found in the Supplementary Material S1.

For the AICD model, 163 digitized pressure-drop data points from Du et al. were used, covering four nozzle diameters (2.5–4.0 mm) and five water-cut conditions (0%–100%). Within each nozzle-diameter/water-cut curve, the data were sorted by flow rate and assigned to five folds. The pooled validation results gave R ² = 0.940, RMSE = 0.276 MPa, and MAPE = 21.81%, indicating acceptable predictive stability over the investigated nozzle-diameter, water-cut, and flow-rate ranges. After cross-validation, the final AICD parameters were recalibrated using the complete dataset. The reference values were D _ref = 3.159 mm and μ _ref = 3.690 mPas, and the calibrated parameters were C = 5.0 × 10⁻⁵, z = 2.308, y = 0.998, K _w = −0.876, β = 0.245, and K _m = 0.0385. The full-dataset fit yielded R ² = 0.942, RMSE = 0.272 MPa, and MAPE = 21.63%, showing that the model reasonably captures the coupled effects of nozzle diameter, mixture properties, water cut, and flow rate on AICD pressure drop. The AICD pressure drop calibration and validation results are shown in Figure 5.

The ICD model was calibrated and evaluated using 33 nozzle-type ICD pressure-drop data points digitized from the ResFlow ICD curves of Gualdrón et al. (2014), covering different fluid viscosities. Because the original figure does not report physical nozzle area, the fitted parameter was interpreted as the equivalent flow-capacity term C _d A _n. Stratified five-fold cross-validation was performed by sorting the data within each viscosity series by flow rate. The pooled validation results were R ² = 0.995, RMSE = 0.093 MPa, and MAPE = 13.90%, indicating good predictive capability of the classical nozzle-type ICD equation for the selected data. The validation errors showed no clear dependence on viscosity. The final parameter was then recalibrated using the complete dataset, giving α = 5.244 × 10⁹ m^-4 and C _d A _n = 1.381 × 10⁻⁵ m². Assuming C _d = 1, this corresponds to an equivalent nozzle diameter of 4.193 mm. The ICD pressure drop calibration and validation results are shown in Figure 6.

The ICV model was calibrated and evaluated using 25 pressure-flow data points digitized from Yang et al., covering five valve openings (15–75 mm) and five pressure differentials (0.5–2.5 MPa). Stratified five-fold cross-validation was performed by sorting the data within each valve-opening group by pressure differential. The pooled validation results were R ² = 0.9999, RMSE = 4.72 × 10⁻⁴ m³/s, and MAPE = 0.394%, indicating excellent predictive robustness across valve openings and pressure ranges.

After cross-validation, the final parameters were recalibrated using the complete dataset, yielding A ∞ = 2.294 × 10⁻³ m², s ₅₀ = 20.885 mm, and m = 1.956, with ρ _o = 741 kg/m³ and A _out = 2.83 × 10⁻³ m². The full-dataset fit achieved R ² = 0.9999, RMSE = 4.33 × 10⁻⁴ m³/s, and MAPE = 0.374%, confirming that the ICV model accurately captures the dependence of flow rate on valve opening and pressure differential. The ICV pressure drop calibration and validation results are shown in Figure 7.

3.2 Reservoir–wellbore–FCD coupled simulation results

3.2.1 Model validation and computational performance

After calibration, the ICD, AICD, and ICV models were incorporated into the multi-segment well formulation to establish a unified reservoir-wellbore-flow-control-device coupled simulation platform. A horizontal well in a heterogeneous reservoir with a finite bottom-water zone was selected as the base case. To ensure a consistent comparison, all reservoir, wellbore, and operating conditions were kept identical among cases, except for the flow-control-device parameters. The main model parameters are summarized in Table 1. A four-compartment horizontal-well completion was adopted as the base-case configuration. This design provides a representative balance between inflow-control flexibility and completion complexity, enabling comparative evaluation of different flow-control technologies under the same reservoir and operating conditions.

TABLE 1. Parameters of the base-case reservoir model.

Before comparing different flow-control technologies, the reservoir-wellbore coupling simulator was validated using a no-flow-control-device case. The same reservoir, fluid, wellbore, and production conditions were implemented in the proposed simulator and ECLIPSE. Because no device-induced pressure loss was included, this case directly tests the reservoir-wellbore coupling implementation. As shown in Figure 8, the predicted liquid rate and water-cut evolution agree well with ECLIPSE, supporting the reliability of the simulator for subsequent ICD, AICD, and ICV evaluations.

