non-Darcy Flow Effects Research Articles

Coupling Upscaled Discrete Fracture Matrix and Apparent Permeability Modelling in DFNWORKS for Shale Reservoir Simulation

Modelling non-Darcy flow behaviour in shale rocks, composed of nanometer-sized pores and multi-scale fracture networks, is crucial for various subsurface energy applications. However, incorporating multiple physical mechanisms across numerous scales is not trivial. This work proposes an improved and practical upscaling workflow for coupling an Upscaled Discrete Fracture Matrix (UDFM) model and a pressure-dependent apparent permeability (Kapp) model to capture the effects of non-Darcy flow in multi-scale fractured shale reservoirs.First, a 3D DFN is upscaled into octree-refined continuum meshes, where equivalent rock parameters and rock-fluid functions are defined using the UDFM approach. Then, the flow simulation is coupled with a pressure-dependent Kapp updating scheme using an existing Kapp model and a multiple-restart technique. The effects of non-Darcy flow mechanisms (e.g., slip flow, transitional flow, Knudsen diffusion) are captured. The constructed models are then used to study the impacts of fracture network connectivity and pressure interference on production. The results of this new approach are compared against those obtained from another commercial package while preserving the advantages of DFNWORKS. Neglecting non-Darcy flow behaviours could significantly underestimate gas production and water recovery. It is illustrated that the nanoscale flow mechanisms help to enhance matrix-matrix and matrix-fracture flow. The constructed models are also utilized to study the effects of disconnected or isolated fractures, pressure interference, water retention, and shut-in durations on well performance. The proposed flexible strategies can be adopted in other commercial/open-source fractured-porous-media subsurface-flow simulation frameworks.

Predicting Water Inflow in Tunnel Construction: A Fracture Network Model with Non-Darcy Flow Considerations

Fractures are widely distributed in karst areas, and when flow rates are high, they exhibit complex nonlinear behavior that cannot be accurately described by Darcy’s law. In this work, a hydro-mechanical coupling model based on a discrete fracture network is proposed to predict tunnel water inflow, accounting for the impact of non-Darcy flow. The model’s feasibility has been validated by comparing it with experimental results and the field measurements of flow rates at the Bodaoling Tunnel in Guizhou, China. The results show that Darcy flow tends to overestimate water inflow by approximately 25% compared to non-Darcy flow. The non-Darcy effect grows with the increase in initial fracture width and empirical constant q. When q exceeds 8.77 × 10−6, the growth rate of the Forchheimer number along the fracture width slowed down, and the inhibitory effect of non-Darcy flow on flow became gentle. Additionally, in a complex fracture network, the inflow rate limited by non-Darcy flow at one point drives the water flow through a connect fracture to another point, which increases the difficulty in water inflow prediction. This work highlights the importance of non-Darcy flow and fracture networks when accurately predicting water inflow in tunnels.

Modeling two-phase flow behaviour in a shale gas reservoir with complex fracture networks and flow dynamics

In this work, a robust and pragmatic method has been developed, validated, and applied to describe two-phase flow behaviour of a multifractured horizontal well (MFHW) in a shale gas formation. As for a fracture subsystem, its permeability modulus, non-Darcy flow coefficient, and slippage factor have been defined and embedded into the governing equation, while an iterative method is applied to update the gas/water saturation in each fracture segment within discrete fracture networks. Different from the traditional treatment that a water-source/sink in the matrix is simplified by assuming it as a constant term, a skin factor on a fracture face is defined and introduced to represent the change in relative permeability in the matrix domain at each timestep, while the adsorption/desorption term is incorporated into the diffusivity equation to accurately calculate the shale gas production by taking the adsorbed gas in nanoscale porous media into account. Then, the theoretical model can be applied to accurately capture the two-phase flow behaviour in different subdomains. The accuracy of this newly developed model has been confirmed by the numerical simulation and then it is extended to field applications with excellent performance. The stress-sensitivity, non-Darcy flow, and slippage effect in a hydraulic fracture (HF) are found to be obvious during the production, while the initial gas saturation in a matrix and HFs imposes an evident influence on the production profile. As for an HF with a high gas saturation, the dewatering stage is missing and water from the matrix can be neglected during a short production time. For the matrix subsystem, a high-water saturation in the matrix near an HF can affect gas production during the entire stage since gas relative permeability in the HF remains low. In addition, the adsorption/desorption in the matrix subsystem can increase gas production but decrease water production. Compared to the observed gas/water production rates for field applications, the solutions obtained from the method in this work are found to be well matched, confirming its reliability and robustness.

