Fracture-matrix flow diagnostics for CCUS-oriented fractured gas reservoirs: a simplified analytical method and field application

1 Introduction

CCUS is increasingly viewed as an integrated energy-system and subsurface-engineering process rather than as a stand-alone capture technology. In parallel, CO₂-based reservoir fracturing and CCUS have become prominent research focuses in reservoir stimulation and enhanced oil and gas recovery, because CO₂ can simultaneously serve as a stimulation or displacement medium and provide opportunities for geological carbon storage. Recent studies have addressed thermo-hydraulic-mechanical coupling and fracture-controlled flow behavior in enhanced geothermal reservoirs (Li et al., 2026), particle transport and suspension in CO₂ fracturing fluids for reservoir stimulation and enhanced oil recovery (Li et al., 2025), and CO₂ replacement in gas-hydrate reservoirs for simultaneous methane production and carbon sequestration (Wu et al., 2026). Broader reviews have likewise identified CO₂-assisted fracturing and geological carbon storage as active research hotspots and have highlighted the emerging integration of fracturing, enhanced hydrocarbon recovery and long-term CO₂ storage (Han et al., 2024; Zhao et al., 2026). Within this broader research context, depleted gas reservoirs and fractured formations can offer large pore volumes, extensive geological information and existing well infrastructure. These advantages are accompanied by specific engineering risks: connected fractures may enhance injectivity but can also create preferential migration pathways, whereas matrix blocks provide storage capacity but communicate with fractures over longer time scales (IPCC, 2005; Bachu, 2008). Rapid diagnostics that separate fracture transmissibility, matrix storage participation and near-wellbore impairment are therefore essential for storage-site screening, injection design, pressure management and monitoring optimization.

Production-dynamics analysis provides a practical basis for rapid reservoir evaluation. Decline curve analysis (DCA) remains widely used because it requires limited data and can deliver fast production forecasts (Kamari et al., 2017; Khanal et al., 2017). However, classical empirical decline models assume boundary-dominated behavior and relatively stable operating conditions. These assumptions are often inconsistent with early fractured- or tight-gas production, where transient fracture depletion, changing bottomhole pressure, multiphase cleanup and delayed matrix recharge may dominate the observed response (Cheng and Yang, 2021; Hu et al., 2017; Nguyen and Chan, 2005; Liu et al., 2019). If such data are used directly to infer productivity, injectivity or connected volume, the resulting well-test interpretation can distort engineering decisions.

Rate-transient and hybrid decline methods partly address these limitations by combining production data with concepts from pressure-transient analysis. Fetkovich-type workflows and hybrid analytical methods improve performance forecasting under transient conditions (Boogar et al., 2011; Clarkson and Qanbari, 2015), and fracture-dominated gas-reservoir workflows have extended these ideas to unconventional and fractured systems (Clarkson, 2013; Duong, 2014). Recent deterministic decline and analytical production-analysis studies further clarify the applicability of these methods under complex reservoir conditions (Sureshjani and Gerami, 2011; Yuan et al., 2020; Yehia et al., 2023). Nevertheless, many workflows still collapse the reservoir into a single effective continuum or require parameter-rich inversion when fracture and matrix systems respond on different time scales.

The dual-continuum view is more appropriate for naturally fractured reservoirs. In this representation, the fracture network controls transmissibility and early pressure communication, while the matrix provides storage and delayed recharge. The same physical separation is central to CCUS operation. In cyclic CO₂ injection, gas storage or pressure-supported subsurface-energy systems, fracture-dominated pressure propagation controls short-term injectivity and containment risk, whereas matrix-dominated storage controls long-term pressure support and capacity. A compact pressure-buildup method capable of distinguishing these components from routine field data can reduce uncertainty before detailed reservoir simulation or site-specific geomechanical analysis is performed.

To examine the transferability of the proposed diagnostic beyond a single field case, the framework is evaluated using pressure-buildup datasets from two fractured-gas-reservoir wells within the same reservoir block. The two cases are analyzed using the same pressure-buildup interpretation procedure and parameter-conversion workflow, allowing the consistency of the inferred fracture-, matrix-, and near-wellbore responses to be assessed across independent field datasets. The objective is to provide a regression-friendly tool that supports rapid reservoir evaluation, improves the reliability of well-test interpretation and generates engineering indicators for CCUS-oriented storage screening, cyclic operation design and pressure management. Compared with full numerical inversion, the proposed workflow emphasizes implementability, physical interpretability and direct use of routine pressure and production data.

