Inter-well interference occurs throughout gas well production. During infill well fracturing, pressure changes in offset wells reflects the degree of hydraulic fractures interference. Stronger fracturing-induced interference correlates with higher wellhead pressure increases, while weaker interference causes smaller fluctuations. The cumulative pressure increases per stage in each well quantifies interference intensity between the monitored and fracturing wells. Additionally, the ratio of each stage’s pressure increase to the total cumulative represents the relative contribution of individual fracturing stages [18].

The wellhead pressure rise of the parent well was monitored during the fracturing of the infill, and the results are shown in Figs. 2 and 3. Well 4 fractured 21 segments, the pressure of well 1 responded to 13 segments with a pressure increase of 0.01~5.71 MPa, well 2 responded to 15 segments with a pressure increase of 0.03~3.9 MPa, and well 3 responded to 13 segments with a pressure increase of 0.01~0.41 MPa during the fracturing period. Well 5 was fractured in 23 sections, the pressure response of well 1 was 8 sections with a pressure increase of 0.05~0.7 MPa, the pressure response of well 2 was 19 sections with a pressure increase of 0.01~0.5.94 MPa, and the pressure response of well 3 was 13 sections with a pressure increase of 0.01~1.04 MPa during the fracturing period, the results are shown in Table 2.

The wellhead pressure increases in monitoring wells were calculated using the fracturing timeline of each infill well stage (Tables 3 and 4). Using Well 4 as a case study. Well 1 recorded a total pressure rise of 17.47 MPa during Well 4’s fracturing, with notably high spikes in Stages 14, 19, 20 and 21 (13.51%, 25.42% and 32.68%, respectively), indicating strong fracture-driven interference. Well 2 displayed a total increase of 11.57 MPa, with higher responses (>10%) in Stages 6, 11, 18 and 19, demonstrating substantial interference. Well 3 experienced only a minor rise of 0.74 MPa, suggesting weak interference with Well 4.

During Well 5’s hydraulic fracturing, cumulative pressure increases were 1.95 MPa (Well 1), 27.35 MPa (Well 2), and 2.73 MPa (Well 3), with strongest interference between Wells 2 and 5 (Stages 20–22: 18.35%, 21.72%, 19.05%). Well positioning significantly influenced pressure responses: closer distances correlated with stronger interference, while no fracturing response was observed between infill Wells 4 and 5.

In fracture networks with large cracks, tracer output displays a sharp, narrow single-peak curve. In systems dominated by microfractures, the curve shows a short, broad single or multi-peak pattern, where the peak count depends on the number of high-permeability channels [19,20]. Therefore, fracture connectivity can be determined by analyzing tracer curve shapes, as illustrated in Fig. 4.

A fracturing fluid, containing 44 gas-phase tracers was injected via infill wells CN4 and CN5. Subsequent to the opening of the wells, varying concentrations of tracers were observed in all three parent wells, with concentration curves illustrated in Fig. 5. Wells 1 and 2 (from Well 4) and Well 2 (from Well 5) showed elevated tracer concentrations with double peaks, indicating connectivity through large fractures. Well 3 exhibited low concentrations with a single late peak, suggesting microfracture-dominated connectivity. Wells 3 and 5 did not detect tracer injection from well 4, whereas wells 1 and 4 did not detect tracer injection from well 5. Cross-well tracer monitoring showed no mutual tracer detection between Wells 4 and 5. Peak intensity and curve width analysis revealed stronger connectivity in well pairs 1–4, 2–4, and 2–5 compared to 3–5.

As shown in Fig. 6, tracer concentrations peaked then declined. By the final monitoring stage, concentration in multiple wells dropped to undetectable levels, signifying that fractures between infill and parent wells gradually closed under stress, reducing inter-well flow.

Fig. 7 shows the spatial distribution of micro-seismic monitoring results for Platform CN1. Green dots denote the parent well events, while purple dots denote child well events. Both color-coded event clusters are symmetrically distributed along the wellbore. Prior to infill drilling, micro-seismic events between parent wells were sparsely distributed. Following infill operations, the micro-seismic events between parent and child wells demonstrate uniform spatial coverage across the entire pad. Additionally, micro-seismic data from this platform indicate a well-defined natural fracture network connecting wells 1, 2, 4, and 5. This fracture system is marked by clustered micro-seismic events, consistent with tracer detection results.

In January 2023, five wells commenced production. Post-infill reopening of parent wells resulted in higher initial output compared to pre-infill levels (Table 5).