The simulator was implemented in MATLAB R2023b and run on a PC with an Intel Core i7 processor and 16 GB RAM. For the base case, the average Newton iteration number was 3.5 per time step, with a maximum of 8, and the 10-year simulation required approximately 450 s. Although the localized equivalent-resistance units increased the computational time relative to the noFCD case, convergence remained stable, indicating that different FCD models can be incorporated without substantially compromising numerical performance. The computational performance is shown in Table 2.

TABLE 2. Computational performance of the reservoir–wellbore–FCD coupled simulation model.

3.2.2 Comparative performance of ICD, AICD, and ICV

ICDs, AICDs, and ICVs have different hydraulic mechanisms, geometries, and parameter definitions, their original literature-based models produce different pressure losses under the same flow conditions. Direct comparison using the original parameters would therefore confound device-control effects with differences in nominal resistance magnitude. Since matching pressure-drop data are not available for all device types, a normalization procedure was introduced to provide a consistent basis for comparison. To establish a controlled comparison, a hydraulic-resistance normalization procedure was introduced. For each device type d, the original pressure-drop relationship was multiplied by a dimensionless normalization factor in Equation 24:or, equivalently is given in Equation 25,

Δ p d norm = γ d Δ p d raw , d ∈ ICD , AICD , ICV (24)

R d norm = γ d R d raw (25)

The normalization factor was determined under a common reference flow rate, fluid condition, and initial device state in Equation 26:where q _ref is the reference flow rate, Δp _ref is the prescribed reference pressure drop, and ξ _d,ref denotes the device-specific reference state.

γ d = Δ p ref Δ p d raw q ref , ξ d , ref (26)

The normalization factor is kept constant during the coupled simulation. It scales only the overall resistance magnitude while preserving the intrinsic response of each device: fixed resistance for the ICD, fluid-dependent resistance for the AICD, and opening-dependent resistance for the ICV. In the base case, the well was produced at a constant liquid rate of 100 m³/d and divided into four segments, with three devices installed in each segment. The resulting reference flow rate per device was approximately 8 m³/d. A common reference additional pressure drop of 1 MPa was specified. The ICD was used as the hydraulic reference, giving γ_ICD = 1. Under the same condition, the original AICD and ICV models predicted pressure drops of 0.3261 MPa and 2.103 × 10⁻⁵ MPa, respectively, yielding the corresponding normalization factors:and

γ AICD = 1 0.3261 ≈ 3.07

γ ICV = 1 2.103 × 10 − 5 ≈ 4.755 × 10 4

These factors were used only to match the initial hydraulic restriction among the three devices and did not alter their dynamic response laws. Thus, the normalization compares different control mechanisms under the same initial pressure-drop condition rather than representing devices with identical physical geometries.

After normalization, the AICD inlet-size and ICV opening parameters were adjusted so that ICDs, AICDs, and ICVs produced the same additional pressure drop during the water-free stage. This ensured comparable initial throttling strength among the three completion technologies. The resulting parameters and normalized pressure drops are summarized in Table 3.

TABLE 3. Device parameters after initial pressure-drop normalization.

Unlike passive devices such as ICDs and AICDs, an ICV regulates local resistance by adjusting valve opening. Since real-time ICV optimization requires monitoring, control logic, and multi-objective decision-making, it is beyond the scope of this study. Therefore, a simple and reproducible control rule was adopted to ensure a consistent comparison among device types. A single-adjustment strategy was applied: when the water cut of any compartment exceeded 80%, the valve opening of the corresponding high-water-cut segment was reduced once to increase local resistance and limit subsequent water invasion. The updated valve opening was calculated as follows using Equation 27:where s _i denotes the ICV opening, s i 0 is the initial opening of segment i, and s i n e w is the updated opening after adjustment. S _min is the minimum allowable opening, which is set to 0 in this study. γ is the adjustment-strength coefficient controlling the magnitude of valve regulation and is set to 0.5. F _w,i and f _w,avg denote the water cut of segment i and the average water cut among all compartments, respectively.

s i n e w = max s min , s i 0 1 − γ ⁡ max 0 , f w , i − f w , a v g max 1 − f w , a v g , 0.001 (27)

To quantitatively evaluate the performance of different flow-control technologies, comparative simulations were conducted under a constant liquid-production-rate constraint. The target liquid production rate was set to 100 m³/d, and the production period was 10 years. Under the normalized initial pressure-drop condition, the water-control performance and incremental oil recovery of ICDs, AICDs, and ICVs were compared. The results are summarized in Table 4.