2 Materials and methods

2.1 Dual-continuum representation and pressure processes

The reservoir is represented as a coupled fracture-matrix system. Fractures provide the dominant transmissibility and control short-time pressure communication with the wellbore, whereas the matrix is the principal storage domain and recharges the fracture system after pressure depletion. During shut-in, pressure recovery is interpreted as a sequence of three overlapping mechanisms: rapid near-wellbore pressure dissipation associated with near-wellbore flow resistance, cleanup effects and short-time wellbore-fluid re-equilibration, fracture-network pressure redistribution, and delayed matrix-to-fracture recharge. The assumed pressure distribution during the early transient stage is schematically illustrated in Figure 1.

The simplified model is based on four assumptions. First, the matrix constitutes the principal storage domain, whereas the fracture network provides the dominant transmissive pathway. During shut-in, matrix-to-fracture exchange is represented by a pseudo-steady transfer process. Second, pressure equilibration occurs at three spatial scales: matrix-to-fracture exchange, pressure redistribution within the fracture network, and near-wellbore pressure relaxation. Third, elastic wellbore-volume changes are neglected in the reservoir-scale matrix-fracture material balance because the wellbore volume is small relative to the connected reservoir pore volume; the local near-wellbore pressure response is nevertheless retained through the wellbore compressibility term. Fourth, the earliest data dominated by non-ideal wellbore storage, gauge stabilization, and short-time wellbore-fluid re-equilibration are excluded from regression.

2.2 Analytical derivation of the multi-exponential formulation

To account for the pressure dependence of the gas deviation factor, the analytical derivation is formulated using the pressure-transformed variable p = P/Z, where P is the actual pressure and Z is the gas deviation factor. The fitted response is subsequently converted back to actual pressure P for field interpretation and presentation. Let p _b, p _f, p _f’ and p _w denote the transformed pressures corresponding to the average matrix pressure, average fracture pressure, fracture pressure adjacent to the wellbore, and bottomhole pressure, respectively.

Under pseudo-steady matrix-fracture exchange, taking q _b as positive from the matrix toward the fracture system, the matrix and fracture material-balance relations can be written as Equation 1:where q _b is the matrix-to-fracture flow rate; V _b and V _f are the effective matrix and fracture storage volumes, respectively; C _b and C _f are the corresponding effective compressibilities; A ₁ is the matrix-fracture transfer coefficient; and t is the shut-in time.

q b = − V b C b d p b d t = A 1 p b − p f = V f C f d p f d t (1)

Eliminating q _b and p _f from Equation 1 gives Equation 2:

d 2 p b d t 2 + A 1 V b C b + V f C f V b C b V f C f d p b d t = 0 (2)

The matrix-fracture attenuation coefficient is defined by Equation 3:and applying the long-time condition p _b, p _f → p _s together with the initial material-balance condition given by Equation 4:where p _s is the stabilized transformed reservoir pressure, and p _b0 and p _f0 are the transformed matrix and fracture pressures at the beginning of shut-in, respectively.

α 1 = A 1 V b C b + V f C f V b C b V f C f (3)

V b C b p b 0 − p s = V f C f p s − p f 0 (4)

The average fracture pressure is then given by Equation 5:

p f = p s − p s − p f 0 e − α 1 t (5)

As illustrated in Figure 1, the fracture pressure adjacent to the wellbore differs from the average fracture pressure during fracture-network redistribution. The original fracture-flow representation is given by Equation 6:where B _f represents the initial pressure difference associated with pressure redistribution within the fracture network.

p f ′ = p f − B f e − α 2 t (6)

The remaining pressure difference between the fracture system and the wellbore is governed by Equation 7:where V _w is the effective wellbore volume, C _w is the effective compressibility of the wellbore system, and A ₂ is the near-wellbore flow coefficient. Letting α ₃ = A ₂/(V _w C _w) and substituting the matrix-fracture and fracture-redistribution solutions into the near-wellbore balance yields the compact pressure-loss expression:where p _s is the stabilized reservoir pressure, p _w(t) is bottomhole pressure during shut-in.

V w C w d p w d t = A 2 p f ′ − p w (7)

Δ p t = p s − p w t = C e − α 1 t + D e − α 2 t + E e − α 3 t (8)

The coefficients in Equation 8 follow from the analytical solution given by Equation 9:

C = α 3 p s − p f 0 α 3 − α 1 , D = α 3 B α 3 − α 2 , E = p s − p w 0 − C − D (9)

Here, C, D and E are pressure-loss coefficients, while α ₁, α ₂ and α ₃ are the corresponding attenuation coefficients. Accordingly, C, D and E have dimensions of pressure, whereas α ₁, α ₂ and α ₃ have dimensions of inverse time.