To verify the inter-well connectivity, an interference test was conducted on the platform in April 2023. Two wells between Wells 4 and 5 remained open during the test due to partially closed wellhead gates. Wells CN1, CN4, and CN5 were selected as test wells to evaluate connectivity by analyzing pressure fluctuation timing and patterns in observation wells [21]. The distance from well CN1 to 4 is 251 m, and the results of the interference test for the well CN1 and 4 groups are illustrated in Fig. 8. The CN4 well exhibited an opening pressure excitation response time [22] of 1.8 h, a propagation speed of 139 m per hour, an excitation duration of 307.87 h, and a pressure drop of 1.79 MPa. The CN4 well exhibited a shut-in excitation reaction time of 2.67 h, a propagation velocity of 94 m per hour, an excitation duration of 122.62 h, and a pressure increase of 1.29 MPa.

The distance from CN4 to well 5 was 483 m, and the results of the interference test for the CN4 and well 5 groups are illustrated in Fig. 9. The reaction time for the CN4 well shut-in excitation is 10.43 h, the propagation speed is 46 m per hour, the excitation duration is 112.55 h, and the pressure increase is 0.17 MPa.

The interference test findings indicate that wells CN1 and CN4 demonstrate connectivity through propped fractures. With a spacing of 483 m between Wells CN4 and CN5, pressure interference is evident, confirming that infill wells establish hydraulic connectivity with parent wells. This connectivity provides pressure support, enhancing parent well productivity during early production phases.

During fracturing, flowback, and production operations, child wells induce notable interference on parent wells. As child well pressure declines, fracture connectivity initially remains high but gradually decreases due to stress-induced fracture closure. Therefore, quantifying transient flow rates between parent and infill wells is critical for accurate EUR evaluation of infill wells.

Assumptions in this study: 1.

Pre-infilling conditions: -

The parent wells, comprising a total of n wells, had been in production for several years prior to the deployment of infill wells.

A schematic diagram of the connectivity of the infill well to the parent well is shown in Fig. 10.

Shale gas reservoirs contain both free gas and adsorbed gas. Free gas is stored in fractures and matrix pores, while adsorbed gas is bound to the internal surfaces of the matrix [24]. During production, reservoir pressure declines. When the pressure falls below the critical desorption threshold, adsorbed gas begins to desorb. Assuming t isothermal reservoir conditions, the Langmuir adsorption isotherm equation is used to derive the material balance equation [25,26], namely: (1)VE=VLppL+p

V_L represents the Langmuir volume, indicating the maximum theoretical saturated adsorption capacity of shale when formation pressure approaches infinity. P_L denotes the Langmuir pressure, corresponding to the pressure at which 50% of gas adsorption capacity is achieved on the Langmuir isotherm curve. A lower Langmuir pressure indicates that adsorbed gas is less prone to desorption during production.

Under conditions of initial formation pressure, denoted as p_i, the reserves of shale gas comprise the total amount of both free and adsorbed gas, specifically: (2)G=Gf+Ga=Gf+ρBGfBgiSgiφ⋅VLpipL+pi

Based on the principle of mass conservation (ρ₁V₁ = ρ₂V₂), the original subsurface adsorbed gas volume in the adsorbed phase can be calculated as: (3)Gais=ρBGfBgiSgiφ⋅VLpipL+pi

Assuming constant densities for both the adsorbed gas phase and free gas phase, the volume of the remaining subsurface adsorption gas adsorption term volume is expressed as follows: (4)Gas=ρBGfBgiSgiφ⋅VLppL+p

When the formation pressure drops, the volume of expansion of the rock with bound water is: (5)ΔVep=GfBgiSgi(Cf+CwSwi)(pi−p)

As the formation pressure diminishes and a portion of the free-state adsorbed gas is extracted, the volume of the remaining free-state adsorbed gas in the subsurface is: (6)ΔVed=Bg(Ga−Gas)=ρBBgGfBgiSgiφ(VLpipL+p−VLppL+p)

According to the principle of subsurface volume equilibrium can be obtained:

Original free gas volume + Original adsorbed gas volume = Remaining free gas volume + Remaining adsorbed gas desorption volume + Remaining adsorbed gas adsorption term volume + Rock and bound water expansion volume (7)GfBgi+ρBGfBgiSgiφ⋅VLpipL+pi=(Gf−Gp−Gk+Gv)Bg+BgρBGfBgiSgiφ(VLpipL+pi−VLppL+p) +ρBGfBgiSgiφ⋅VLppL+p+GfBgiSgi(Cf+CwSwi)(pi−p)

Setting A=(1+BgiρBSgiφVLpipL+p)−1, then (8)Gf=GA

By bringing Eq. (8) into Eq. (7) and dividing both sides by GBgi at the same time: (9)(1+ρB1Sgiφ(VLpipL+pi−VLppL+p)+BgρB1SgiφVLppL+p−1Sgiφ(Cf+CwSwi)(pi−p))A⋅pz=piziG−Gp−Gk+GvG

