Hydraulic Fracture Conductivity Research Articles

Uncertainty analysis for seawater intrusion in fractured coastal aquifers: Effects of fracture location, aperture, density and hydrodynamic parameters

In this study we use polynomial chaos expansion (PCE) to perform uncertainty analysis for seawater intrusion (SWI) in fractured coastal aquifers (FCAs) which is simulated using the coupled discrete fracture network (DFN) and variable-density flow (VDF) models. The DFN-VDF model requires detailed discontinuous analysis of the fractures. In real field applications, these characteristics are usually uncertain which may have a major effect on the predictive capability of the model. Thus, we perform global sensitivity analysis (GSA) to provide a preliminary assessment on how these uncertainties can affect the model outputs. As our conceptual model, we consider fractured configurations of the Henry Problem which is widely used to understand SWI processes. A finite element DFN-VDF model is developed in the framework of COMSOL Multiphysics®. We examine the uncertainty of several SWI metrics and salinity distribution due to the incomplete knowledge of fracture characteristics. PCE is used as a surrogate model to reduce the computational burden. A new sparse PCE technique is used to allow for high polynomial orders at low computational cost. The Sobol’ indices (SIs) are used as sensitivity measures to identify the key variables driving the model outputs uncertainties. The proposed GSA methodology based on PCE and SIs is useful for identifying the source of uncertainties on the model outputs with an affordable computational cost and an acceptable accuracy. It shows that fracture hydraulic conductivity is the first source of uncertainty on the salinity distribution. The imperfect knowledge of fracture location and density affects mainly the toe position and the total flux of saltwater entering the aquifer. Marginal effects based on the PCE are used to understand the effects of fracture characteristics on SWI. The findings provide a technical support for monitoring, controlling and preventing SWI in FCAs.

Well test analysis for a well with stress-sensitive natural fracture permeability and stress-dependent hydraulic fracture conductivities

The commonly used methods in dual-porosity systems assume constant reservoir permeability over an entire range of formation pressure and constant hydraulic fracture conductivity inside the fractures. In this paper, the hydraulic fracture conductivity and natural fracture permeability were considered as a function of pressure. Based on finite-conductivity vertical fracture bilinear flow model in stress sensitive dual-porosity reservoirs, the analytical solutions were solved by perturbation and Laplace transform method. The features of typical curves were studied. The pressure and pressure derivative curves with stress-sensitivity were compared with the curves without stress-sensitivity. The influences of inter-porosity coefficient, storativity ratio, wellbore storage coefficient, permeability modulus and the hydraulic fracture conductivity on the typical curves were analysed with different seepage regimes. The results show that both the pressure and pressure derivative curves move upward in pressure-sensitive formations, especially for the end of the curves. The upward trend behaves more obviously due to stress sensitivity of the fractures. Field examples were applied to verify the validity of the proposed model. The novel well test model improves the accuracy of well test interpretation results, which is essential to the design and evaluation of stimulation treatments in these reservoirs. [Received: August 21, 2017; Accepted: September 10, 2018]

Псевдоскин-фактор и оптимальная проводимость трещины гидроразрыва в круговом пласте

Псевдоскин-фактор и оптимальная проводимость трещины гидроразрыва в круговом пласте

Well test analysis for a well with stress-sensitive natural fracture permeability and stress-dependent hydraulic fracture conductivities

Well test analysis for a well with stress-sensitive natural fracture permeability and stress-dependent hydraulic fracture conductivities

On the Application of the Channel-Fracturing Technique to Soft Rock Formations

Summary The application of the channel-fracturing technique can result in a significant increase in the conductivity of hydraulic fractures and reduced proppant usage. In soft rock formations, the conductivity of the partially propped fractures would depend not only on the volume fraction of the open channels, but also on the elastic deformation of open channels and fracture closure resulting from proppant consolidation and embedment. In this study, an analytical approach is developed for identifying the optimal proppant column spacing that maximizes the effective conductivity. The latter parameter can guide the design of the proppant-injection schedule and well-perforation scheme. To demonstrate the approach, we conduct a parametric study under realistic field conditions and identify the folds of increase in fracture conductivity and reduction in proppant use resulting from the optimized application of the channel-fracturing technique. The outcomes of the parametric study could be particularly useful in the application of the developed approach to soft rock formations.

Evaluating the performance of hydraulic-fractures in unconventional reservoirs using production data: Comprehensive review

Understanding the performance of the reservoir productivity in the post-stimulation conditions has recently gained an extensive emphasis from the specialist researchers and operators. Although there have been different tools used to evaluate the fracturing process and to predict the well performance, using production data as an indirect tool to calibrate the fracturing design and to forecast the reservoir performance has been considered the most potential technique. However, different methods with a high ambiguity have been used in this area of research over the last decade. Therefore; developing, screening, and specializing different methods and techniques to diagnose and evaluate the post-fracture reservoir performance by using flowback data has a significant priority. Determining the performance of hydraulic fractures from flowback data is considered the actual calibration to estimate the effective volume, length, height, conductivity, and width of hydraulic fractures. This paper presents a comprehensive review on most of the approaches, which have been recently introduced in this area of research, including their applicability, pros and cons. Furthermore, this study explains how each method can be valid at a specific time range. The potential tools, which could be more successful to be used in this direction of research, have been extensively discussed and recommended.

