Triple-porosity Model Research Articles

Pressure Transient Analysis for a Horizontal Well in Heterogeneous Carbonate Reservoirs Using a Linear Composite Model

Carbonate reservoirs usually have strong anisotropy. Oil and gas recovery from fractured reservoirs is highly challenging due to complicated mechanisms involved in production from these reservoirs. A horizontal well completed in these reservoirs may extend through multiple zones, including homogeneous, dual-porosity, and triple-porosity formations. Traditional well test models assume that the entire length of a horizontal or multilateral well remains in the same formation with uniform properties. A well test model for pressure transient analysis of horizontal wells extending through a carbonate reservoir consisting of natural fractures, rock matrix, and vugs with different properties is presented in this study. The focus of this study is on dual-porosity (fracture-matrix) and triple-porosity (fracture-matrix-vug) reservoirs, considering the pseudosteady interporosity flows from rock matrix and vugs into fractures. A multizone triple-porosity model was established and solved by using the point source function, Green’s function, and coupling of multiple reservoir sections. The corresponding type curves were developed, and sensitivity analysis was carried out. The type curves of flow stage division reveal that a horizontal well traversing a three-section reservoir including homogeneous, dual-porosity (fracture-matrix)/triple-porosity (fracture-vug-matrix), and homogeneous sections identifies the stages of pseudosteady interporosity flow from matrix and vug into fracture, fracture pseudoradial flow, system linear flow, system pseudoradial flow, and pseudosteady flow occur in sequence. The greater the difference of permeability between the dual-porosity/triple-porosity section and the two homogeneous sections, the more obvious the interporosity flow on the pressure derivative curve. This approach satisfies the need for pressure transient analysis for a horizontal well that traverses two or more regions with distinct properties in heterogeneous carbonate reservoirs.

A triple porosity hydro-mechanical model for MX-80 bentonite pellet mixtures

This paper describes the application of a triple porosity model to characterise the hydro-mechanical behaviour of MX-80 bentonite pellet mixtures. The macroscopic behaviour of the system was assumed to be fundamentally controlled by three functional levels, the microstructure (associated with the pores existing inside the clay particle aggregates), the Macrostructure 1 (which integrates the space between the aggregates inside the pellets) and the Macrostructure 2 (related to the void space between the pellets). The role played by each functional level in the overall behaviour of the system was modelled by means of an overlapping continua approach. The usual framework in the simulation of the behaviour of compacted bentonite blocks has been adapted to describe the behaviour of the microstructure and the Macrostructure 1. To model the behaviour of the Macrostructure 2, a simplified formulation of granular materials was adopted.To illustrate the capacity of the proposed approach, two hydration tests were simulated in which significantly different pellet mixtures were used: an open mixture with a dry density of 953kg/m3, and a closed mixture with 1520kg/m3 of dry density. Despite the difference between the two mixtures, the model allowed very satisfactory fits to be obtained using in both cases the same material parameters. This shows the consistency of the proposed conceptual framework.Since the response of the two Macrostructural levels is differentiated, the model provides a richer description of the mixture behaviour than that obtained using a double porosity model. However, the interest of the model lies not only in its descriptive richness. The differentiation of the effect of both Macrostructural levels improves the description of the time evolution of the system compared with that obtained when using a double porosity model. However, if the Macrostructure 2 is small (as occurs in the second of the two tests analysed), or there is sufficient confinement for the inter-pellet void space to be considerably reduced when the microstructure swells, double porosity models can satisfactorily characterise the performance of the bentonite pellet mixture.

