Unstimulated Reservoir Volume Research Articles

Modeling for Volume-Fracturing Vertical Wells in Tight Oil Reservoir considering NMR-Based Research on Imbibition

Abstract The lateral broadband fracturing (LBF) technique for vertical well in tight oil reservoir has been proven to provide much larger stimulated reservoir volume (SRV) by widening its width. Although this new fracturing technique has been successfully applied to the development of tight oil reservoirs in Ordos Basin, China, there is still a lack of models and methods to characterize the imbibition of matrix-fracture system, which is heterogeneous permeability distribution. In this paper, a multilinear fractal model considering Nuclear Magnetic Resonance-based research on imbibition (MFMI) is established to characterize the flow characteristics of lateral broadband fracturing vertical wells (LVWs) in tight oil reservoirs by combining the dual-porosity fractal model considering imbibition and the quad-linear flow model. Due to the application of LBF, the nonuniform distribution of fracture system is characterized by fractal porosity and fractal permeability. In addition, the imbibition in SRV of tight oil reservoir is quantitatively characterized by Nuclear Magnetic Resonance (NMR) data. And the production performance of LVWs is quantified by the MFMI. By using the Laplace transformation, Bessel function, iteration, and Stehfest numerical inversion algorithms, the approximate analytic solutions of our established model, including primary hydraulic fractures, SRV, and unstimulated reservoir volume (USRV), are derived. The solutions of pressure and production are used to compare and analyze in order to discuss the influence of parameters related to lateral broadband fracturing (such as fractal parameters, reservoir parameters, and width of SRV) on flow behavior of LVWs in a tight oil reservoir. The modeling results show that the fractal parameters of fracture system have great effect on the fluid flow in LVWs, and LBF contributes to imbibition production.

The Laplace-transform embedded discrete fracture model for flow simulation of stimulated reservoir volume

Hydraulic fracturing is a commonly adopted approach to enhance the production of unconventional reservoirs; however, the resulted complex fracture network increases the difficulty in the prediction of the flow behaviors. In this work, for the first time, we propose the Laplace-transform embedded discrete fracture model focusing on the simulation of fluid transport in simulated reservoir volume (SRV). The main hydraulic fracture is represented explicitly by the fracture segments referring to the recently developed simulation scheme, namely the embedded discrete fracture model. The equivalent model and multiple continua model are employed to characterize the fluid flow in SRV. The Laplace-transform finite-different method is used to numerically model the flow among unstimulated reservoir volume, SRV, and main hydraulic fracture with sufficient flexibility to characterize the arbitrary fracture/SRV geometries. As the solution is performed in Laplace domain, the backward Euler difference for time discretization is not necessary. Thus, the stability and convergence problems caused by time discretization are avoided. A series of numerical test cases are discussed to examine the performance of the proposed model. The simulation workflow is validated through the comparison with discrete fracture model and embedded discrete fracture model in real space. It is demonstrated that the proposed Laplace-transform embedded discrete fracture model is accurate for single flow with complex SRV distribution. On the basis of the Laplace-transform embedded discrete fracture model, we provided three applications of the new method: (1) analysis of the SRV effect on fluid flow behavior, (2) pressure transient analysis considering reservoir heterogeneity, (3) production performance analysis with time-varying production rate.

A hybrid model for the combined impact of non-Darcy flow, stimulated matrix permeability, and anomalous diffusion flow in the unconventional reservoirs

Abstract A hybrid model for unconventional gas reservoirs that couples three different parameters is presented in this paper. The first is the anomalous diffusion in a fractal porous media. The second is the stimulated or induced matrix permeability in the stimulated reservoir volume (SRV). The third is the non-Darcy flow permeability in the hydraulic fractures. This model is generated from the multi-linear flow model for fractal reservoirs controlled by diffusive flow mechanism with adjustment for fluid flux through hydraulic fracture face considering minimum fracture relative permeability (kmr) and non-Darcy flow Number (FND). Pressure distributions, flow regimes, and reservoir performances have been investigated for three types of unconventional reservoirs. The first is formations with homogenous matrix permeability where petrophysical properties of stimulated and un-stimulated reservoir volume are the same. The second is fractal reservoirs with different petrophysical properties in the two volumes without considering normal or classic diffusion mechanism. The third is the fractal reservoirs where anomalous diffusive flow mechanism dominates fluid flow. A set of comparisons has been generated between the three types for better understand the impact of non-Darcy flow permeability and stimulated matrix permeability on reservoir performance under normal and anomalous diffusion flow mechanisms. The outcomes of this study are: (1) Generating a new analytical model that describes pressure distribution in fractal unconventional reservoirs and couples non-Darcy flow, stimulated or induced matrix permeability with the anomalous diffusion in porous media. (2) Understanding the impact of these different parameters on reservoir performance. (3) Developing different models for all types of flow regimes that are expected to be observed during the entire production life. (4) Comparing the productivity index of reservoirs: having homogeneous matrix permeability, fractal with normal diffusion, and fractal with anomalous diffusion. The most interesting points in this study are: (1) Minimum fracture relative permeability (kmr) significantly enhances the productivity index by eliminating the impact of non-Darcy flow while non-Darcy flow number (FND) works conversely (2) Increasing stimulated matrix permeability enhances reservoir performance (3) The impact of non-Darcy flow permeability of hydraulic fractures is seen at early and intermediate production time where transient flow is dominant. (4) Two different trends are recognized for the impact of anomalous diffusion flow: the first is a positive impact on the transient flow period and the second is negative in the pseudo-steady state flow.