TABLE 4. Comparison of cumulative incremental oil production for different flow-control devices.

Water breakthrough mainly occurs during early production, the first 30 days of water-cut evolution are shown in Figure 9. Without flow-control devices, water breakthrough occurs on day 25, followed by a rapid increase in water cut, indicating fast bottom-water invasion through high-conductivity paths. In contrast, ICDs, AICDs, and ICVs delay breakthrough to day 29 and show similar early-stage water-control performance.

Figure 10 compares cumulative oil production over 10 years for the ICD, AICD, ICV, and noFCD cases. All three flow-control technologies improve inflow distribution, reduce the adverse effects of water invasion, and increase cumulative oil production relative to the noFCD case. The devices were normalized to the same initial additional pressure drop, their early throttling effects and long-term production profiles are similar. However, the enlarged view in Figure 10 and the statistics in Table 4 show measurable differences. The ICV gives the highest cumulative oil increment, followed by the AICD and ICD, with 10-year increments of 7322.4, 7277.5, and 7256.1 m³, respectively.

These results indicate that device-specific dynamic responses still affect late-stage production under identical initial throttling conditions. The AICD autonomously increases resistance in high-water-cut regions, whereas the ICV actively restricts water-producing segments by valve adjustment. Thus, both provide slightly better long-term performance than the conventional ICD.

Figure 11 presents the evolution of water-cut differences between AICD/ICV and ICD during the production period, where the vertical axis is defined in Equation 28:

Δ f w = f w , AICD / ICV − f w , ICD (28)

The water-cut differences among the three flow-control technologies remain small, consistent with the initial pressure-drop normalization. During the early stage, approximately the first 1,000 days, the AICD and ICV show slightly lower water cuts than the ICD, indicating moderate delay of water invasion. At later times, the AICD-ICD difference gradually diminishes, whereas the ICV maintains a lower water cut due to active restriction of high-water-cut segments. These results show that device-specific control mechanisms still influence long-term water-production behavior, although the overall differences are modest.

Figure 12 shows the oil and water production rates of individual compartments for different completion scenarios. In the noFCD case, Compartment 2 exhibits the earliest and strongest increase in water production, indicating preferential bottom-water breakthrough through a high-conductivity path. As production continues, this compartment becomes the dominant source of produced water, reducing development efficiency. With ICDs, AICDs, and ICVs, water production from Compartment 2 is effectively suppressed, and inflow becomes more evenly distributed among compartments. This allows the other compartments to maintain higher oil contributions, delaying water invasion and increasing cumulative oil production.

3.3 Sensitivity analysis

3.3.1 Sensitivity analysis of initial pressure-drop level

The base case has initial segment pressure drops of 0.2630, 0.4008, 0.1268, and 0.0685 MPa. To evaluate the effect of initial throttling strength, a pressure-drop sensitivity analysis was conducted. Using the base case as the reference, five pressure-drop levels were tested, corresponding to 0.33, 0.5, 1.0, 1.5, and 2.0 times the baseline values. The ICD was used as the reference device for parameter design, and the resulting nozzle diameters and segment pressure drops are listed in Table 5.

TABLE 5. ICD sensitivity cases for different initial pressure-drop levels.

Figure 13 shows the effect of initial pressure-drop level on 10-year cumulative oil production and average water cut. The results reveal a clear trade-off between water-control performance and well productivity. As the average initial pressure drop increases from 0.0716 to 0.2148 MPa, cumulative oil production rises to a maximum of 60,307.3 m³, while average water cut decreases to its minimum. This indicates that moderate throttling improves inflow distribution, suppresses excessive inflow from high-permeability and high-water-cut intervals, delays water invasion, and enhances oil recovery. Under the present conditions, the optimal average initial pressure drop is approximately 0.2148 MPa.

To evaluate the effect of initial pressure-drop level on AICD performance, the same pressure-drop levels used for the ICD analysis were applied. The resulting parameters for the five sensitivity cases are summarized in Table 6.