Well Test Analysis for a Well in Gas Storage Reservoirs With the Formation Containing High Salinity Water

Abstract The production capacity of the gas wells is seriously affected by salt deposition during the injection and production process for underground gas storage with high salt content, so it is necessary to predict the production performance through well test technology. However, the existing well test analysis methods cannot be reliably used to interpret the well test data affected by salt deposition phase change and high-speed non-Darcy flow during the injection and production process. Therefore, this paper first determines the relationship between salt deposition and temperature and pressure through flash calculation of phase equilibrium of saltwater and hydrocarbon system, then establishes a porosity and permeability model considering the effect of salt deposition, and further establishes a high-speed injection-production well test analysis model considering the effect of salt deposition in combination with Forchheimer’s percolation law. Finally, the model is solved by numerical method, and the dynamic changes of reservoir pressure and salt deposition are simulated and calculated. The results show that the higher the salinity of formation water is, the greater the risk of salt deposition in the reservoir is, and the permeability of the reservoir will significantly decrease after salt deposition occurs; the non-Darcy flow effect will aggravate the risk of salt deposition in the reservoir. The research results provide a theoretical method for the evaluation of reservoir parameters and production performance prediction of salt gas storage reservoirs.

Injectivity assessment for CCS field-scale projects with considerations of salt deposition, mineral dissolution, fines migration, hydrate formation, and non-Darcy flow

This paper aims to review the main mechanisms identified in the lab scale that impact CO2 injectivity during CCS projects in saline aquifers and evaluate their relevance in field scale through numerical models. They may include water vaporization, salt precipitation in the dry-out zone, mineral dissolution, which can result in fines migration in porous media, CO2 hydrate formation, and effects of non-Darcy flow. All those mechanisms are observed from lab experiments and significantly impact reservoir petrophysical properties such as porosity and permeability and consequently on injectivity in field operations. This study includes these mechanisms in numerical models to quantify their impacts on the CO2 injectivity well index in synthetic and real field cases. In addition, a sensitivity analysis was performed for a range of brine compositions of seawater and higher salinities. This analysis shows an additional injectivity reduction as the salinity increases due to the halite scale, in agreement with the lab data from the literature. Another dependence evaluated in this study is when the ratio between capillary and viscous forces is decreased, reducing the injectivity. Additionally, when mineral reaction dissolution is considered in our modeling, it is possible to observe two occurring competitive phenomena, where the mineral dissolution can compensate for part of the injectivity loss due to salt deposition in the dry-out zone. That is especially relevant when the reservoir rock matrix is rich in reactive minerals, such as calcite and dolomite. However, mineral dissolution may lead to fines, and the risk of fines migration can lower the injectivity by at least 10% within five years of CO2 injection, according to our results. The mineral dissolution is also considered in these calculations, and the loss in injectivity is the net result of dissolution and fines migration. The gain in porosity–permeability as the results of mineral dissolution was modeled using the Kozeny-Carman equation. The results show the importance of considering the uncertainty of injectivity loss in CCS projects, where the amount of CO2 captured for storage must be injected often with no other alternatives, highlighting the need to provide flexibility in project planning to deal with such risks.