Setting Enhanced gas deviation factor: (10)z∗=z[1+ρB1Sgiφ(VLpipL+pi−VLppL+p)+BgρB1SgiφVLppL+p−1Sgiφ(Cf+CwSwi)(pi−p)]A

The material balance equation, which accounts for adsorption-desorption processes and inter-well connectivity, is as follows: (11)pz∗=pizi∗⋅[G−Gp−Gk+GvG]

From Eq. (11), Accounting for adjacent well interference exhibiting sequential j − 1 → j → j + 1 chained conductivity, the material balance equation for the j well (1 < j < n) is: (12)pjzj∗=pizi∗⋅[Gj−Gpj−Gj(j+1)+G(j−1)jG]

In Eq. (12): G_j(j+1) and G_(j−1)j are the cumulative gas flurries from well j to well j + 1 and from well j − 1 to well j, respectively, at a given time, 10⁸ m³. In this paper, it is assumed that well j crossflow to well j + 1, and j − 1 crossflow to well j. The amount of crossflow between well j and a non-adjacent well is zero.

The material balance equation of the 1st well is: (13)p1z1∗=pizi∗⋅[G1−Gp1−G12G]

The material balance equation for the n-th well is: (14)pnzn∗=pizi∗⋅[Gn−Gpn+G(n−1)nG]

Eq. (11) is the material balance equation for shale gas wells, which accounts for adsorption, desorption, and inter-well connectivity. To facilitate the crossflow calculation, this study employed the methodology outlined in reference [27] for the solution.

When the reserves are known, Eqs. (12)–(14) are actually functions about the pressure of each well, then Eqs. (12)–(14) are rewritten as: (15)Fj(p1,p2,⋅⋅⋅,pn−1,pn)=pjzj∗−pizi∗Gj(Gj−Gpj−Gj(j+1)+G(j−1)j)=0 (16)F1(p1,p2,⋅⋅⋅,pn−1,pn)=p1z1∗−piziG1(G1−Gp1−G12)=0 (17)Fn(p1,p2,⋅⋅⋅,pn−1,pn)=pnzn∗−piziGn(Gn−Gpn+G(n−1)n)=0

For the calculation of gas crossflow from well j to well k at a given time in Eq. (12), we assume Darcy’s law applies, resulting in the following equation: (18)qjkBg(p)=αkjkAjkμg(p)Ljk(pj−pk)

There is: (19)Bg=ZTpscpTsc (20)qjk=pTsczTpscαkjkAjkμg(p)Ljk(pj−pk)

Setting: (21)D=1+ρB1Sgiφ(VLpipL+pi−VLppL+p)+BgρB1SgiφVLppL+p−1Sgiφ(Cf+CwSwi)(pi−p)

Then it is obtained from Eq. (10): (22)z∗=zDA,z=z∗DA

The pseudo-pressures for Well j and Well k are respectively defined as: (23)mj=∫pscpjpμgzdp=∫pscpjpμgz∗DAdp,mk=∫pscpkpμgzdp=∫pscpkpμgz∗DAdp

Then: (24)qjk=αkjkAjkLjkTscpscT(mj−mk)

To quantitatively characterize the connectivity between Well j and Well k, connected conductivity: (25)Tjk=kjkAjkLjk

Since the accurate acquisition of average permeability and the contact area between wells is practically challenging, the introduction of connectivity transmissibility avoids potential errors from the direct calculation.

Then Eq. (24) can be rewritten as: (26)qjk=αTjkSr(mj−mk),Sr=TscpscT

At the moment t + Δt, the cumulative gas crossflow from well j to well k is solved using the iterative step-by-step method, which is calculated as: (27)Gjk(t+Δt)=Gjk(t)+0.5[qjk(t)+qjk(t+Δt)]Δt

Substituting Eq. (24) into Eq. (25) obtains: (28)Gjk(t+Δt)=Gjk(t)+0.5Tjk0Sr{[mj(t)−mk(t)]+[mj(t+Δt)−mk(t+Δt)]}Δt

To ascertain the formation pressure of each well at any given moment and the volume of inter-well crossflow, the Newton-Raphson iterative method for nonlinear systems of equations was employed in conjunction with the established material balance calculation model for a well group. The calculation formula is as follows: (29)∂Fj∂p1Δp1l+1+∂Fj∂p2Δp2l+1+∂Fj∂p3Δp3l+1+⋯+∂Fj∂pnΔpnl+1=Fj(p1l,p2l,p3l,⋯pnl)

In Eq. (29), l is the number of iterations. According to Eq. (29), the nonlinear iterative matrix equation can be constructed: (30)[∂F1∂p1∂F1∂p2⋯∂F1∂pn∂F2∂p1∂F2∂p2⋯∂F2∂pn⋮⋮⋯⋮∂Fn∂p1∂Fn∂p2⋯∂Fn∂pn][Δp1l+1Δp2l+1⋮Δpnl+1]=[F1(p1l,p2l,⋯,pnl)F2(p1l,p2l,⋯,pnl)⋮Fn(p1l,p2l,⋯,pnl)]