Within the assumptions of the model, the C-α ₁ component originates from matrix-fracture pressure equilibration, the D-α ₂ component represents pressure redistribution within the fracture network, and the E-α ₃ component represents near-wellbore pressure relaxation. The third component reflects the combined effect of near-wellbore flow resistance and local wellbore storage rather than an isolated formation-damage parameter. The expected hierarchy is α ₃ > α ₂ > α ₁: near-wellbore effects dissipate fastest, fracture-network transients are intermediate, and matrix recharge persists longest.

Equation 8 is the core diagnostic expression. It provides a compact representation of the three pressure-relaxation processes retained in the adopted dual-continuum model; their mechanistic interpretation is illustrated in Figures 2, 3.

As shown in Figure 3, the labels Q–S and U–W are geometric reference points introduced only to illustrate the graphical decomposition of the pressure-buildup response. The curve QRS represents the matrix–fracture equilibration component, and RS is the approximately linear late-time segment used to characterize the matrix-controlled response. The segment MN represents the near-wellbore pressure-relaxation component. The curve UVW represents the fracture-controlled component. After the near-wellbore contribution becomes negligible, the segment VW approaches a linear trend; extrapolation of this segment to t = 0 provides the reference intercept associated with the reference fracture-network response without the additional near-wellbore pressure-loss contribution. The difference between the actual early-time intercept and this extrapolated reference is used to identify the additional near-wellbore pressure loss.

2.3 Parameter estimation and inversion workflow

After fitting Equation 8, the coefficients are converted into effective, scale-dependent reservoir indicators. The total connected pore volume is estimated by material balance using Equation 10:where V _t is the total connected pore volume, G _p is cumulative gas production before buildup, B _g is gas formation volume factor, C _t is effective total compressibility and Δp is the pressure depletion between the initial and stabilized states.

V t = G p B g / C t Δ P (10)

The fracture-controlled volume is estimated from the early production interval using the fitted fracture-flow component in Equation 8. Under the effective fracture-storage approximation adopted in the original formulation, the second exponential term, De^−α ₂ ^t, is taken as the characteristic pressure-loss response associated with the connected fracture system over the interpreted interval. Accordingly, the equivalent formation flow rate at the beginning of this interval is approximated by the elastic response of the fracture-controlled volume, as given by Equation 11:

q i B g = − V f C f d D e − α 2 t dt t = 0 (11)

The derivative in Equation 11 is evaluated using Equation 12:the effective fracture-controlled volume is estimated as:where q _i is the representative early production rate and C _f is fracture-system compressibility. Because the calculation uses an effective fitted fracture-flow response and an assumed compressibility, V _f is interpreted as an effective lower-bound fracture-controlled volume rather than a unique intrinsic fracture pore volume. The corresponding effective matrix-controlled volume is then obtained from Equation 14:

− d D e − α 2 t dt t = 0 = α 2 D (12)

V f = q i B g α 2 D C f (13)

V b = V t − V f (14)

The practical workflow consists of five steps: data screening, exclusion of wellbore-storage dominated early data, regression of Equation 8, conversion of fitted coefficients into effective reservoir parameters, and engineering interpretation for deliverability, injectivity and storage assessment.

2.4 Interpretation scope for CCUS-oriented diagnostics

The method is designed for pressure-buildup or pressure-monitoring records that contain a recognizable fracture-controlled pressure recovery followed by delayed matrix recharge. It is most useful when production before shut-in is constant or piecewise constant and when early wellbore-storage effects can be excluded. For CCUS-oriented applications, the same requirements correspond to monitoring intervals in which pressure signals preserve information on fracture transmissibility, matrix participation and near-wellbore impairment.

The interpreted parameters are effective and scale-dependent. They should be integrated with geological, petrophysical and operational evidence rather than interpreted as unique rock properties. In a CCUS workflow, this pressure-diagnostic method is most valuable as a front-end engineering tool: it can rapidly rank wells or candidate reservoirs, constrain injectivity and pressure-management scenarios, and provide physically based parameters for subsequent compositional, geomechanical and full-field simulation studies.

3 Results

3.1 Pressure attenuation coefficients

Sensitivity analysis was used to clarify how the six fitted coefficients in Equation 8 influence diagnostic curve shape. A one-at-a-time sensitivity analysis was performed for the six fitted coefficients. When one coefficient was varied, the remaining five coefficients were held constant at their respective central values within the investigated parameter ranges. The baseline values were C = 0.05 MPa, D = 0.03 MPa, E = 0.04 MPa; α ₁ = 0.002 h^-1, α ₂ = 0.01 h^-1 and α ₃ = 2.5 h^-1.