The performance of complex-structure fractured reservoirs considering natural and induced matrix block size, shape, and distribution

This paper introduces an analytical approach for the performance of the fractured reservoir considering the impact of the matrix block size, shape, and distribution. The objective is better understanding the roles of the variable interporosity flow systems, fracture flowing systems, and reservoir matrix heterogeneity in the responses of the wellbore pressure drop, flow rate, cumulative production, and productivity index. This understanding could help to eliminate the uncertainties and increase the accuracy in characterizing the conventional and unconventional reservoirs where very complex structures of a significant disorder in the matrix block size, shape and distribution could be existed in the porous media.The study uses the well documented multilinear flow model to describe the pressure distribution in the naturally fractured reservoirs depleted by multiple hydraulic fractures considering different matrix block sizes, shapes, and distributions. The analytical models of the flow rate, cumulative production, and the productivity index are also developed in this study from the multilinear flow model. The reservoirs of interest are assumed to have stimulated porous media extending between hydraulic fracture and unstimulated volume extending beyond the fracture tips toward the reservoir boundary. The unstimulated reservoir volume is assumed consisting of uniformly distributed single matrix block size and shape because there is no impact for the hydraulic fracturing process. While the stimulated reservoir volume is considered consisting of a variable matrix block size, shape, and distribution because of the impact of hydraulic fracture propagation. The petrophysical properties of the two porous media, as well as the storativity and interporosity flow coefficient, are assumed functions of the matrix characteristics in the two volumes. The matrix block dimensions (radius or length) are correlated exponentially with the distance from the hydraulic fracture face toward the no-flow boundary between these fractures. Three fracture-matrix fluid flux functions are developed for the reservoirs where the matrix blocks could have a spherical, slab, and cylindrical configuration.The study has reached several conclusions. A positive impact on the reservoir performance is seen when the matrix block size becomes small or when the small size matrix blocks control the distribution of the blocks in the porous media. Reservoir performance is enhanced also when there are several matrix block sizes compared to a single size or very few sizes. It is observed that the reservoirs with spherical blocks may give better performance than the reservoir with slab or cylindrical matrix blocks. In terms of matrix block size and distribution, heterogeneous reservoirs may have a higher productivity index than homogenous reservoirs. The variable matrix block size and distribution in the stimulated reservoir volume is more beneficial than the unstimulated volume. The novel point presented in this paper is developing several analytical models for the wellbore pressure drop, flow rate, cumulative production, and productivity index of hydraulically fractured reservoirs with a consideration given to the matrix block size, shape, and distribution.

Fluid flux throughout matrix-fracture interface: Discretizing hydraulic fractures for coupling matrix Darcy flow and fractures non-Darcy flow

The objective of this paper is focusing deep insights on reservoir fluid flux from a structurally complicated matrix to non-uniformly propagated hydraulic fractures. A hypothetical unconventional reservoir is considered with stimulated and un-stimulated reservoir volume. A Semi-analytical multilinear flow regimes model is developed for pressure distribution by coupling matrix Darcy flow model and hydraulic fracture non-Darcy flow model. Hydraulic fractures are discretized to several segments with a specific fluid flux to these segments. The study has reached to several conclusions such as: fluid flux from SRV matrix to hydraulic fractures may have a significant impact on reservoir performance and discretizing hydraulic fractures to several segments may give different pressure behavior, flow rate, and productivity index than single segment fracture. The novel point presented in this study is presenting a semi-analytical model that couples matrix Darcy flow and hydraulic fracture non-Darcy flow using trilinear dual porosity model and discretizing hydraulic fractures.