The inflow performance relationship in fractured, vertical, and dewatered coalbed-methane wells

Although not greatly studied, the inflow performance relationship (IPR) in dewatered and vertical coalbed methane (CBM) wells is essential in the development of a CBM reservoir. The dynamics of the stress sensitivity effect (SSE) and the matrix shrinkage effect (MSE), as well as the hydraulic fracture propagation, have all been neglected, especially for the exterior region, which is larger than the drainage radius. A novel IPR model has now been built that integrates dynamic SSE–MSE and hydraulic fracture propagation into the skin factor, and is validated with real production data from the Qinshui Basin, China. The absolute open flow rate given the SSE–MSE is 60.5% larger than without SSE–MSE. If the positive effect of the SSE–MSE on the permeability in the exterior region is neglected, the absolute open flow rate is reduced by 21%. The MSE has a greater effect on the fracturing skin factor than the SSE and tends to lower the fracturing skin factor, benefitting the production of CBM. Moreover, in light of the SSE or MSE, the non-Darcy flow effect is weaker due to restraints on the velocity of flow or the permeability. Useful and essential theoretical guidance for real CBM production can thus be gleaned from this novel IPR model.

Hydraulic diffusivity estimations for US shale gas reservoirs with Gaussian method: Implications for pore-scale diffusion processes in underground repositories

This paper first presents so-called unified Gaussian solutions for the spatial advance of diffusion transients triggered by a sudden change in pressure, molecular mass concentration and/or temperature. The mathematical description with a Gaussian solution for the pressure transient is similar to that for molecular diffusion and quantifies the diffusion of pressure into the reservoir space due to a change in molecular density initiated at the well intervention point. The resulting pressure gradients due to the pressure transient quantify, via Darcy's Law, the fluid-particle velocity resulting from that gradient everywhere in the reservoir. Also based on the Gaussian pressure transient, a Gaussian decline curve fitting formula is derived, uniquely scaled by the hydraulic diffusivity. The physics-based, Gaussian decline curve equation was utilized to match 30-year production data from 68 counties in four major US shale gas plays to compute their hydraulic diffusivities. The average hydraulic diffusivities of Marcellus, Haynesville-Bossier, Barnett and Utica shale are 7.43 × 10−9 m2 s−1, 7.9 × 10−9 m2 s−1, 12.3 × 10−9 m2 s−1, and 59.0 × 10−9 m2 s−1, respectively. The empirical history-matched estimates of the pressure-gradient-driven diffusion rates in shale are similar or faster than the shale diffusion-rates measured in the laboratory. It can be assumed that the empirical diffusion rate accounts for the integrated effects of Darcy and non-Darcy flow. Computation of the Gaussian Péclet number in gas plays confirms that the advective flux is much faster than the combined Fickean and non-Fickean mass transport rates. The implications for gas recovery from shale formations, and secure disposal of nuclear waste in the subsurface shale repositories (wellbores and cavities) are discussed. In particular, our field estimations being faster than the laboratory diffusion rates calls for caution because mass transport from leaking containers at disposal sites would diffuse several orders of magnitude faster than suggested by the slower laboratory rates.

Two-phase Flow Model and Productivity Evaluation of Gas and Water for Dual-Medium Carbonate Gas Reservoirs

Fluid flow in the dual-medium carbonate gas reservoir is characterized by stress sensitivity and non-Darcy flow effect. In order to accurately describe the unsteady flow of gas and water in the dual-medium gas reservoir, a two-phase flow model of gas and water is built. First, reservoir space and fluid flow characteristics of carbonate gas reservoirs are investigated, and the flow model that considers both the stress sensitivity and non-Darcy flow is built based on the fundamental flow theory, after fully investigating the reservoir space and fluid flow characteristics of carbonate gas reservoirs. Then, the perturbation theory is introduced, and the model is solved in the Laplace space, after which the obtained Laplace space analytical solution is converted into the real-space solution. Finally, the productivity evaluation model for the dual-medium gas reservoir with the gas-water two-phase flow is built, based on the flowing material balance method and Newton iteration. The presented productivity evaluation model is applied to analyze the effects of stress sensitivity and non-Darcy flow on the two-phase flow model of gas and water for the dual-medium gas reservoir and the reservoir productivity. The results indicate that a higher stress sensitivity coefficient is demonstrated to indicate higher stress sensitivity and accelerated production decline of the reservoir, while a lower non-Darcy flow effect coefficient represents a stronger non-Darcy effect and boosted drop of initial production of the reservoir. Hence, it is not reasonable to neglect the effects of stress sensitivity and non-Darcy flow during the evaluation of the productivity of a dual-medium carbonate gas reservoir. The model presented in this research provides important references for improving the recovery performance of dual-medium gas reservoirs.