How transport properties of a shale gas reservoir change during extraction: A strain-dependent triple-porosity model

In this study, we consider a shale gas reservoir as a triple-porosity media consisting of organic matrix, inorganic matrix, and fractures. A strain-dependent triple-porosity model is established by accurately expressing the deformation of each medium to reveal the change in the transport properties of a shale gas reservoir during production and to predict the reservoir recovery. The deformation of each medium is based on a combination of mechanical deformation and desorption-induced shrinkage behavior, and fracture aperture as well as the difference of effective stress in each medium were considered. We find that the transport properties of shale gas reservoirs are related to the porosity and diffusion coefficient of the organic matrix, and the porosity and permeability of the fracture system and inorganic matrix. The triple-porosity model is then incorporated into the governing equations for gas flow. The finite element method is used to solve the governing equations. By comparing the simulation result with field data, analytical solution, and previous simulation result, we are able to verify the accuracy of our model. Then, we analyze and reveal in detail how the transport properties of shale gas reservoirs change during extraction through the combined evolution of gas pressure, volumetric strain, and strain induced by the adsorption/desorption of gas in the organic matrix. Finally, we conduct sensitive analysis focusing on how the initial transport properties affect their evolutions. We find that the relationship between mechanical deformation and strain induced by adsorption/desorption is not always competitive during gas extraction.

Development of new analytical model for series and parallel triple porosity models and providing transient shape factor between different regions

Fluid flow architecture in fractured reservoirs is mainly based on the dual porosity model. In this model, the matrix block is considered as a fluid storage source and fracture as a flow path. Nevertheless, in naturally fractured reservoirs, different properties of matrix blocks and fracture systems have caused the triple porosity model to be more applicable than the traditional dual porosity model.The existed triple porosity models presented so far are mainly based on pseudo steady state flow in the matrix block and vug and via a semi-analytic form. In this paper, two analytical models of triple porosity model are presented with consideration of transient flow; the first model being: the series flow of the matrix block to the vug and the vug to the fracture, and the second model: transient parallel flow of the matrix block and vug to the fracture. In this paper, for the first time, an analytical and transient shape factor between different regions is put forward.Using the developed new solution, various flow regimes in triple porosity model have been identified. In the series triple porosity model, changing the parameters of vug and matrix did not affect the early production while it influenced the rate of the middle and lately times. The shape factor between the matrix and vug was independent of the physical properties of vug while the shape factor between vug and fracture was influenced by the physical properties of vug and matrix. In the parallel triple porosity model, the shape factor of matrix-fracture and vug-fracture were not dependent on the properties of the other regions of rock. Moreover, a decrease in inter-porosity coefficient and an increase in storativity ratio increased the shape factor in transient time.Additionally, in order to validate the analytical model, the results of the model are compared with the numerical simulations. This study presents a new analytical and transient shape factor which finds application in simulation of triple porosity formations.

Using image logs to identify fluid types in tight carbonate reservoirs via apparent formation water resistivity spectrum

Hydrocarbon-bearing zone identification of tight reservoirs plays a crucial role in hydrocarbon exploration and development. However, tight carbonate reservoirs are generally characterized by complex lithology, low porosity, strong heterogeneity, and weak fluid logging responses, which present a major challenge to detect hydrocarbon-bearing zones using conventional methods. To address this challenge, this paper develops a new method defined as Rwa spectrum, taking advantage of the high vertical resolution and borehole coverage of the image logs. The Rwa spectra can be derived from the histogram distribution of the apparent resistivity values of formation water (Rwa) in a sliding window, combining the Simandoux equation and the triple-porosity model. The results show that a very broad Rwa spectrum with long tails corresponds to hydrocarbon-bearing zones, and the peak shape of it is flat. In contrast, the narrow Rwa spectrum corresponds to water-bearing zones, and the peak shape of it is a sharp spike. Furthermore, two Rwa spectrum parameters, namely AVERAGE (reflects the size of main peak values) and VARIANCE (reflects shape changes of the Rwa spectra) are defined to quantificationally detect hydrocarbon-bearing zones. For oil zones in Yingxi field, the AVERAGE had a value higher than 10 and the VARIANCE was higher than 10. And for water zones, the AVERAGE had a value lower than 4.5 and the VARIANCE was lower than 5. The resistivity values decrease linearly with the increase in pyrite content of the reservoirs of high pyrite content, which disturbs the response to resistivity values from different fluid types (oil, gas or water). Hence, this method is suitable for the formation of no or little pyrite contents (lower than 0.2), and the case where the salinity value of drilling mud is similar to that of formation water. Moreover, the method has been validated by production test data, providing unusual perspectives on the identification of fluid types in tight carbonate reservoirs.