Water-Gas Two-Phase Flow Behavior of Multi-Fractured Horizontal Wells in Shale Gas Reservoirs

Hydraulic fracturing is a necessary method to develop shale gas reservoirs effectively and economically. However, the flow behavior in multi-porosity fractured reservoirs is difficult to characterize by conventional methods. In this paper, combined with apparent porosity/permeability model of organic matter, inorganic matter and induced fractures, considering the water film in unstimulated reservoir volume (USRV) region water and bulk water in effectively stimulated reservoir volume (ESRV) region, a multi-media water-gas two-phase flow model was established. The finite difference is used to solve the model and the water-gas two-phase flow behavior of multi-fractured horizontal wells is obtained. Mass transfer between different-scale media, the effects of pore pressure on reservoirs and fluid properties at different production stages were considered in this model. The influence of the dynamic reservoir physical parameters on flow behavior and gas production in multi-fractured horizontal wells is studied. The results show that the properties of the total organic content (TOC) and the inherent porosity of the organic matter affect gas production after 40 days. With the gradual increase of production time, the gas production rate decreases rapidly compared with the water production rate, and the gas saturation in the inorganic matter of the ESRV region gradually decreases. The ignorance of stress sensitivity would cause the gas production increase, and the ignorance of organic matter shrinkage decrease the gas production gradually. The water film mainly affects gas production after 100 days, while the bulk water has a greater impact on gas production throughout the whole period. The research provides a new method to accurately describe the two-phase fluid flow behavior in different scale media of fractured shale gas reservoirs.

Analytical modeling and probabilistic evaluation of gas production from a hydraulically fractured shale reservoir using a quad-linear flow model

During hydraulic fracturing, secondary fractures are created around hydraulic fractures and serve as important channels connecting the shale matrix and the hydraulic fractures. We developed an analytical model to simulate shale gas production from a multi-stage fractured horizontal well. The analytical model is based on the trilinear flow model, but it is free from the assumption that the length of secondary fractures is equal to the half-distance between hydraulic fractures. This analytical model captures the fundamental characteristics of a hydraulically fractured shale reservoir by incorporating transient gas flow in the matrix, secondary fractures, and hydraulic fractures. Because this model describes four linear flow systems (unstimulated reservoir volume, matrix in the stimulated reservoir volume, secondary fracture, and hydraulic fracture), it is called the quad-linear flow model. Production data from two shale gas wells were used to validate the model. Moreover, using the variance-based method and quasi-Monte Carlo simulation, we developed a stochastic framework to perform a probabilistic assessment of shale gas production. We also conducted a global sensitivity study with nine uncertainty parameters to identify important parameters and their interactions that affect well productivity. The results indicate that the existence of dense secondary fractures (the distance between secondary fractures is small) results in higher initial production rate and ultimate recovery, but a sharper decline in production rate. Increasing the length of the secondary fractures can more effectively enhance gas production in the presence of dense secondary fractures. Moreover, the benefits of dense secondary fractures are mostly limited to a high porosity shale reservoir.

ANALYTIC EVALUATION METHOD OF FRACTAL EFFECTIVE STIMULATED RESERVOIR VOLUME FOR FRACTURED WELLS IN UNCONVENTIONAL GAS RESERVOIRS

It has been proved that effective stimulated reservoir volume (ESRV) is a significant area dominant to the production of the fractured well in unconventional gas reservoirs. Although ESRV properties can be estimated based on the microseismic technology and the analysis of actual fracturing data, the operations are complicated and results are inaccurate. Due to the complex structure of stimulated reservoir volume (SRV) with fractal and chaotic characteristics, a fractal evaluation model for ESRV (ESRV-FEM) of fractured wells in unconventional gas (both tight and shale gas) reservoirs is developed. Multiple gas transport mechanisms, SRV and unstimulated reservoir volume (USRV) are included. According to the pressure transient analysis (PTA), influences of multiple transport mechanisms on gas transport behaviors in ESRV are conducted. Moreover, the fractal index representing the heterogeneity degree is applied to estimate the ESRV under different inter-porosity flow coefficients and storage ratio conditions based on the ESRV-FEM. In addition, the presented ESRV-FEM is validated by an actual field case. The results show that gas adsorption has a significant effect on the radial flow duration time in SRV, and the heterogeneity makes the radial flow on PTA curves no longer show a horizontal line with the value of 0.5. Calculated ESRV sizes are compared with the assumed ones under different fractal indexes. The stronger the heterogeneity, the smaller ESRV is. The ESRV size of a fractured well in shale gas reservoirs is only 52.11% of SRV size when the fractal index equals to 0.6. The ESRV-FEM presented in this paper is expected to provide an effective method for the evaluation of the ESRV of fractured wells in unconventional gas reservoirs.