Effects of foam structure on thermochemical characteristics of porous-filled solar reactor

The foam-structured reactor is one which has hitherto been regarded as of great potential for industrial applications in the field of solar thermochemistry. The utilization mode of ceramic foam has, generally, a significant impact on energy conversion and storage efficiency. This study establishes a numerical model, coupled with computational fluid dynamics and dry reforming of methane reaction kinetics, to find the optimal structural parameters of the ceramic foam. A local thermal non-equilibrium model coupled with the P1 approximation has been developed to address the heat-transfer problems, and the non-Darcy flow effect has been considered to calculate the momentum dissipation in the porous zone. Based on ample simulation examples, the effects of porosity and foam cell size on the reaction temperature, surface heat loss, thermal efficiency, CH4/CO2 conversion, H2/CO yield, carbon deposition, and solar-to-chemical efficiency are illustrated in detail. The results indicate that using the ceramic foam with high porosity and large cell size is able to attain the best thermochemical characteristics, of which the validity can be assured, insofar as the various operating conditions in this study are concerned. Furthermore, as compared to the best single-layer structure, the application of the optimized double-layer foam structure is a more effective solution, which is able to further improve the energy storage efficiency by a remarkable 9.23%.

Cell performance and flow losses of proton exchange membrane fuel cells with orientated-type flow channels

Orientated-type flow channels of proton exchange membrane fuel cells having baffles increase the cell performance, however, the higher power loss accounted by baffles, is a non-ignorable disadvantage. Previous literature proves that the baffles in channels cause the increase in power losses, while how the baffles affect the power losses, including the frictional losses and local losses, are still not analyzed before. Therefore, in this paper, a two-dimensional model is developed to study the friction loss and local loss in the flow channels with baffles. The numerical model, which couples the non-Darcy flow effect, is validated by comparing with self-conducted experimental results. Experimental and simulation results reveal that: orientated-type flow channels facilitate enhance the power output, and with the enlargement of baffles, the performance is further enhanced. In addition, the frictional losses and local losses in the orientated-type flow channels are comparatively studied by a numerical approach for the first time. It is found that using the materials with low surface roughness can decrease the friction loss; and avoiding sudden expanded segments at leeward sides of baffles can reduce the local loss. The experimental results and simulation results can further help improve the flow channel design.

Novel Mathematical Model for Transient Pressure Analysis of Multifractured Horizontal Wells in Naturally Fractured Oil Reservoirs.

Multifractured horizontal wells have gained significant attention within the petroleum industry for commercial development. Despite considerable developments of transient pressure analysis or flow rate behaviors for horizontal wells in naturally fractured reservoirs, some significant problems are yet to be resolved, including high heterogeneity of reservoirs, pressure sensitivity of hydraulic fractures, and non-Darcy flow effect, which may occur during the production life. This paper presents a more pragmatic mathematical model for multifractured horizontal wells in naturally fractured reservoirs based on the fractal system, the theory of permeability modulus, and the time-fractional calculus correspondingly as an extension of the classic trilinear flow model. This new model comprises three modules: high heterogeneity of the reservoir based on the fractal system, the permeability modulus typically showing the pressure sensitivity of hydraulic fractures, and the anomalous diffusion describing non-Darcy flow turbulence. This investigation evaluates a trilinear dual-permeability dual-porosity flow model, with the dual-porosity model for the unstimulated outer reservoir flow region, the dual-permeability model for the stimulated inner reservoir flow region, and the permeability modulus for the flow region of hydraulic fractures. The comprehensive sensitivity analysis conducted indicates how the key parameters, such as fractal dimension, hydraulic fracture permeability modulus and conductivity, interporosity flow coefficient, storativity ratio, etc., affect the transient pressure behaviors, along with their reasons for the change in behavior. Application to a field case study further demonstrates the validity of the mathematical model, and the results presented may play a guiding role in well test interpretation.