The attenuation coefficients α ₁, α ₂ and α ₃ control the characteristic time scales of matrix-fracture equilibration, fracture-network redistribution and near-wellbore pressure relaxation, respectively. Increasing α₁ shortens the matrix-fracture equilibration component. For a fixed matrix pressure-change coefficient C, a larger α ₁ is consistent with a smaller effective matrix-storage contribution or faster pressure communication between the matrix and fractures. Increasing α ₂ shortens the fracture-network redistribution component when D is fixed, indicating a shorter characteristic response of the connected fracture system. Increasing α ₃ shortens the near-wellbore relaxation component when E is fixed; because α ₃ contains both near-wellbore flow resistance and local wellbore compressibility, it is interpreted as a relaxation-rate parameter rather than as an independent measure of near-wellbore impairment magnitude. These effects of the attenuation coefficients on diagnostic curve shape are summarized in Figure 4.

3.2 Pressure-change coefficients

The pressure-change coefficients C, D and E determine the magnitude assigned to each pressure-loss component. Increasing C magnifies the matrix-fracture equilibration; conversely, a smaller C at fixed α ₁ indicates a larger effective matrix storage volume. Increasing D enlarges the fracture-flow contribution, within the effective fracture-storage approximation used for volume estimation, whereas a smaller D at fixed α ₂ indicates a larger effective fracture-controlled volume. Increasing E strengthens the near-wellbore pressure-relaxation contribution. When E is very small, the response shifts almost directly from wellbore-storage effects to fracture-dominated flow, suggesting limited additional near-wellbore resistance. These effects of the pressure-change coefficients are summarized in Figure 5.

3.3 Pressure-buildup fitting

The six parameters in Equation 8 were obtained through nonlinear regression of the measured pressure-buildup data. The objective function was defined as the mean squared relative pressure error using Equation 15:where X is the number of pressure data points included in the regression interval,Δp _o is the measured pressure change, andΔp _c is the pressure change calculated from Equation 8.

Φ = 1 X ∑ i = 1 X Δ p o t i − Δ p c t i Δ p o t i 2 (15)

The nonlinear optimization was performed using the Trust-Region Reflective method. The initial values were selected based on the characteristic magnitudes of the three pressure-loss components identified from the semi-log diagnostic plots. The attenuation coefficients were constrained according to the expected time-scale ordering: α ₁<α ₂<α ₃ to maintain the physical interpretation of the near-wellbore, fracture-network, and matrix-equilibration processes. The corresponding initial parameter vector was set as C = 0.01, D = 0.01, E = 0.01; α ₁ = 10^–4, α ₂ = 10^–3, α ₃ = 10^–2. To avoid non-physical solutions, all pressure-loss coefficients and attenuation coefficients were restricted to positive values. The parameter bounds used in the regression were 0∼10. The regression was considered converged when the relative change in the objective function between successive iterations was less than 10^–4. A maximum of 10⁴ iterations was imposed as an additional stopping criterion.

4 Field applications and cross-well validation

4.1 Field background and well-test workflow

Two field wells were selected to evaluate the proposed pressure-buildup diagnostic under different well and operating conditions within the same reservoir block. Well A and Well B are horizontal wells located in a CCUS pilot block of a Bohai Sea gas field, China. Both wells contain pressure-buildup records suitable for identifying fracture-network pressure redistribution and delayed matrix participation after exclusion of the earliest wellbore-storage-dominated data.

Well A was selected as the primary field application case because its pressure-buildup response records the coupled effects of fracture communication, matrix recharge, and near-wellbore impairment under conditions relevant to CO₂ storage-oriented operation. The producing interval is located in Tertiary–Quaternary strata within a Paleozoic buried-hill system. Drilling was completed in June 2020. The final measured depth is 5,276 m and the true vertical depth is 4,466.9 m.

Trial production began on 26 July 2020 using a 9.44 mm choke. The estimated gas rate was 5.70 × 10⁴ m³/d and wellhead pressure was 13.8 MPa. By the end of August, gas rate increased to 8.33 × 10⁴ m³/d while wellhead pressure declined to 12.2 MPa, indicating incomplete flowback of completion fluids. A systematic well test was conducted from 9 to 19 September 2021 using memory pressure gauges. Five operating modes were tested from 10 to 13 September, followed by a pressure-buildup test from 13 to 19 September. The lower gauge provided the data used for interpretation, and the corresponding pressure and temperature records are shown in Figure 6.

Well B was completed on 13 August 2022 with a measured depth of 5,698 m and a true vertical depth of 4,372 m. Prior to shut-in, the well was produced at approximately 6.22 × 10⁴ m³/d and wellhead pressure was 12.4 MPa.