Pressure-rate convolution and deconvolution response for fractured conventional and unconventional reservoirs using new decline rate model

Abstract This paper introduces new approach for pressure-rate convolution and deconvolution analysis of multi-stages hydraulically fractured conventional and unconventional reservoirs. This approach demonstrates the impact of variable Sand face flow rate on reservoir performance. A new model for P/R deconvolution is used to convert pressure pulse from variable flow rate to single and constant rate response. The target of this study is fractal reservoirs with and without stimulated and unstimulated reservoir volume. Multi-linear flow regimes approach is used to describe pressure behavior in the reservoirs while decline flow rate behavior is described by newly proposed model in this study. This model depicts, instead of van Everdingen model, indirectly the declining rate with time by using pressure responses with production time. Decline flow rate behavior simulated by linear and bi-linear flow models are also studied and compared with the one obtained by the new model. Several analytical models are used in this study by applying P/R convolution and deconvolution technique and solved for constant and variable flow rate considering different reservoir configurations and operating conditions. The results are interpreted and analyzed for better understanding pressure behaviors, flow regime types, and productivity index trends for continuously changing flow rate especially at early production time. Estimating stimulated reservoir volume ( V s r v ) is considered one of the applications of convolved pressure since it is calculated from pseudo-steady state flow when late time boundary dominated flow regime is reached. The outcomes of this study can be summarized as: 1) Introducing new approach for pressure-rate convolution and deconvolution technique for multi-stages hydraulically fractured reservoirs by applying new decline flow rate model that indirectly simulates variable flow rate with time. 2) Generating analytical models for dimensionless pressure and flow rate for constant and variable flow rate using the concept of P/R convolution and deconvolution. 3) Comparing the result of newly proposed models with the results obtained by applying van Everdingen model for decline rate behavior. 4) Studying the applicability of linear and bi-linear flow models in converting variable flow rate pressure response to single and constant flow rate pressure response. 5) Applying the deconvolution technique to simulate pressure response at late production time to estimate stimulated reservoir volume. The most interesting points are: 1) The main difference in wellbore pressure behavior between variable and constant flow rate can be seen at early production time, however intermediate production time could also show very limited changes for the case of variable rate wellbore pressure. 2) A unit slope line flow regime could be developed for varied flow rate pressure response at very early production time similar to the wellbore storage dominated flow regime. 3) Productivity index calculated by the proposed models for variable flow rate is greater than the index for constant flow rate. 4) The impact of petrophysical properties of porous media and hydraulic fracture characteristics on pressure response are similar in the two cases of variable and constant flow rate. 5) The decline rate models for linear and bi-linear flow are not applicable in pressure deconvolution technique.

Production-Performance Analysis of Composite Shale-Gas Reservoirs by the Boundary-Element Method

Summary A shale-gas reservoir with a multiple-fractured horizontal well (MFHW) is divided into two regions: The inner region is defined as stimulated reservoir volume (SRV), which is interconnected by the fracture network after fracturing, while the outer region is called unstimulated reservoir volume (USRV), which has not been stimulated by fracturing. Considering an arbitrary interface boundary between SRV and USRV, a composite model is presented for MFHWs in shale-gas reservoirs, which is based on multiple flow mechanisms, including adsorption/desorption, viscous flow, diffusive flow, and stress sensitivity of natural fractures. The boundary-element method (BEM) is applied to solve the production of MFHWs in shale-gas reservoirs. The accuracy of this model is validated by comparing its production solution with the result derived from an analytical method and the reservoir simulator. Furthermore, the practicability of this model is validated by matching the production history of the MFHW in a shale-gas reservoir. The result shows that the model in this work is reliable and practicable. The effects of relevant parameters on production curves are analyzed, including Langmuir volume, Langmuir pressure, hydraulic-fracture width, hydraulic-fracture permeability, natural-fracture permeability, matrix permeability, diffusion coefficient, stress-sensitivity coefficient, and the shape of the SRV. The model presented here can be used for production analysis for shale-gas-reservoir development.