Inflow performance relationship of vertical wells in fractured vuggy media during semi-steady state flow regime

The inflow performance relationship (IPR) is one of the essential key parameters that control the fluids production/injection rate from wells. The presence of the vugs in addition to fractures in carbonate reservoirs introduce many difficulties related the estimation of IPR of future wells. In this study, a novel analytical IPR of dual-permeability, triple porosity model is derived for the first time. The introduced IPR formula is derived for the standard scenario model of a vertical and fully penetrating well in a circular reservoir under single-phase flow of slightly compressible fluid. The three governing flow equations (matrix flow equation, fracture flow equation and interaction between vugs and other two continuum equation) are solved simultaneously as a system of differential equations for semi-steady state (SSS) flow regime. The generated SSS IPR is the same as Darcy's straight line IPR multiplied by an error parameter (E23) which is bounded between zero and one. A detailed investigation of the effect of the reservoir petro-physical parameters like storativities, inter-porosities and fracture to matrix permeability ratio are presented. The newly presented IPR of dual-permeability, triple porosity system can be reduced to sub-models IPRs by further modification of error parameter to fit sub-model as single permeability, triple porosity (E13) or dual permeability, dual porosity (E22). The presented IPR formula has the advantage of dividing the pressure drop of the fluid flow to two components, one for the internal resistance between different continuums (which is resented by E) and the other one is the radial flow in the same continuum toward/from well-bore. The generated IPR model is double verified using both cell pressure centred finite volume numerical simulation and conventional pressure transient analysis.

A Semianalytical Model for Simulating Fluid Flow in Naturally Fractured Reservoirs With Nonhomogeneous Vugs and Fractures

Summary Carbonate reservoirs comprise fractures, vugs, and cavities. Vugs have a large contribution to reserves of oil and gas, and the fractures provide effective paths for fluid flow in the reservoir. The triple-porosity (TP) model is an effective conceptual method for capturing rock matrix and vugs and the microfractures connecting them. However, these fractures and vugs are always nonhomogeneous. Macrofractures and vugs cannot be handled with a continuum scheme because of their low density and high conductivity. In this approach, the TP conceptual model is implemented to characterize rock matrix, microvugs, and fractures. To capture the heterogeneity of fractures and vugs, macrofractures and vugs are represented explicitly with the discontinuum model. The boundaries of macrovugs and macrofractures are discretized into several elements. The boundary-element method (BEM) is used to handle flow into macrofractures and vugs. The finite-difference method is applied to handle flow within macrofractures. The flow within macrovugs is assumed to be pseudosteady state. With a simple discretization of the boundaries of macrovugs and macrofractures, the proposed model is shown to efficiently simulate the behavior of fractured carbonate reservoirs with heterogeneity. The computational accuracy is demonstrated using an analytical model and numerical simulation. On the basis of the proposed model, the effect of the heterogeneity of macrofractures and vugs on pressure-transient behavior is analyzed. The results show that macrofractures and vugs cannot be handled with triple-continuum models analytically. There will be several “dips” on the derivative of the pressure curve if macrovugs are discretely handled. Also, discretely handling the fractures and vugs will make the calculated dimensionless pressure and the derivative pressure lower than those calculated with the triple-continuum models. After increasing the porosity of macrovugs, the pressure and the derivative will go down in the flow regimes dominated by macrovugs. The conductivity of macrofractures has a great impact on almost all the flow regimes except for boundary-dominated flow. Finally, a field case is used to show the application of the proposed semianalytical model. The novelty of the new model is its ability to model the transient behavior of carbonate reservoirs with nonhomogeneous fractures and vugs. Furthermore, it provides an efficient method for characterizing the heterogeneity of multiscaled fractures and vugs.