TABLE 6. AICD sensitivity cases for different initial pressure-drop levels.

As water cut increases, the AICD autonomously raises flow resistance, leading to a continuous increase in additional pressure drop. When this pressure loss becomes sufficiently large, the effective reservoir-to-wellbore drawdown can no longer sustain the prescribed liquid rate, and the simulator switches automatically from constant-rate to bottom-hole-pressure control. Thus, AICD design requires a balance between water-control effectiveness and long-term productivity. Figure 14 shows the effect of initial pressure-drop level on 10-year cumulative oil production and average water cut for the AICD. Overall, AICD performance is relatively insensitive to the investigated pressure-drop range. The maximum difference in cumulative oil production is 1,217.74 m³, about 2% of the average value, while the maximum variation in average water cut is only 0.39%, or approximately 0.46%.

Together with Supplementary Figure S2 in Supplementary Material S2, these results show that excessive pressure drop can trigger an earlier switch from constant-rate to bottom-hole-pressure control, and reduce effective production drawdown. Therefore, AICD design should balance water-control performance and productivity preservation. Finally, the case with an average initial pressure drop of 0.2148 MPa was selected as the base configuration.

To evaluate the effect of initial pressure-drop level on ICV performance, the same scaling method used for the ICD and AICD cases was applied. The achievable pressure-drop range of the ICV is limited by its maximum flow capacity. At the lowest target pressure-drop level, several valves reach the maximum opening of 80 mm and cannot further reduce flow resistance. To represent active control, one valve-opening adjustment was allowed during production according to the predefined control rule. The resulting ICV parameters are summarized in Table 7.

TABLE 7. ICV sensitivity cases for different initial pressure-drop levels.

Figure 15 shows the effect of initial pressure-drop level on 10-year cumulative oil production and average water cut for the ICV. ICV performance is relatively sensitive to this parameter: the cumulative oil production difference reaches 2,843 m³, approximately 4.83% of the average value, while average water cut varies by 0.79%, or about 0.94%.

As the initial pressure drop increases, cumulative oil production first increases and then decreases, whereas average water cut generally declines. The highest cumulative oil production, 60,383.12 m³, is obtained at an average initial pressure drop of 0.215 MPa, with a relatively low average water cut. Therefore, this case was selected as the base configuration for subsequent ICV simulations.

3.3.2 Sensitivity analysis of reservoir heterogeneity

Reservoir heterogeneity is another key factor influencing horizontal-well performance. To quantify its effect on different flow-control technologies, heterogeneity was characterized using the permeability coefficient of variation (CV). Different heterogeneity levels were generated by modifying the permeability distribution among reservoir segments while maintaining a constant average permeability of 1,150 mD. This isolates the effect of permeability distribution from overall reservoir productivity, enabling independent evaluation of its influence on inflow distribution, water invasion, and cumulative oil production. The permeability distributions and corresponding simulation results are summarized in Table 8.

TABLE 8. Reservoir heterogeneity cases and corresponding simulation results.

Figure 16 shows the effect of permeability heterogeneity on 10-year cumulative oil production and average water cut. Reservoir heterogeneity significantly affects flow-control performance, but the response differs among device types.

For ICDs and ICVs, cumulative oil production reaches a maximum at moderate heterogeneity (CV = 0.251) and decreases at both lower and higher heterogeneity levels. In contrast, AICD cumulative oil production increases monotonically with heterogeneity and reaches its maximum at CV = 0.637. This reflects the fluid-responsive behavior of the AICD, which autonomously increases resistance in high-water-cut intervals and becomes more effective as permeability contrast increases. Overall, ICDs and ICVs perform best under low-to-moderate heterogeneity, whereas the AICD becomes more advantageous under stronger heterogeneity.

3.3.3 Sensitivity analysis of initial water saturation

Initial water saturation controls the initial distribution of movable oil and water and strongly affects production in reservoirs with a finite bottom-water zone. To evaluate the adaptability of different flow-control technologies, cases with varying initial water saturation were simulated while all other parameters were kept constant. The 10-year cumulative oil production was used as the evaluation metric, and the results for ICDs, AICDs, and ICVs are summarized in Table 9.

TABLE 9. Results of the initial water saturation sensitivity analysis.