Bivariate Log-Normal Distribution of Stimulated Matrix Permeability and Block Size in Fractured Reservoirs: Proposing New Multilinear-Flow Regime for Transient-State Production

Summary This paper investigates the impacts of varied stimulated matrix permeability and matrix-block size on pressure behaviors and flow regimes of hydraulically fractured reservoirs using bivariate log-normal distribution. The main objective is assembling the variance in these two parameters to the analytical models of pressure and pressure derivative considering different porous-media petrophysical properties, reservoir configurations, and hydraulic-fracture (HF) characteristics. The motivation is eliminating the long-run discretization treatment in the porous media required by applying analytical models to describe the variance in the previously discussed parameters with the distance between HFs. Several analytical models for pressure response were generated in this study for hydraulically fractured reservoirs with rectangular-shaped drainage areas. These models take into account the change in stimulated matrix permeability from the maximum value close to the HF face to the minimum value at the so-called no-flow boundary between fractures. They also consider the change in the matrix-block size, corresponding to the change in the induced-fracture density (number of fractures per foot of length), from the minimum value close to the fracture face to the maximum value at the no-flow boundary. Bivariate log-normal distribution was used to describe the change in the stimulated matrix permeability and matrix-block size. The formations of interest are composed of stimulated reservoir volume (SRV), where the matrix is stimulated by the fracturing process, and unstimulated reservoir volume (USRV), where the stimulation process does not affect the matrix. The outcomes of this study can be summarized as Generating new analytical models for pressure and pressure derivative in hydraulically fractured reservoirs that consider the change in stimulated matrix-block size and permeability using bivariate log-normal distribution Understanding the effect of using the probability-density function (PDF) of matrix-block size and permeability in the pressure distribution of different reservoirs Observing the new multilinear-flow regime that develops at intermediate production time and represents several simultaneous linear-flow regimes inside HFs, SRV, and USRV Developing analytical models for the new multilinear-flow regime Studying the effects of petrophysical properties of HFs, induced fractures, and matrix as well as reservoir size and configuration on pressure behavior The most interesting points in this study are The applicability of bivariate log-normal distribution for describing the variance and nonuniform distribution of matrix-block size and permeability. The large variance in the matrix-block size and permeability causes significant decrease in wellbore-pressure drop. Small value of standard deviation of matrix-block size and permeability indicates the possibilities for significant decrease in wellbore pressure drop. The means of matrix-block size and permeability may not have significant effects on reservoir-pressure distribution. The new multilinear-flow regime is characterized by a one-eighth slope on the pressure-derivative curve and is seen always after HF linear flow and before boundary-dominated flow regime. Multilinear-flow regime develops to bilinear-flow regime with a one-quarter slope for uniform distribution of equal matrix-block size and permeability.

Integrated analysis of pressure response using pressure-rate convolution and deconvolution techniques for varied flow rate production in fractured formations

This paper introduces an integrated analysis for pressure transient behavior of conventional and unconventional multi-porous media reservoirs considering varied flow rate conditions. It focuses on the applications of pressure-rate convolution and deconvolution techniques for analyzing pressure records of homogenous single porous media, double porous media, and triple porous media reservoirs. The tasks covered in this paper are: Deconvloving pressure response, characterizing and developing analytical models for new flow regime that represents the impact of varied flow rate at early production time, estimating productivity index, and calculating stimulated reservoir volume (Vsrv). The reservoirs of interests in this study are depleted by horizontal wells intersecting multiple hydraulic fractures and composed of stimulated and unstimulated reservoir volume with different configurations and geometries.Multi-linear flow regimes approach is used to describe pressure behavior in the reservoirs while declining flow rate scheme is described by van Everdingen model. These two models are assembled to deconvolve pressure responses from varied to single flow rate condition. The deconvolved pressure and pressure derivative are used in characterizing the new flow regime that is observed for the case of varied flow rate during early production time and generating analytical models in dimensionless form and field units for oil and gas reservoirs. They are also used to calculate stimulated reservoir volume using very late production time, pseudo-steady state flow is reached, without the need for running well test to this time. Productivity index for constant and varied flow rate are calculated and compared using pressure responses of the two cases. The methodology used in this paper has experienced reservoirs with hydraulic fractures of different characteristics, stimulated reservoir volume (Vsrv) between hydraulic fractures, and unstimulated reservoir volume (Vusrv) in the outer drainage are beyond fracture tips.The outcomes of this study can be summarized as: 1) Introducing an integrated analysis of pressure behavior using pressure-rate convolution and deconvolution techniques for hydraulically fractured conventional and unconventional reservoirs. 2) Deconvloving pressure response from varied to single flow rate condition by applying multi-linear flow regimes approach collaboratively with decline flow rate model proposed by van Everdingen. 3) Characterizing the impact of variable production rate on pressure response for different reservoir types, configurations, and geometries as well as different hydraulic fracture characteristics. The most interesting points are: 1) The main differences in wellbore pressure behavior between variable and constant flow rate can be seen at early production time. 2) The new flow regime that could be developed for varied flow rate at very early production time is characterized by slope of (1.30−1.35) on pressure derivative curve. 3) Productivity index calculated by deconvolved pressure for variable flow rate is slightly less than the index for constant flow rate at early production time, however, the index has the same value for the two conditions at late production time.