4.2 Interpretation of well A

Well A is used as the primary field application case. The conventional deliverability analysis, pressure-buildup fitting, component decomposition, and conversion of fitted coefficients into effective reservoir indicators are first performed for this well.

Well A was tested under five choke sizes. The deliverability test data are summarized in Table 1. The tests at 6.10, 6.95, 7.78 and 8.20 mm were used to establish the deliverability equations. According to the method of Li et al. (2021), the calculated AOF of Well A is approximately 7.95 × 10⁴ m³/d. This value provides useful productivity benchmarks, but they do not separate matrix-fracture equilibration, fracture-network redistribution, near-wellbore pressure loss or fracture-controlled volume. Accordingly, the AOF result is retained as conventional deliverability benchmark, but it dose not interpreted directly as sustainable CO₂ injection or storage capacities. This distinction is particularly important in fractured systems, where short-time fracture communication and delayed matrix participation occur on different time scales.

TABLE 1. Productivity test data for Well A.

The pressure-buildup data were fitted using Equation 8, as shown in Figure 7a. A cutoff comparison was performed using regression starting times of 0.001 h and 1 h. The difference in the pressure-fitting error between the two fitting windows was approximately 3.2%. This relatively small change indicates that the overall pressure-match quality is not strongly affected by the cutoff selection. Nevertheless, because the data before approximately 1 h exhibit clear wellbore-storage and other short-time non-ideal effects, 1 h was adopted as the final cutoff for reservoir-parameter interpretation. Regression was performed after the onset of a stable semi-log trend, so that the interpreted interval is dominated by the fracture-network and matrix-fracture pressure-relaxation components retained in Equation 8.

The fitted model coefficients and production-performance inputs are listed in Table 2. The fitted pressure-loss coefficients are C = 6.256 MPa, D = 3.305 MPa and E = 3.224 MPa, and the corresponding attenuation coefficients are α ₁ = 0.0042 h^-1, α ₂ = 0.065 h^-1 and α ₃ = 0.8756 h^-1. The coefficients C, D and E are defined in the P/Z-transformed pressure domain and retain pressure units because Z is dimensionless. The effective fluid compressibility used in the fracture-volume calculation is 0.058 MPa^-1. The ordering α ₃ > α ₂ > α ₁ is consistent with rapid near-wellbore relaxation, intermediate fracture-network redistribution and delayed matrix-fracture equilibration.

TABLE 2. Production-performance inputs and fitted coefficients for Well A and Well B.

For Well A, the fitted near-wellbore pressure-loss component has an initial amplitude of E = 3.224 MPa, and an attenuation coefficient of α ₃ = 0.8756 h^-1, corresponding to a characteristic relaxation time of approximately 1.14 h. Based on the completion history and early production behavior, this localized pressure loss may be associated with mud invasion and incomplete flowback of completion fluids. For CCUS-oriented evaluation, the result suggests that near-wellbore flow impairment may constrain early injectivity potential; cleanup, stimulation or completion optimization should therefore be evaluated before the production-test result is transferred to an injection-allocation decision.

The lower-bound estimate of the fracture-controlled reservoir volume is approximately 2058.2 m³, while the matrix-controlled reservoir volume is approximately 11,039.85 m³. These values are effective, scale-dependent indicators rather than unique intrinsic rock properties. The component-wise decomposition of pressure loss is shown in Figure 8a. The two controlled-volume estimates sum to 13,098.05 m³, of which approximately 15.7% is fracture controlled and 84.3% is matrix controlled. These reservoir-volume indicators are not directly commensurate with the AOF values, which are surface-rate benchmarks in m³/d. A rigorous conversion of these production-derived indicators into sustainable CO₂ injection rates or storage capacities would require a specified injection-pressure window together with CO₂ PVT properties.

4.3 Cross-well consistency evaluation using well B

Well B was analyzed independently using the same pressure-buildup fitting procedure and parameter-conversion workflow applied to Well A. Because the two wells are located within the same block, the fracture-system compressibility was not independently re-estimated for Well B. Instead, C _f = 0.058 MPa^-1, identical to the value used for Well A, was retained in the fracture-volume calculation. This treatment avoids introducing an additional reservoir-property input and provides a consistent basis for cross-well comparison. The fracturing-fluid volume used in Well B was approximately 18% greater than that used in Well A. This completion difference was not introduced as an additional fitting parameter and is used only as supporting engineering evidence when interpreting the fitted pressure response.