Figure 17a shows the effect of initial water saturation on 10-year cumulative oil production for ICDs, AICDs, and ICVs, cumulative oil production decreases markedly with increasing initial water saturation for all device types. The decline rate becomes smaller at high saturation levels. Figure 17b shows that AICD and ICV generally provide higher cumulative oil production than ICD, with the AICD maintaining a positive increment over the full saturation range. However, the effect of initial water saturation is much larger than the differences among device types. Thus, initial water saturation is the dominant factor controlling production performance, while flow-control devices mainly improve recovery by redistributing inflow and delaying water invasion.

3.4 Model limitations, applicability, and future development

Although the proposed framework provides a consistent numerical representation of different flow-control technologies, several limitations remain. First, the ICD, AICD, and ICV correlations were evaluated using literature-derived data and grouped cross-validation, while the underlying reservoir–wellbore model was benchmarked against ECLIPSE E100. These tests support the numerical implementation and predictive stability of the component models within the investigated ranges but do not constitute field-scale validation of the complete coupled framework. Second, the present study considers only oil–water two-phase flow and neglects gas effects, device degradation, plugging, erosion, and other completion failures. Third, the ICV is operated using predefined opening schedules rather than closed-loop control based on real-time production data. In addition, the normalized device representations are intended for controlled mechanism comparison and should not be interpreted as specific commercial completion designs.

The framework is primarily applicable to heterogeneous reservoirs completed with horizontal wells and inflow-control devices, particularly reservoirs underlain by a finite bottom-water zone where inflow redistribution and water-breakthrough control are important. By separating device-specific pressure-loss relationships from the reservoir–wellbore governing equations, additional FCD models can be incorporated without modifying the core coupling structure. However, its quantitative predictions remain limited to the reservoir conditions, device-characterization ranges, and operating assumptions considered in this study.

Future work will focus on field- and laboratory-scale validation, extension to oil–water–gas flow, and the incorporation of device degradation and completion-failure mechanisms. Closed-loop optimization of ICV settings using real-time production data will also be investigated. In addition, physics-informed and data-driven pressure-drop models may be introduced through the equivalent-resistance interface to improve adaptability, uncertainty representation, and field-scale predictive capability.

4 Conclusion

• A unified equivalent-resistance framework was developed to incorporate ICD-, AICD-, and ICV-specific pressure-loss relationships into the same reservoir–wellbore coupled multi-segment well formulation. The framework separates the device-specific constitutive relationships from the reservoir–wellbore governing equations, allowing the device type to be changed without modifying the coupling structure or numerical solution procedure.
• Under the common normalized pressure-drop condition, all three FCD cases improved inflow uniformity and delayed water breakthrough relative to the no-FCD case. The water-free production period increased from 25 to 29 days, while cumulative oil production increased by more than 7200 m³ for each FCD case over 10 years. Under the investigated reservoir conditions and predefined control strategies, the ICV produced the highest cumulative oil production, followed by the AICD and ICD.
• Among the tested controllable parameters, the reference pressure-drop level had the strongest influence on production performance. The best result among the investigated cases was obtained at approximately 0.215 MPa. Device performance also depended strongly on permeability heterogeneity: ICDs and ICVs performed favorably under moderate heterogeneity, whereas the AICD showed greater adaptability under highly heterogeneous conditions. Changes in initial water saturation had a larger effect on overall production than the performance differences among the three devices.
• The results indicate that FCD selection should account for reservoir heterogeneity, initial water conditions, and the required hydraulic restriction rather than relying on a universally preferred device. The device correlations were assessed through grouped cross-validation using published data, and the underlying no-FCD reservoir–wellbore model was benchmarked against ECLIPSE E100. Nevertheless, the present conclusions are limited to oil–water flow in a heterogeneous reservoir underlain by a finite bottom-water zone, normalized device representations, and predefined ICV control schedules. Future work should include independent laboratory and field validation, oil–water–gas flow, device degradation, and closed-loop ICV optimization.

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Supplementary material

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/feart.2026.1917305/full#supplementary-material

Supplementary material Supplementary material at the source

Supplementary material Supplementary material at the source

Footnotes

Edited by: Leilei Zhang, Rice University, United States

Reviewed by: Airong Li, Xi’an Shiyou University, China

Mohamed Reda, Al-Azhar University, Egypt