A novel hydro-mechanical coupled analysis for the fractured vuggy carbonate reservoirs

A novel hydro-mechanical coupled analysis is proposed for calculating the pore pressure and stress evolution of fractured vuggy carbonate reservoirs under depletion or injection. Different from the conventional dual- and triple-porosity models in which the vugs are considered as continuous porosity, the vugs are treated as virtual volumes in this study. The fluid exchange at the vug-to-matrix interface is dynamically calculated with time evolution and the pore pressure in the vug is updated through considering both the fluid material balance and the volume change due to the mechanical deformation of the vug. The fluid-mechanical interaction in the rock matrix and natural fractures is calculated based on the framework of Biot’s poroelasticity theory. The mechanical and hydraulic interactions between vugs and matrix are maintained and the stress evolution owing to the depletion can be dynamically updated. The results in this study show that the depletion or injection process is greatly affected by the existence of vugs and natural fractures. Natural fractures provide highly conductive channels that lead to the preferential flow paths. The large fluid storage of vugs impedes the pressure diffusion process and brings perturbation to the pressure pattern near the vugs. The response of a vug to the depletion can be divided into three different stages depending on the depletion time. The effects of fluid storage, matrix/fracture permeability, natural fractures and fluid injection are investigated. The proposed hydro-mechanical coupled analysis provides a new modeling method for studying the hydraulic and mechanical behaviors of fractured vuggy carbonate reservoirs.

A triple porosity scheme for fluid/solid substitution: theory and experiment

ABSTRACTQuantifying the effects of pore‐filling materials on elastic properties of porous rocks is of considerable interest in geophysical practice. For rocks saturated with fluids, the Gassmann equation is proved effective in estimating the exact change in seismic velocity or rock moduli upon the changes in properties of pore infill. For solid substance or viscoelastic materials, however, the Gassmann theory is not applicable as the rigidity of the pore fill (either elastic or viscoelastic) prevents pressure communication in the pore space, which is a key assumption of the Gassmann equation. In this paper, we explored the elastic properties of a sandstone sample saturated with fluid and solid substance under different confining pressures. This sandstone sample is saturated with octadecane, which is a hydrocarbon with a melting point of 28°C, making it convenient to use in the lab in both solid and fluid forms. Ultrasonically measured velocities of the dry rock exhibit strong pressure dependency, which is largely reduced for the filling of solid octadecane. Predictions by the Gassmann theory for the elastic moduli of the sandstone saturated with liquid octadecane are consistent with ultrasonic measurements, but underestimate the elastic moduli of the sandstone saturated with solid octadecane. Our analysis shows that the difference between the elastic moduli of the dry and solid‐octadecane‐saturated sandstone is controlled by the squirt flow between stiff, compliant, and the so‐called intermediate pores (with an aspect ratio larger than that of compliant pore but much less than that of stiff pores). Therefore, we developed a triple porosity model to quantify the combined squirt flow effects of compliant and intermediate pores saturated with solid or viscoelastic infill. Full saturation of remaining stiff pores with solid or viscoelastic materials is then considered by the lower embedded bound theory. The proposed model gave a reasonable fit to the ultrasonic measurements of the elastic moduli of the sandstone saturated with liquid or solid octadecane. Comparison of the predictions by the new model to other solid substitution schemes implied that accounting for the combined effects of compliant and intermediate pores is necessary to explain the solid squirt effects.

A New Analytical Solution of the Triple-Porosity Model for History Matching and Performance Forecasting in Unconventional Oil Reservoirs

Summary Production data from hydraulically fractured horizontal wells in ultralow-permeability reservoirs have been observed to exhibit a half-slope straight line on a log-log plot of rate vs. time. Using these observations, many analytical models of linear flow have been developed to analyze the well performance in these reservoirs. However, it is relatively complicated to solve these models with the Laplace transform and numerical inversion. In this paper, a new analytical solution of a triple-porosity model is derived for unconventional oil reservoirs. The partial-differential equations (PDEs) are transformed into ordinary-differential equations (ODEs) by integration, instead of the Laplace transform. A rate-vs.-time solution in real-time space can be obtained, bypassing the numerical inversion for the Laplace transform. Our model is validated by comparison with both the numerical-model and Laplace-transform solutions. The physical meanings of the model parameters are analyzed through sensitivity analysis. The new model is then applied to field-production data for history matching and forecasting. Besides matching the production data, the pore volume (PV) of the matrix and fracture media can be estimated, which helps quantitative analysis of unconventional reservoirs.