The formula for each variable in the Jacobi coefficient matrix on the left-hand side of Eq. (30) is: (31)∂Fj∂pj=1zj∗−pjzj∗dzj∗dpj+pizi∗Sr2Gj(Tj(j+1)−T(j−1)j)(pjμgz∗DA)jt+ΔtΔt

Connectivity exists between neighboring wells, then: (32)∂Fj∂pj+1=pizi∗SrTj(j+1)2Gj(pμgz∗DA)j+1t+ΔtΔt,∂Fj∂pj−1=pizi∗SrT(j−1)j2Gj(pμgz∗DA)j−1t+Δt

No connectivity between non-adjacent wells: (33)∂Fj∂pk=0(j<k),∂Fj∂pm=0(j>m)

According to Eqs. (31)–(33), it can be seen that the constructed Jacobi iteration coefficient matrix is a tridiagonal coefficient matrix. Therefore, the pressure of each well at each time step can be solved by Eq. (30).

Formation pressure and crossflow in the CN1 platform infill well group were determined using the methodology from Section 3.1. Initial parent and child well pressures were derived from Diagnostic Fracture Injection Testing (DFIT), and initial reserves were estimated via declining production analysis. Inter-well conductivity was initialized using Eq. (25). The model computed formation pressure at discrete time steps, iteratively updating conductivity and crossflow values based on pressure build-up data. Results are shown in Fig. 11.

Fig. 11 indicates strong agreement between simulated and measured pressures, validating the model’s reliability. After infill drilling, the child well’s initial pressure was lower than the parent well. However, prolonged parent well production prior to child well activation caused reservoir pressure decline. Consequently, child well pressure exceeded parent well pressure during activation, triggering crossflow.

To validate the computational accuracy, this study uses the Rate Transient Analysis (RTA) module in IHS Harmony™ [28] to simulate parent well formation pressure before infill drilling (pr-2700 days in Fig. 11). A comparison between our method and RTA results (Fig. 12) shows consistent pressure trends and numerical alignment, with a mean relative error <5%, confirming the method’s reliability for single-well pressure prediction.

However, after child well activation (i.e., post-fracturing), the original single-well model fails to accurately predict pressures due to hydraulic connectivity between parent and child wells via engineered fractures. Post-infill pressure calculations therefore rely on measured formation pressure data (Fig. 11).

Figs. 13 and 14 calculate the instantaneous and cumulative crossflows from each child well to the parent well, respectively. Well 4 had 471 × 10⁴ m³ of crossflow to well 1 and 579 × 10⁴ m³ of crossflow to well 2. Well 5 had 433 × 10⁴ m³ of crossflow to well 2 and 313 × 10⁴ m³ of crossflow to well 3.

As production continues, child well pressure declines, reducing the pressure differential between child and parent wells. Consequently, instantaneous crossflow to the parent well gradually decreases. The study defines negligible crossflow as instantaneous values below 10% of the parent well’s pre-infill production rate. Using this threshold, the cumulative crossflow volume from child to parent wells—equivalent to the parent well’s EUR increment post-infill—was calculated (Table 6).

EUR can be estimated via the Rate Transient Analysis (RTA) method once a gas well reaches boundary-dominated flow (BDF). Shale gas wells typically require years of linear flow before achieving BDF [29,30]. Diagnostic plots for Wells CN4 and CN5 (Figs. 15 and 16) confirm both wells have entered BDF due to inter-well interference: infill well production propagates into parent well depletion zones, accelerating BDF onset. The multi-stage fractured horizontal well model was applied to calculate EUR. Results show simulated EURs for Wells CN4 and 5 are 0.78 × 10⁸ m³ and 0.85 × 10⁸ m³, respectively.

The EUR for the CN1 platform can be ascertained once it is confirmed that shale gas infill wells are suitable for EUR calculations using the horizontal well multi-stage fracturing analytical model. Additionally, parent wells can be employed to compute post-infill EUR by adding the pre-infill calculated EUR to the total crossflow volume. Table 7 presents the EUR calculations for the parent wells both prior to and following infill.

Post-infill analysis reveals EUR increments of 0.04~0.12 × 10⁸ m³ across three parent wells, cumulatively reaching 0.22 × 10⁸ m³. The CN2 well is located between the two child wells and obtains recharge from the two infill wells, with the largest incremental increase in EUR. The total EUR of the two infill wells is 1.63 × 10⁸ m³ and adding the increased EUR of the parent well, the EUR of the infill platform increases by 1.85 × 10⁸ m³.