Fractal Model for Predicting Elemental Sulfur Saturation in the Presence of Natural Fracture.

Sour gas reservoirs are an important part of unconventional gas reservoirs, which are widely distributed in the world. However, elemental sulfur deposition, channel plugging, and productivity reduction consequentially occur in the development of high sour gas fields as pressure drops. The accurate prediction of sulfur deposition is a very important work for sour gas reservoirs. In this paper, a fractal model is presented for predicting elemental sulfur saturation in the presence of natural fracture. The model takes into consideration the effects of non-Darcy flow. In addition, the influence parameters such as fractal dimension, fractal index, and non-Darcy flow are studied. The results showed the following: (1) sulfur deposition was overestimated by Hu’s model, and this paper model is more accurate for prediction of sulfur deposition; (2) elemental sulfur deposition decreases with the increase of the fractal dimension, while elemental sulfur deposition increases with the decrease of the fractal index; and (3) non-Darcy flow should be considered because it causes a faster rate of sulfur deposition. This research will provide a basis and reference for predicting elemental sulfur saturation in the presence of natural fracture for sour gas reservoirs.

Improving two-phase mass transportation under Non-Darcy flow effect in orientated-type flow channels of proton exchange membrane fuel cells

Orientated-type flow channels of proton exchange membrane fuel cells cause non-Darcy effect occurring in flow regions. Therefore, the species transportation is affected by inertial effect. However, how the inertial force affects convection and diffusion of different species has not been discussed before. Thus, a modified two-dimensional, non-isothermal, two-phase and steady state model considering non-Darcy effect is employed in this study, and reactants and products transportations through diffusion and convection under inertial effects are quantitatively analyzed for the first time. Simulation results reveal that the convective transportation of reactants increases more under the influence of inertial force; water vapor transportation through convection increases the water content in porous regions. At the same time, liquid water expels more rapidly from gas diffusion layers under baffle regions, and enlarging baffle volumes increases the regions where the liquid water is rapidly removed under the inertial effect.

FRACTAL ANALYSIS OF SHALE GAS TRANSPORT THROUGH MICROPORES AND MICROFRACTURES

In order to commercially develop shale gas reservoirs, it is necessary to understand the gas transport mechanisms in shale matrix and how matrix permeability evolves during reservoir depletion. In this work, improved apparent permeability models to describe gas transport through microstructures (i.e. micropores and microfractures) in organic matter (OM) and inorganic matter (iOM) of shale matrix are proposed. The models are able to consider the combined effects of poromechanics, non-Darcy flow, gas sorption and fractal dimension of microstructures on gas flow behavior. The obtained results indicate that microfracture aperture declines by a larger margin than micropore diameter when reservoir depletes. A greater microstructure size fractal dimension and maximum microstructure size lead to a larger apparent permeability, while a greater tortuosity fractal dimension leads to a smaller apparent permeability. In shale matrix, the apparent permeability of inorganic microstructures is much larger than that of organic microstructures. In OM or iOM, when micropores and microfractures have the same cross-section area, the apparent permeability of micropores is larger than that of microfractures. Furthermore, for microstructures in OM, the contribution of different flow regimes to total gas flow varies with pore pressure and microstructure size. For microstructures in iOM, the contribution of slip flow dominates the gas transport. The obtained results provide new insights for understanding gas transport behavior in shale reservoirs from a microscopic perspective.