Triple-Porosity Modelling for the Simulation of Multiscale Flow Mechanisms in Shale Reservoirs

Shale gas reservoir is a typical type of unconventional gas reservoir, primarily because of the complex flow mechanism from nanoscale to macroscale. A triple-porosity model (M3 model) comprising kerogen system, matrix system, and natural fracture system was presented to describe the multispace scale, multitime scale, and multiphysics characteristic of gas flows in shale reservoir. Apparent permeability model for real gas transport in nanopores, which covers flow regime effect and geomechanical effect, was used to address multiscale flow in shale matrix. This paper aims at quantifying the shale gas in different scales and its sequence in the process of gas production. The model results used for history matching also showed consistency against gas production data from the Barnett Shale. It also revealed the multispace scale process of gas production from a single well, which is supplied by gas transport from natural fracture, matrix, and kerogen sequentially. Sensitivity analysis on the contributions of shale reservoir permeability in different scales gives some insight as to their importance. Simulated results showed that free gas in matrix contributes to the main source of gas production, while the performance of a gas shale well is strongly determined by the natural fracture permeability.

Hybrid Coupled Multifracture and Multicontinuum Models for Shale Gas Simulation by Use of Semi-Analytical Approach

Combining the advantages of multicontinuum and multifracture representations provides an easy-to-use tool to adequately capture the characteristic of the multiscaled fracture system in shale gas reservoir. A hybrid model is established on the basis of simplified conceptual productivity assumption, where the matrix volume is divided into two sub-domains (triple-porosity model and dual-depletion flowing model) and the fracture volume is represented by discrete finite conductivity fracture. In addition, the mechanisms of instant desorption, viscous flow and dual-depletion in matrix are taken into account. The rate transient responses are then obtained by use of semi-analytical approach. Based on the model, type curves are plotted and verified by comparing with alternative reliable methods. Different flow regimes in shale gas reservoirs can be identified and detected. The Generalized Likelihood Uncertainty Estimation methodology, based on probabilistic aggregation theory, is employed to integrating those two productivity models together such that the production can be predicted more accurately. A field example is applied to validate the applicability of this new model. Finally, it is concluded that the proposed model can predict the rate and cumulative rate more easily and practically.

Multi-porosity multi-physics compositional simulation for gas storage and transport in highly heterogeneous shales

Shale gas reservoir is comprised of highly heterogeneous porosity systems including hydraulic/secondary fractures, inorganic and organic matrix. Multiple non-Darcy flow mechanisms in the shale matrix further bring challenges for modeling. In this paper, we developed a framework combining a multi-physics compositional simulator with Multi-Porosity Modeling preprocessor for gas storage and transport in shale. A Triple-Porosity Model is used to characterize the three porosity systems in shale gas reservoirs. In the fracture porosity the heterogeneous impact of secondary fractures distribution on matrix-to-fracture fluid transfer is revealed by shape factor distribution. They are upscaled with superior accuracy from a detailed Discrete Fracture Network Model (DFN) sector model, where orthogonal hydraulic fractures are explicitly discretized. With the occurrence of nano-pores in shale matrix, the interaction between pore-wall and gas molecules is considered via Knudsen diffusion and gas slippage. Gas adsorption on the pore-wall of organic matrix is modeled by extended Langmuir isotherm. The inter-porosity and intra-porosity connectivities in the Triple-Porosity Model are flexibly controlled by arbitrary connections. Our results show that gas production in the Triple-Porosity Model with shape factor upscaled from DFN exhibits different production performance from models with uniform shape factor distribution. The deviations are caused by the dominance of different regions at different production periods. Connection topology in the shale gas reservoir is also comprehensively assessed. We demonstrate that the intra-porosity connections in the inorganic and organic matrix have negligible impact on the global gas flux, while the inter-porosity connections have different levels of importance for the gas production. Moreover, different combinations of flow and storage mechanisms are investigated. We show that Langmuir desorption maintains reservoir pressure, but gas slippage and Knudsen diffusion accelerate the pressure drop. Both mechanisms contribute to improve the gas production and the consideration of them simultaneously improve gas production most.