The pressure-buildup fitting result for Well B is shown in Figure 7b. The calculated pressure response reproduces the overall measured pressure-recovery trend, while the corresponding pressure-derivative curve captures the principal transition between the early fracture-dominated response and the later matrix-controlled behavior. The fitted pressure-loss coefficients are C = 6.842 MPa, D = 3.612 MPa, and E = 2.986 MPa, and the corresponding attenuation coefficients are α ₁ = 0.0038 h^-1, α ₂ = 0.058 h^-1, and α ₃ = 0.9325 h^-1. As for Well A, the fitted coefficients satisfy the expected ordering α ₃ > α ₂ > α ₁, which is consistent with rapid near-wellbore relaxation, intermediate fracture-network redistribution, and delayed matrix-fracture equilibration.

The corresponding characteristic relaxation times, calculated as τᵢ = 1/αᵢ, are approximately 263.2 h, 17.2 h, and 1.07 h for the matrix-fracture, fracture-network, and near-wellbore components, respectively. The component decomposition in Figure 8b is consistent with this separation of time scales. The near-wellbore component decays rapidly during the initial period, the fracture-region pressure loss persists over an intermediate interval, and the slowly attenuating matrix-region component becomes dominant at late time. The persistence of the matrix-related contribution indicates that the pressure response of Well B cannot be represented solely by rapid fracture communication.

Using the equivalent formation-flow rate of 27.81 m³/h, the fitted fracture coefficient D = 3.612 MPa, α ₂ = 0.058 h^-1, and the common fracture-system compressibility C _f = 0.058 MPa^-1, Equation 13 gives an effective fracture-controlled volume of approximately 2.29 × 10³ m³, consistent with the reported value of 2,289.1 m³. With a total connected pore volume of 14,271.62 m³, the corresponding matrix-controlled volume is 11,982.52 m³. The fracture- and matrix-controlled volumes therefore account for approximately 16.0% and 84.0% of the total connected pore volume, respectively.

4.4 Cross-well comparison and validation

The results from Wells A and B demonstrate a consistent three-component pressure-relaxation structure despite differences in their production conditions and fitted coefficients. For both wells, the attenuation coefficients maintain the ordering α₃ > α₂ > α₁, confirming the same physical sequence of rapid near-wellbore dissipation, intermediate fracture-network redistribution, and long-duration matrix-fracture equilibration. The pressure and pressure-derivative comparisons in Figures 7a,b, together with the component decompositions in Figures 8a,b, therefore show that the same analytical formulation can reproduce the principal pressure-buildup characteristics of two wells within the same block.

Quantitatively, Well B has slightly larger matrix- and fracture-related pressure-loss coefficients than Well A. The fitted C coefficient increases from 6.256 to 6.842 MPa, corresponding to an increase of approximately 9.4%, while D increases from 3.305 to 3.612 MPa, or approximately 9.3%. In contrast, the near-wellbore coefficient E decreases from 3.224 to 2.986 MPa, approximately 7.4% lower than that of Well A. The attenuation coefficient α₃ also increases from 0.8756 to 0.9325 h^-1, indicating slightly faster dissipation of the near-wellbore contribution. Taken together, the smaller E and larger α₃ indicate that the fitted near-wellbore pressure-loss component in Well B is both smaller in amplitude and more rapidly attenuated than in Well A.

The total connected pore volume increases from 13,098.05 m³ for Well A to 14,271.62 m³ for Well B, an increase of approximately 9.0%. The effective fracture-controlled volume increases from 2058.2 to 2,289.1 m³, corresponding to an increase of approximately 11.2%, while the matrix-controlled volume increases from 11,039.85 to 11,982.52 m³, or approximately 8.5%. Despite these differences in absolute volume, the internal partitioning remains very similar: the fracture-controlled fraction is approximately 15.7% for Well A and 16.0% for Well B, whereas the matrix-controlled fraction is approximately 84.3% and 84.0%, respectively. This similarity supports a consistent effective fracture–matrix storage partitioning between the two wells at the investigated pressure-diagnostic scale.

The comparison should nevertheless be interpreted as an engineering association rather than a unique causal attribution. No additional fracture-geometry, proppant-placement, or independent conductivity data are introduced in the present analysis. Therefore, the 18% difference in fracturing-fluid volume is used as completion evidence supporting the pressure-diagnostic interpretation, rather than as an independent variable in the inversion. The observed agreement between the completion history and the fitted response strengthens the physical plausibility of the cross-well interpretation without increasing the data requirements of the proposed workflow.