Two-Dimensional Numerical Analysis of Non-Darcy Flow Using the Lattice Boltzmann Method: Pore-Scale Heterogeneous Effects

Abstract This study simulates pore-scale two-dimensional flows through porous media composed of circular grains with varied pore-scale heterogeneity to analyze non-Darcy flow effects on different types of porous media using the lattice Boltzmann method. The magnitude of non-Darcy coefficients and the critical Reynolds number of non-Darcy flow were computed from the simulation results using the Forchheimer equation. Although the simulated porous materials have similar porosity and representative grain diameters, larger non-Darcy coefficients and an earlier onset of non-Darcy flow were observed for more heterogeneous porous media. The simulation results were compared with existing correlations to predict non-Darcy coefficients, and the large sensitivity of non-Darcy coefficients to pore-scale heterogeneity was identified. The pore-scale heterogeneity and resulting flow fields were evaluated using the participation number. From the computed participation numbers and visualized flow fields, a significant channeling effect for heterogeneous media in the Darcy flow regime was confirmed compared with that for homogeneous media. However, when non-Darcy flow occurs, this channeling effect was alleviated. This study characterizes non-Darcy effect with alleviation of the channeling effect quantified with an increase in participation number. Our findings indicate a strong sensitivity of magnitude and onset of non-Darcy effect to pore-scale heterogeneity and imply the possibility of evaluating non-Darcy effect through numerical analysis of the channeling effect.

A New Prediction Model of Water Breakthrough Time of Horizontal Well in Inclined Edge-Water Low Permeability Gas Reservoir

At present, the existing water breakthrough time models in edge-water gas reservoirs are mainly based on the vertical well scheme and ignore the impact of the formation dip angle and non-Darcy flow effect, thus resulting in some differences between the predicted and actual measured data. To improve the accuracy of prediction, we have considered the effect of gravity caused by the dip angle in the edge-water gas reservoir. The established mathematical model of a low permeability edge-water gas reservoir is based on the theory of gas-water two-phase seepage. The prediction model of water breakthrough time in a horizontal well considers the influence of the formation dip angle, starting pressure gradient, and non-Darcy flow effect. The prediction model sensitivity analysis has been carried out. The results show that the predicted time of the new model is closer to the actual water breakthrough time in the gas reservoir than that of the existing models. The sensitivity analysis results show that the water breakthrough time decreases with increase in the gas well production, and increases with increase in formation dip angle, horizontal well length, and original distance between the gas-water interface and the well bottom. For the same horizontal well length, the water breakthrough time calculated considering the non-Darcy flow effect is shorter than the time calculated without considering the non-Darcy flow effect. The research results provide the necessary background for accurate prediction of the water breakthrough time in edge-water gas reservoirs.

Revising Transient-Pressure Solution for Vertical Well Intersected by a Partially Penetrating Fracture with Non-Darcy Flow Effect

The principle purpose of this work is to formulate an accurate mathematical model to evaluate the transient pressure behavior of a well intercepted by a partially penetrating vertical fracture (PPVF) with non-Darcy flow effect. Fracture conductivity is taken into account by coupling the three-dimensional flow in reservoir and the two-dimensional flow within fracture; the Barree-Conway model is incorporated into the model to analyze non-Darcy flow behavior in fracture, which leads to the nonlinearity of the governing equations. A high-effective iterative algorithm using a combined technique of fracture-panel discretization and dimension transform is developed to render the nonlinear equations amenable to analytical linear treatment. On the basis of the solutions, the pressure response and its derivative type curves were generated to identify the evolution of flow regimes with time. Furthermore, the influences of fracture conductivity, penetration ratio, and non-Darcy characteristic parameters on pressure response are investigated. The results show that PPVF exhibits five typical flow regimes, and analytical solutions for each flow regime are similar to that for a fully penetrating vertical fracture (FPVF) that can be correlated with the penetration ratio and apparent conductivity. The non-Darcy flow effect is found to have more significant effect on the low and moderate conductivity, especially in early-stage flow regimes. When the penetration ratio is smaller than 0.5, the pressure behavior exhibit a more remarkable variation with penetration ratio. This study provides a better insight into understanding the influence of non-Darcy flow on flow regime identification.