Nitrogen enhanced drainage of CO2 rich coal seams for mining

Coal seams with high CO2 gas contents can be difficult to drain gas for outburst management. Coal has a high affinity for CO2 with adsorption capacities typically twice that of CH4. This paper presents an analysis of nitrogen injection into coal to enhance drainage of high CO2 gas contents. Core flooding experiments were conducted where nitrogen was injected into coal core samples from two Australian coal mining basins with initial CO2 gas contents and pressures that could be encountered during underground mining. Nitrogen effectively displaced the CO2 with mass balance analysis finding there was only approximately 6%–7% of the original CO2 gas content residual at the end of the core flood. Using a modified version of the SIMED II reservoir simulator, the core flooding experiments were history matched to determine the nitrogen and methane sorption times. It was found that a triple porosity model (a simple extension of the Warren and Root dual porosity model) was required to accurately describe the core flood observations. The estimated model properties were then used in reservoir simulation studies comparing enhanced drainage with conventional drainage with underground in seam boreholes. For the cases considered, underground in seam boreholes were found to provide shorter drainage lead times than enhanced drainage to meet a safe gas content for outburst management.

Probability distribution method based on the triple porosity model to identify the fluid properties of the volcanic reservoir in the Wangfu fault depression by well log

Due to the powerful anisotropy of the physical properties of volcanic reservoirs, their component minerals and pore configuration are very complex, rendering fluid identification very difficult. This paper first computed the cementation exponent, which was based on triple porosity model, then used the varied matrix density and matrix neutron to compute the porosity, and finally combined with resistivity well log, and a P1/2 probability distribution curve was built. The fluid properties were predicted from the shape of the P1/2 probability distribution curve. Good results were achieved when these methods were used in the volcanic reservoir of the Wangfu fault depression, which indicated that these methods can be used in the fluid property identification of volcanic reservoirs and can also be referred to for other lithology reservoirs.

Numerical study of a stress dependent triple porosity model for shale gas reservoirs accommodating gas diffusion in kerogen

A model accommodating multi-scale pores containing kerogen within an inorganic matrix is used to explore the complex multi-mechanistic transport mechanisms of shale gas reservoirs. These include the complex evolution of pressure, diffusion and flow within both kerogen and inorganic components and their interaction with effective stresses. A general poromechanical model is proposed considering desorption and molecular diffusion in the kerogen, viscous flow in the inorganic matrix and fracture system, and composite deformation of the triple porosity assemblage. The model is verified by history matching against field data for gas production rate. The simulation results indicate that the pattern of gas flow is sequential during gas depletion – pressure first declines in the fracture, followed by the inorganic phase and then in the kerogen. The evolution of permeability is pressure dependent and the evolution of pressure is closely related to the intrinsic gas diffusion coefficient in the kerogen, inorganic matrix intrinsic permeability and fracture intrinsic permeability. A series of sensitivity analyses are completed to define key parameters affecting gas production. The study shows that dominant influence of the fracture network in acting as the main permeable conduit. The intrinsic permeability and porosity of the fracture have a positive correlation with gas production, while fracture spacing has a negative correlation to gas production. Kerogen also plays a critical role in gas production for shale reservoirs with higher total organic carbon. The enhancement of inorganic matrix permeability and gas diffusion coefficient in kerogen could efficiently guarantee a long-term gas production with a higher rate.