The time-scale parameters also remain comparable between the two wells. Relative to Well A, α₁ decreases from 0.0042 to 0.0038 h^-1 and α₂ decreases from 0.065 to 0.058 h^-1, indicating slightly slower matrix-fracture equilibration and fracture-network redistribution in Well B. The characteristic matrix-fracture, fracture-network, and near-wellbore relaxation times are approximately 238.1 h, 15.4 h, and 1.14 h for Well A and 263.2 h, 17.2 h, and 1.07 h for Well B, respectively. Thus, although the fitted magnitudes differ between the two wells, their separation of characteristic time scales is highly consistent.

The cross-well agreement in model structure, attenuation ordering, effective fracture-volume magnitude, and completion-consistent near-wellbore behavior provides additional support for the transferability of the proposed diagnostic within the investigated block. At the same time, the comparison should remain scale aware. The calculated V _f, V _b, and V _t values are effective pressure- and material-balance-based reservoir indicators and should not be interpreted as direct measurements of geological fracture or matrix pore volume, or as sustainable CO₂ storage capacity. For Well B, the total connected pore volume estimated using the same material-balance workflow as for Well A is 14,271.62 m³, resulting in an effective matrix-controlled volume of 11,982.52 m³ after subtraction of the fracture-controlled volume. The similar fracture–matrix volume partitioning obtained for the two wells therefore provides an additional well-level consistency check of the simplified fracture–matrix decomposition within the investigated block, while broader geological validation is still required before these effective volumes are interpreted as intrinsic reservoir properties.

5 Discussion

5.1 Correction of well-test interpretation bias

The two field cases show why a mechanism-based pressure-buildup diagnostic is useful for CCUS-oriented fractured reservoirs. Conventional AOF and productivity interpretations provide a single capacity benchmark, but they do not indicate whether that capacity is controlled by short-lived fracture depletion, sustainable matrix recharge or near-wellbore impairment. In fractured systems, an uncorrected productivity or injectivity estimate may therefore lead to unreasonable production allocation, excessive injection rates or poorly designed cyclic injection-production schedules. The proposed workflow constrains such interpretations by identifying which portion of the pressure response is attributable to connected fractures, matrix storage or near-wellbore pressure-loss effects.

For Well A and Well B, the consistent separation of near-wellbore, fracture-network, and matrix-fracture pressure responses indicates that this diagnostic can be transferred between wells within the same fractured reservoir block. The method may therefore be used to qualify rather than directly revise the injection or storage capacity inferred from routine gas-well tests. A fracture-dominated early response with weak matrix participation indicates that strong short-time pressure communication does not by itself demonstrate stable long-term storage participation. A strong near-wellbore component indicates that apparent injectivity limitation may be partly associated with completion or flow impairment, suggesting that cleanup, stimulation or completion optimization should be assessed before changing injection allocation. A strong matrix-fracture equilibration component indicates delayed storage participation, which can be carried forward as a constraint for subsequent cyclic-operation evaluation.

5.2 Preliminary implications for cyclic injection-production and circulation design

In CCUS and underground gas storage operations, reservoir performance is often governed by cyclic injection, shut-in, monitoring and production or withdrawal stages. The three fitted components provide preliminary diagnostic indicators for evaluating these cycles rather than direct design limits. The fracture-flow term characterizes the relative pressure-communication time scale and the effective connected fracture-controlled volume, which can be used to screen injection-ramp scenarios for subsequent verification. The matrix-recharge term provides an indicator of delayed storage participation and may help identify candidate shut-in or soaking periods for pressure redistribution. The near-wellbore term identifies whether a substantial part of the observed pressure loss is localized near the wellbore, in which case rate adjustment alone may not resolve the underlying impairment.

This interpretation is especially relevant where inaccurate well-test results lead to unreasonable allocation in cyclic injection-production systems. If a conventional test overestimates sustainable capacity, excessive injection may elevate pressure too rapidly and reduce containment margin. If the test underestimates capacity because near-wellbore damage masks matrix support, the storage project may be designed too conservatively. The proposed method provides a screening framework that separates transient fracture-network response from delayed matrix participation before more detailed injection testing or simulation is performed.

5.3 Preliminary storage-candidate screening and pressure-management implications

The workflow can also provide early-stage screening indicators for CCUS-oriented reservoir evaluation. A high fracture-controlled contribution is consistent with strong short-time pressure communication and may indicate injectivity potential, but it does not by itself establish sustainable injectivity or containment because connected fractures may also act as preferential pressure-propagation pathways. A high matrix-controlled contribution indicates a larger delayed storage participation at the interpreted scale, whereas a large near-wellbore contribution suggests that completion or flow impairment should be assessed before reservoir-scale performance is judged.