Pressure Performance of Highly Deviated Well in Low Permeability Carbonate Gas Reservoir Using a Composite Model

It is commonly believed that matrix and natural fractures randomly distribute in carbonate gas reservoirs. In order to increase the effective connected area to the storage space as much as possible, highly deviated wells are widely used for development. Although there have been some studies on the composite model for highly deviated wells, they have not considered the effects of stress sensitivity and threshold pressure gradient in a dual-porosity gas reservoir. In this paper, a semi-analytical composite model for low permeability carbonate gas reservoir was established to study the effect of non-Darcy flow. By employing source function, Fourier transform and the perturbation method, the pressure performance and typical well test curves were obtained. Eight flow regimes were identified, and their characteristics were discussed. As a result, it can be concluded that the effects of stress sensitivity and threshold pressure gradient would make pseudo-pressure and derivative curves rise, which is the characteristic of non-Darcy flow to determine whether there is stress sensitivity or threshold pressure gradient.

An Analytical Model for Production Analysis of Hydraulically Fractured Shale Gas Reservoirs Considering Irregular Stimulated Regions

Shale gas reservoirs are typically developed by multistage, propped hydraulic fractures. The induced fractures have a complex geometry and can be represented by a high permeability region near each fracture, also called stimulated region. In this paper, a new integrative analytical solution coupled with gas adsorption, non-Darcy flow effect is derived for shale gas reservoirs. The modified pseudo-pressure and pseudo-time are defined to linearize the nonlinear partial differential equations (PDEs) and thus the governing PDEs are transformed into ordinary differential equations (ODEs) by integration, instead of the Laplace transform. The rate vs. pseudo-time solution in real-time space can be obtained, instead of using the numerical inversion for Laplace transform. The analytical model is validated by comparison with the numerical model. According to the fitting results, the calculation accuracy of analytic solution is almost 99%. Besides the computational convenience, another advantage of the model is that it has been validated to be feasible to estimate the pore volume of hydraulic region, stimulated region, and matrix region, and even the shape of regions is irregular and asymmetrical for multifractured horizontal wells. The relative error between calculated volume and given volume is less than 10%, which meets the engineering requirements. The model is finally applied to field production data for history matching and forecasting.

Integrated optimum design of hydraulic fracturing for tight hydrocarbon-bearing reservoirs

Although hydraulic fracturing is not a new technology, it has not yet been implemented in the United Arab Emirates. Abu Dhabi National Oil Company (ADNOC), the regional producer in United Arab Emirates, has set out to initiate the utilization of this treatment during year 2019. In this work, a systematic design procedure for hydraulic fracturing in tight petroleum-bearing reservoirs is proposed. The design caters for surface and subsurface flow parameters, and it is hoped to provide basic guidelines for ADNOC in this respect. The proposed design process incorporates both unified fracture design (UFD) methodology and the fracture geometry (PKN) model. Excel spreadsheets were developed and utilized to run sensitivity analysis for optimal performance and predict long-term production profiles before and after fracturing. The excel spreadsheets made are flexible in use, in the sense that they resolve issues with infinite/finite fractures, high/low surface injection rate as well as investigate for non-Darcy flow effects. Reliable published data were used to perform the necessary calculations. The results of the performance calculations have shown that it is possible to access commercial quantities of hydrocarbons from a tight reservoir. In addition, improved productivity by 15-folds and increased gas recovery of 1.02 MMMscf over the first 8 years of production can be achieved by proper hydraulic fracturing design and implementation in tight gas reservoirs. The results of calculations of non-Darcy effect revealed a threshold velocity of approximately 0.2 fps above which these effects could become significant in predicting the overall flow efficiency inside the fracture. To the authors’ knowledge, the literature has not fully addressed the hydraulic fracturing design analytically, and the methodology proposed in this work provides a complete design package which incorporates the UFD concept, the PKN model, the non-Darcy model, and long-term prediction of post-fracturing production performance, and applying the proposed approach in a case study.