Pressure transient analysis of multiple fractured horizontal well in composite shale gas reservoirs by boundary element method

The composite shale gas reservoir consists of an inner and an outer region. Inner region is stimulated reservoir volume (SRV) and contains shale matrix and natural fractures. Outer region represents un-stimulated reservoir volume (USRV) and contains shale matrix only. The interface boundary between SRV and USRV is often arbitrarily shaped rather than the regular, which can be derived from micro-seismic events of shale gas reservoirs with multiple fractured horizontal well (MFHW) Considering arbitrary interface boundary between SRV and USRV and outer boundary, a composite model is presented for MFHW in composite shale gas reservoirs, which based on multiple mechanisms, including adsorption/desorption, viscous flow, diffusive flow and stress sensitivity of natural fractures.Boundary element method (BEM) is introduced to solve the pressure response of MFHW in composite shale gas reservoirs. The accuracy of this model is validated by comparing its pressure response solution with the result derived from an analytical and a numerical method, respectively. According to pressure performance analysis of MFHW in composite shale gas reservoirs, eight flow regimes are identified: the early linear flow, the early radial flow, the second linear flow, the second radial flow, inter-porosity flow from shale matrix to natural fractures, the transition flow, diffusive flow and the third radial flow. The effects of relevant parameters on pressure response are analyzed, including mobility ratio, storability ratio, inter-porosity coefficient, diffusion coefficient, adsorption index and the shape of interface boundary. The result shows that BEM can be perfectly used to analyze the pressure performance of MFHW of composite shale gas reservoirs with arbitrary shaped interface boundary and outer boundary; the presented model can be used to interpret pressure data more accurately for shale gas reservoirs and provide more accurate dynamic parameters which are important for efficient reservoir development.

Analytical model for production performance analysis of multi-fractured horizontal well in tight oil reservoirs

The combination of horizontal well drilling and reservoir stimulating via multiple fracturing has been proved to be an effective technology to exploit low permeability unconventional tight oil reservoirs. Through multiple fracturing, the very-complex fracture network called the stimulated reservoir volume (SRV) around primary fractures can be generated, which is expected to affect well performance significantly. The pores in tight oil reservoirs with multi-fractured horizontal wells (MFHWs) can be roughly divided into three major types: matrix, natural fractures and hydraulic fractures, which lead to multi-scaled flow during the development of tight oil reservoirs. Furthermore, non-Darcy flow and stress sensitivity make the fluid flow in such reservoirs become more complicated. So it is very difficult to accurately determine the productivity of MFHWs in these reservoirs. Various analytical models have been established to analyze the transient performance of MFHW fast and accurately. However, the typical seepage characteristics in tight oil reservoirs are seldom considered in these models, such as non-Darcy flow and stress sensitivity.This paper presents a new analytical model for MFHW in tight oil reservoirs, where the reservoir is subdivided into five continuous flow regions: the unstimulated reservoir volume (USRV) regions 1 and 2, the stimulated reservoir volume (SRV) regions 3 and 4, and the hydraulic fracture (HF) region 5. The effects of non-Darcy flow and stress sensitivity are both considered. Laplace transformation, perturbation method and Stehfest numerical inversion are employed to solve the model comprehensively. The model solution is verified with analytical and numerical methods. The effects of related influential parameters on well production performance are investigated. Field example is conducted to show the applicability of the new model, history matching curve and results are obtained according to real production data. The research results summarized in this paper can provide some significance for production performance analysis of MFHW in tight oil reservoirs.

Analytical model of gas transport in heterogeneous hydraulically-fractured organic-rich shale media

Multiple gas transport mechanisms and geological parameters influence total gas production in hydraulically-fractured organic-rich shale reservoirs. The absolute and relative contributions of these processes and parameters vary significantly with the scale of the medium, from pore scale to field scale. The objective of this study is to investigate the impact of these geological parameters and transport processes in organic-rich shale production at field scale.We develop a multi-porosity analytical model which honors pressure- and space-dependent geological properties and gas transport processes in a multi-stage, hydraulically-fractured horizontal well of shale reservoir. The model premises distinct pores in kerogen, inorganic clay, induced fracture, and hydraulic fracture. Multiple flow zones are modeled: unstimulated reservoir volume (USRV), stimulated reservoir volume (SRV), and hydraulic fractures (HF). Compared to the earlier analytical models, the new model accounts for more comprehensive transport mechanisms and medium properties: gas diffusion and desorption in kerogen matrix and organopores, slip flow in inorganic matrix pores, transient Darcy flow from matrix to induced fractures, Darcy flow in both induced and hydraulic fractures, tortuosity of induced fractures, and pressure-dependent permeabilities. These enhanced features introduce important complexities to the analytical solution challenges that are discussed and resolved in detail.Extensive lab and field data for Eagle Ford shale are presented in the new model. Sensitivity analyses are conducted to study the flow contribution from organic and inorganic media. The results show that first, the impacts of gas diffusion, TOC, and organoporosity at pore and core scale are largely eclipsed at field scale by slip flow in inorganic matrix and anomalous diffusion within complex induced-fracture network. Second, fracture tortuosity and the Klinkenberg effect are dominant factors during early- and intermediate-time production. Third, gas diffusion in kerogen matrix is negligible compared to gas desorption and diffusion in organopores. Fourth, permeability variations with pore pressure have a significant impact on late-time production from fractured low-permeability reservoirs.The derived analytical solutions in Laplace space serve as simple but robust tools for studying gas transport in fractured organic shale formation. The field application is validated by matching results for an Eagle Ford shale well. Finally, there is a discussion of the present model’s limitations and potential future extensions.