Pressure management is a potential downstream application, but the present diagnostic does not determine maximum injection pressure, containment limits or observation-well placement by itself. By distinguishing rapid fracture-network pressure communication from delayed matrix participation, the interpreted parameters may provide initial constraints for evaluating injection-pressure ramps, shut-in monitoring duration and the need for additional observation or interference data. The workflow can also be repeated as new pressure-buildup or falloff records become available, providing an updated diagnostic before more detailed compositional-flow and geomechanical analyses.

5.4 Implementation advantages and integration with detailed models

The main operational advantage of the proposed method is its low data requirement. It uses routine pressure and production records, avoids full numerical inversion and produces physically interpretable parameters through direct regression. This makes it suitable for preliminary reservoir ranking, rapid post-test interpretation, field-development screening and early CCUS engineering design. The workflow is not intended to provide every parameter needed for final storage certification; rather, it provides a physically constrained diagnostic layer that can prioritize candidate wells and supply initial constraints for compositional flow modeling, geomechanical containment analysis and integrated full-field studies.

The method should be applied with attention to data quality. The interpretation window must exclude wellbore-storage dominated data, and the fitted coefficients should be checked against geological and completion evidence. Because the parameters are effective at the tested scale, they should be updated when longer monitoring records, multiwell interference tests or independent fracture-characterization results become available. Within these bounds, the approach has broad deployment potential in fractured depleted-gas reservoirs and other geoenergy systems where rapid pressure diagnostics are needed.

The present field validation includes two wells from the same reservoir block and is based on production and shut-in pressure data rather than dedicated CO₂ injection/falloff tests. The cross-well consistency supports the applicability of the proposed diagnostic within the investigated block, but it does not by itself establish transferability to reservoirs with substantially different geological or fluid conditions. Consequently, the CCUS interpretations in Sections 5.1–5.3 should still be regarded as preliminary engineering implications rather than validated design rules. Site-specific injection testing, pressure-interference evidence, CO₂ PVT characterization and coupled flow-geomechanical simulation are required before the method is used to set injection limits or certify storage performance.

6 Conclusion

A simplified material-balance-based pressure-buildup diagnostic method was developed for fractured gas reservoirs using a dual-continuum fracture-matrix representation. The method expresses bottomhole pressure recovery as the sum of three exponential components associated with near-wellbore pressure relaxation, fracture-network redistribution and matrix-fracture equilibration.

The principal contribution is a compact, regression-friendly decomposition that retains the dominant fracture-matrix mechanisms while avoiding parameter-heavy numerical inversion. The fitted coefficients can be converted into effective fracture-controlled volume and matrix-controlled volume, while the fitted near-wellbore component characterizes the magnitude and relaxation rate of localized near-wellbore pressure loss.

Sensitivity analysis shows that attenuation coefficients control the time scale of each pressure-dissipation component, whereas pressure-change coefficients control the magnitude assigned to each component. These diagnostic rules reduce ambiguity in early-time fractured-reservoir interpretation and provide a clearer basis for engineering decisions.

Field applications to Wells A and Well B reproduce the measured pressure-buildup responses and consistently identify rapid near-wellbore relaxation, intermediate fracture-network redistribution, and delayed matrix-fracture equilibration. For Well A, the interpretation gives an initial near-wellbore pressure-loss amplitude of 3.224 MPa, a fracture-controlled volume of approximately 2058.2 m³, and a matrix-controlled volume of approximately 11,039.85 m³. For Well B, using the same fracture-system compressibility adopted for Well A, the estimated effective fracture-controlled volume is approximately 2,289.1 m³. The similar attenuation hierarchy and comparable fracture-controlled volumes obtained from the two wells support the consistency of the proposed diagnostic within the investigated block. For CCUS operation, the results indicate that fracture-controlled pressure communication governs the short-time response, whereas delayed matrix participation and near-wellbore impairment should be considered in injection scheduling and pressure-management evaluation.

For CCUS-oriented reservoir engineering, the method has potential as a front-end diagnostic for well-test interpretation, preliminary cyclic-operation assessment and fractured-reservoir screening. Its simplicity and reliance on routine field data make it useful for prioritizing subsequent analysis. The two-well application demonstrates cross-well consistency within the investigated reservoir block, but it does not validate direct use for injection-limit setting, storage certification, or final pressure-management design, nor does it establish universal transferability to other reservoir settings.

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Nomenclature

AOF Absolute open flow CCUS Carbon capture, utilization and storage DCA Decline curve analysis FMB Flowing material balance MD Measured depth RTA Rate-transient analysis TVD True vertical depth

Footnotes

Edited by: Qingchao Li, Henan Polytechnic University, China

Reviewed by: Fuling Wang, China University of Petroleum, Beijing, China

Yingying Guo, Southern Connecticut State University, United States