Characterizing Tight Oil Reservoirs With Dual- and Triple-Porosity Models

The response of existing transient triple-porosity models for fractured horizontal wells do not converge to that of linear dual-porosity model (DPM) in the absence of natural/microfractures (MFs). The main reason is the assumption of sequential-depletion from matrix to MF, and from MF to hydraulic-fractures (HFs). This can result in unreasonable estimates of MF and/or HF parameters. Hence, the authors proposed a quadrilinear flow model (QFM) in a previous paper which relaxes this sequential-depletion assumption to allow simultaneous matrix–MF and matrix–HF depletion. Also, it is proved that QFM simplifies to both DPM and linear sequential triple-porosity model (STPM). This work considers the implications of applying QFM, STPM, and DPM type-curves and analysis equations on production data of two fractured horizontal wells completed in the Bakken and Cardium Formations. A comparative study of the reservoir parameters estimated from the application of these models to the same production data reveals two key results. First, the application of DPM on the production data from reservoirs with active MF could result in overestimation of HF half-length. This happens to compensate for the extra fluid depletion pathways provided by MF. Second, the application of STPM on the production data from the reservoirs with active matrix–HF communication could result in overestimation of the MF intensity. Results from this study are significant when selecting the appropriate model for interpreting production data from fractured horizontal wells completed in formations with or without active MF. The DPM is appropriate if analog studies (e.g., outcrop, microseismic and image log analyses) reveal high fracture spacing aspect ratio (negligible MF) in the reservoir. Fracture spacing aspect ratio is MF spacing divided by the HF spacing. The STPM is appropriate if analog studies reveal low spacing aspect ratio (e.g., matrix–HF face damage or high MF intensity within a given HF spacing). QFM is appropriate for all fracture spacing aspect ratios.

Numerical investigation of limitations and assumptions of analytical transient flow models in tight oil reservoirs

The complex fracture network created by multistage hydraulic fracturing has been recently described by triple porosity models. Existing triple porosity models typically assume sequential flow from matrix to micro fractures and from micro fractures to hydraulic fracture. Modeling simultaneous depletion of a matrix block into both micro and hydraulic fractures entails solution of a two dimensional continuity equation that is challenging by analytical or even semi-analytical methods. In addition, analysis with analytical models and type-curves provides deterministic and homogeneous estimates, rendering uncertainty analysis of fracture properties difficult.In this paper, we use a commercial reservoir simulator to compute the transient response in a segment of a hydraulically fractured horizontal well with a triple-porosity model, where matrix and fracture elements are explicitly discretized. Some limitations in analytical models such as sequential flow, single-phase flow and fully-connected symmetric fractures are investigated using the actual rate data from two tight oil wells completed in the Cardium and Bakken formations. An early drop in production, as commonly observed in many tight oil wells, could be attributed to gas dissolution with pressure decline and multiphase flow effects. Impacts of pressure interference between natural fractures and inter-well fracture communication are also investigated. Uncertainty in model parameter estimation is studied by assuming that results obtained from analytical solutions would characterize the mean estimate of the corresponding fracture parameters, additional heterogeneous models of natural/induced micro-fracture properties including its total number and intensity (spacing) are assigned stochastically. These models are subsequently subjected to flow simulations, and the variability in production performance captures the sensitivity due to model parameter uncertainties. Our results highlight the non-uniqueness of fracture characterization in production data analysis. It is demonstrated that ignoring the uncertainty in history-matched parameters and assumptions associated with analytical models could potentially over- or under-estimate production by up to 30%. The analysis workflow adopted in this study presents a practical framework for integrating numerical simulations with analytical solutions to study the limitations of analytical transient flow models and to quantify the uncertainty in production performance predictions.