Review on gas flow and recovery in unconventional porous rocks

This study summarizes gas flow process in unconventional porous rocks, including the transportation in tight or shale reservoirs and the spontaneous imbibition happened in them. Fluids flow is greatly affected by the pore structure together with the pore size distribution of porous media. The MRI and BET measurement show peaks in pore throat radius ranging from 2 to 20 nm, whereas the diameter for methane and helium are 0.38 and 0.26 nm, respectively. Yet for different types of reservoir, distinct mechanisms should be utilized based on the flow regimes. Besides, experimental measurement techniques for conventional reservoirs are no long accurate enough for most of the unconventional reservoirs. New attempts have been implemented to obtain more valuable data for accurate reservoir prediction. By reviewing large numbers of articles, a clear and comprehensive map on the gas flow and recovery in unconventional reservoirs is made. Factors influencing the gas flow and recovery are investigated in detail for mathematical simulation process. Reservoir conditions and the sweep efficiency play an important role during gas production process. Besides, adsorbed gas contributes a lot to the total gas recovery. The overall investigations suggest that many parameters that influence the gas flow in unconventional porous rocks should be taken into consideration during the evaluation. Among them, permeability, adsorbed gas dynamics, stimulated reservoir volume as well as the unstimulated reservoir volume, and imbibition effect are the most important ones. This study provides valuable data and reasonable exploitations for characterizing gas flow and recovery in unconventional porous rocks. Cited as : Lin, D., Wang, J., Yuan, B., et al. Review on gas flow and recovery in unconventional porous rocks. Advances in Geo-Energy Research, 2017, 1(1): 39-53, doi: 10.26804/ager.2017.01.04

Pressure transient responses study on the hydraulic volume fracturing vertical well in stress-sensitive tight hydrocarbon reservoirs

Based on the characteristics of stimulated zone and un-stimulated zone after hydraulic volume fracturing of vertical well, as well as considering the stress-sensitive characteristic of the tight oil reservoir, the two-zone composite pressure transient responses model is built. The inner zone represents the stimulated reservoir volume region and is modeled as a dual-porosity radial reservoir, while the outer zone represents the un-stimulated reservoir volume region and is modeled as a single porosity reservoir. The model is solved by the method of superposition, Laplace integral transformation, Stehfest numerical inverse algorithm, and the perturbation technique. Thus the analytical solutions to the model are obtained. On the basis of the field example verification of the model, the flow regimes of the hydraulic volume fracturing vertical well are analyzed. The results of the study show that the new model can provide the reliable pressure transient responses model for hydraulic volume fracturing vertical well, and the flow regimes can be divided into five stages, including the wellbore storage stage, transition flow from matrix system to fracture system, radial flow of SRV zone, transition flow from UN-SRV zone to SRV zone, and radial flow of whole reservoir system. The new model and study are conducive to the well test interpretation of hydraulic volume fracturing vertical well in stress-sensitive tight oil reservoir.

Analytical modeling dynamic drainage volume for transient flow towards multi-stage fractured wells in composite shale reservoirs

This paper presents an analytical solution to predict the expansion of drainage volume for a composite transient linear flow system consisting of stimulated-reservoir volume (SRV) and unstimulated reservoir volume. Correct prediction of dynamic drainage volume (DDV) is essential in production data analysis and well space evaluation. With the prediction of DDV, we can calculate the average pressure and average saturation with different time, which can assist designing different exploitation scenarios.The compound linear flow solution within both SRV and unstimulated matrix is derived under constant-flowing-bottomehole-pressure (FBHP) and constant-rate boundary conditions. Laplace transform and numerical inversion are implemented to obtain the analytical solution. The location of pressure front is calculated using the impulse response concept, which is the maximum rate of pressure response. A multi-variable regression method is applied to determine an empirical equation indicating the relationship between DDV and the square root of time; the empirical equation includes conductivities of both SRV and unstimulated matrix volume, fracture length, and fracture spacing.The results suggest that the DDV demonstrates a linear relationship with square-root-of-time for both linear flow regime within SRV and the compound linear flow in composite fractured reservoirs. The advancement of DDV within stimulated-reservoir volume is much faster than unstimulated matrix, which is approximately 100 times in general. To verify the accuracy of newly derived DDV equations, we analyze the synthetic production data from series of fine-grid numerical simulations. Finally, we make a sensitivity analysis of hydraulic fracture spacing with respect to DDV, which can be implemented to evaluate the fracturing design. In practice, the solution derived can be used to determine optimal fracture spacing.

Pressure and rate transient analysis of composite shale gas reservoirs considering multiple mechanisms

Based on multiple mechanisms, including adsorption/desorption, viscous flow, diffusive flow in shale matrix and stress sensitivity of natural fractures, a new semi-analytical composite model is presented for multi-stage fractured horizontal well (MFHW) in shale gas reservoirs. The simplified composite model of an actual gas reservoir is composed of an inner and an outer region. Inner region represents stimulated reservoir volume (SRV) and contains natural fractures and matrix. Matrix-natural fracture transfer flow is assumed to be pseudo-steady state (PSS) or transient state (TS) which are described by the Warren & Root and the De Swan models respectively. Outer region is un-stimulated reservoir volume (USRV), which is described by single porosity medium model. First, transient flow model for continuous line source in composite shale gas reservoir is established. Perturbation method is applied to linearize the model. Then the line source solution is solved by Laplace transformation. Pressure responses of multi-stage fractured horizontal well is obtained using principle of superposition. The model is verified with the available field data from the Barnett Shale. In addition, transient pressure and production rate of MFHW in shale gas reservoirs with consideration of multiple mechanisms and SRV are analyzed and five typical regimes are identified: radial flow in SRV, interporosity flow, region pseudo-steady flow, diffusive flow and late pseudo-radial flow. In PSS transfer model, type curve has two cavities: the early one is caused by pseudo-steady interporosity flow between natural fractures and matrix and the late one is caused by diffusive flow in the matrix. But in TS transfer model, there is no obvious cavity in interporosity flow period due to subtle pressure fluctuation. The effects of relevant parameters on transient pressure and production rate are analyzed, including SRV radius, stress sensitivity coefficient, adsorption index, storability ratio, interporosity coefficient and diffusivity coefficient. The results demonstrate that larger SRV can reduce formation energy depletion and improve production rate. Stress sensitivity causes more pressure depletion, while desorption and diffusion can compensate for the pressure loss in the formation. The production rate increases as adsorption index σ rises. Storability ratio of natural fractures ωf and interporosity coefficient λ1 mainly affect interporosity flow period while storability ratio of matrix ωm and diffusivity coefficient λ2 mainly have effects on diffusive flow period. The larger the value of these four parameters, the larger the production rate in corresponding periods.

Productivity Model for Shale Gas Reservoir with Comprehensive Consideration of Multi-mechanisms

Multi-stage fracturing horizontal well currently has been proved to be the most effective method to produce shale gas. This method can activate the natural fractures system defined as stimulated reservoir volume (SRV), the remaining region similarly is defined as un-stimulated reservoir volume (USRV). At present, no type curves have been developed for hydraulic fractured shale gas reservoirs in which the SRV zone has triple-porosity dual-depletion flow behavior and the USRV zone has double porosity flow behavior. In this paper, the SRV zone and USRV zone respectively are simplified as cubic triple-porosity and slab dual porosity media. We have established a new productivity model for multifractured horizontal well shale gas with Comprehensive consideration of desorption, diffusion, viscous flow, stress sensitivity and dual-depletion mechanism in matrix. The rate transient responses are inverted into real time space with stehfest numerical inversion algorithm. Type curves are plotted, and different flow regimes in shale gas reservoirs are identified. Effects of relevant parameters are analyzed as well. The whole flow period can be divided into 8 regimes: bilinear flow in SRV; pseudo elliptic flow; dual inter-porosity flow; transitional flow; linear flow in USRV; inter-porosity flow and boundary-dominated flow. The stress sensitivity basically has negative influence on the whole productivity period .The less the value of Langmuir volume and the lager the value of Langmuir pressure, the more lately the inter-porosity flow and boundary-dominated flow occurs. It in concluded that the USRV zone has positive influence on production and could not be ignored.