Capturing the effects of secondary fractures on production data using flow regime equations and specialised plots: An uncertainty analysis approach

Abstract Many fractured horizontal wells are completed in tight oil/gas or shale gas reservoirs which have significant networks of interconnected secondary fractures. However, the existing linear transient dual- and triple-porosity models do not properly account for secondary fractures. While the dual-porosity model assumes negligible secondary fractures, the linear sequential triple-porosity model assumes negligible fluid transfer between the rock matrix and hydraulic fractures. Hence, the application of these models for production data analysis of fractured horizontal wells could result in unreasonable reservoir/fracture parameter estimates and hydrocarbon forecast. For this reason, the quadrilinear flow model (QFM) was developed to account for matrix–hydraulic fracture communication. Although QFM properly accounts for the contribution of secondary fractures during reservoir depletion, reservoir parameter estimation from its type-curve matching procedure has a high degree of uncertainty. This paper proposes simplified QFM flow regime equations to reduce the uncertainty associated with reservoir parameter estimation. This study carefully analyses the general QFM solution by observing the flow regions from dimensionless rate and pressure type-curves. This solution is simplified by eliminating dimensionless parameters with negligible contribution to fluid depletion within the duration of each flow region. The resulting simplified analysis equations are analytically inverted from Laplace space to time space. The simplification process yields (i) analysis equations for different flow-regions of the specialised rate-normalised pressure and pressure derivative plots and (ii) explains the possible physics behind the flow-regions. The effect of secondary fracture networks on reservoir depletion can be investigated by applying QFM analysis equations on specialised rate-normalised pressure and pressure derivative production data plots. The choice of these plots is based on operational well constraints and observable flow regions. The QFM analysis equations are applied to interpret production data of two multifractured horizontal wells completed in the Cardium and Bakken Formations. The results estimate effective half-length of hydraulic fractures, investigate the presence/absence of secondary fractures and propose a workflow for handling the uncertainty in reservoir parameter estimation when applying the specialised analysis equations.

Fractured-Reservoir Modeling and Interpretation

SummaryFractures are common features of many well-known reservoirs. Naturally fractured reservoirs (NFRs) consist of fractures in igneous, metamorphic, and sedimentary rocks (matrix). Faults in many naturally fractured carbonate reservoirs often have high-permeability zones and are connected to numerous fractures with varying conductivities. In many NFRs, faults and fractures frequently have discrete distributions rather than connected-fracture networks. Because faulting often creates fractures, faults and fractures should be modeled together. Accurately modeling NFR pressure-transient behavior is important in hydrogeology, the earth sciences, and petroleum engineering, including groundwater contamination to shale gas and oil reservoirs. For more than 50 years, conventional dual-porosity-type models, which do not include any fractures, have been used for modeling fluid flow in NFRs and aquifers. They have been continuously modified to add unphysical matrix-block properties such as matrix skin factor.In general, fractured reservoirs are heterogeneous at different length scales. It is clear that even with millions of gridblocks, numerical models may not be capable of accurately simulating the pressure-transient behavior of continuously and discretely NFRs containing variable-conductivity fractures. The conventional dual-porosity-type models are obviously an oversimplification; their serious limitations for interpreting well-test data from NFRs are discussed in detail. These models do not include wellbore-intersecting fractures, even though they dominate the pressure behavior of NFRs for a considerable length of testing time. Fracture conductivities of unity to infinity dominate transient behavior of both continuously and discretely fractured reservoirs, but again, dual-porosity models do not contain any fractures. Our fractured-reservoir model is capable of treating thousands of fractures that are periodically or arbitrarily distributed with finite- and/or infinite conductivities, different lengths, densities, and orientations.Appropriate inner-boundary conditions are used to account for wellbore-intersecting fractures and direct wellbore contributions to production. Wellbore-storage and skin effects in bounded and unbounded systems are included in the model. Three types of damaged-skin factors that may exist in wellbore-intersecting fracture(s) are specified. With this highly accurate model, the pressure-transient behavior of conventional dual-porosity-type models are investigated, and their limitations and range of applicability are identified. The behavior of the triple-porosity models is also investigated. It is very unlikely that triple-porosity behavior is caused by the local variability of matrix properties at the microscopic level. Rather, it is caused by the spatial variability of conductivity, length, density, and orientation of the fracture distributions. Finally, we have presented an interpretation of a field-buildup-test example from an NFR by use of both conventional dual-porosity models and our fractured-reservoir model.A substantial part of this paper is a review and discussion of the earlier work on NFRs, including the authors’ work.