Transient-Rate Analysis of Stress-Sensitive Hydraulic Fractures: Considering the Geomechanical Effect in Anisotropic Shale

Summary Production from multistage-fractured horizontal wells (MFHWs) in shale reservoirs causes stress changes that further influence the conductivities of hydraulic fractures. Moreover, many shale rocks are strongly anisotropic. The objective of this study is to semianalytically model hydrocarbon-flow dynamics in reservoirs with MFHWs. The effects of stress-sensitive hydraulic fractures and shale anisotropy are considered. First, this study explores the relationship between principal-stress and pore-pressure changes in anisotropic shale. Second, an exponential correlation is further incorporated to describe the fracture conductivities vs. pore-pressure changes in anisotropic shale. The exponential correlation is validated by matching experimental data of fracture conductivities vs. effective stress. The fracture compressibility df in the exponential equation is stress-dependent rather than constant. Next, this study discretizes each hydraulic fracture into several source segments. For each segment in each timestep, pressure distribution is calculated with source/sink functions. Both the stress field and the hydraulic-fracture conductivities are updated according to the pressure distribution with the previously mentioned correlations before starting the next timestep. In addition to the constant-bottomhole-flowing-pressure condition, nonconstant bottomhole pressure (BHP) in real-field cases can also be entered for this semianalytical model. The model is validated by comparing its results with numerical simulations. A series of type curves q vs. t is generated on the basis of model calculations. The type curves are applied to investigate the effects of initial fracture conductivity Fci, initial fracture compressibility dfi, declining rate of fracture compressibility β, shale anisotropy, and the BHP profiles on MFHW transient-rate behavior. To maximize the hydrocarbon production, the BHP profile must be adjusted on the basis of fracture stress-sensitive characteristics. The semianalytical model is used to analyze two field cases with different pwf profiles under the influence of stress-sensitive hydraulic fractures.

A new low-permeability reservoir core analysis method based on rate-transient analysis theory

Unconventional reservoirs such as shales (mudrocks) and coals may exhibit an ultra-low matrix permeability (<0.001 md) challenging conventional laboratory-based methods for permeability measurement. Small-diameter core plug or crushed rock samples, combined with unsteady-state methods, are currently favored to reduce measurement times for ‘tight’ rocks. For core plug analysis, unsteady-state pulse-decay permeability (PDP) or steady-state methods (SS) are commonly employed in commercial laboratories, with the core plug sample subjected to confining stress. Analysis times, particularly for SS methods, may be excessive for ultra-low permeabilities in the nanodarcy range. Another limitation of both PDP and SS experiments applied to core plugs is that they do not represent the boundary conditions typically used to produce hydrocarbons from unconventional reservoirs in the subsurface through wells.Rate-transient analysis (RTA) is a technique used to quantitatively analyze production data from wells drilled into unconventional reservoirs to extract reservoir (e.g. permeability, hydrocarbons-in-place) and hydraulic fracture (conductivity, fracture length) properties. Multi-fractured horizontal wells (MFHWs) producing from low-permeability reservoirs commonly exhibit the flow-regime sequence of transient linear flow, where hydrocarbons flow through the reservoir orthogonal to hydraulic fractures or the horizontal well, followed by boundary-dominated flow caused by pressure interference between adjacent hydraulic fractures or wells. Transient linear flow may be analyzed using RTA methods to extract fracture or well-length (if permeability is known); the end of linear flow can be used to estimate permeability of the reservoir, and boundary-dominated flow to estimate hydrocarbons-in-place.In this work, a new experimental procedure and set-up, applied to core plugs under stress conditions, is developed to mimic well operating conditions encountered in the field (i.e. producing from a subsurface unconventional reservoir). After injection of methane gas into one end of the core plug, and pressure stabilization, the gas is flowed out of the same end of the core plug at constant pressure (with the aid of a backpressure regulator), and flow rates are measured with a flow meter. This procedure is applied to a core plug extracted from a low-permeability siltstone of the Montney Formation (western Canada). Repeated testing consistently demonstrated a transient linear flow period, as the gas pressure transient propagated along the core plug, followed by boundary-dominated flow after the pressure transient reached the end of the core plug; this sequence is identical to what is commonly observed in the field. Permeability was estimated using both the slope of a square-root of time plot (a common RTA method used to analyze transient linear flow), and the time at the end of linear flow combined with the linear flow distance of investigation (DOI) equation. Permeability from both techniques is in good agreement (±5% for both experiments performed), providing an important redundancy to the analysis procedure. Pore volume (and hence porosity, with bulk volume known) may be estimated from the time at the end of linear flow and the slope of the square-root of time plot – the calculated value is in excellent agreement (±2% for both experiments performed) with that obtained from pore volume/porosity estimates using a helium pycnometer (combined with calipered dimensions). Finally, test times for the ∼0.0007 md core plug sample, after the initiation of the production phase, are on the order of only a few minutes to obtain the two independent estimates of permeability and pore volume, which is faster than that achievable from a PDP test.The new innovative experimental procedure is successful in reproducing the physics of flow in unconventional reservoirs, with the results being analyzable with the same techniques applied to field data.

An analytical model for multiple fractured shale gas wells considering fracture networks and dynamic gas properties

Multi-stage fractured horizontal wells play an important role in developing shale gas reservoirs by significantly improving productivity. By considering fracture networks, gas desorption, stress-sensitive fracture permeability, and pressure-dependent gas PVT properties, an analytical model is developed for shale gas wells. Fracture networks are handled based on transient linear flow, gas desorption is handled by defining a new total compressibility, stress-dependent hydraulic fracture permeability is handled by variable substitution, and pseudo-pressure and pseudo-time are used to handle pressure-dependent PVT properties. After obtaining the solution of the linearized model, a material balance method and successive substitution iteration procedure are proposed to convert the pseudo-time into real time and calculate the production contribution from gas desorption. The results show that induced fractures also have a great impact on the production of the well. Production contribution from free gas and adsorbed gas could be quantified using the proposed material balance principle and iterative method. The rank of parameters that influence the ultimate recovery is the following: half-length of hydraulic fracture, induced fracture length/hydraulic fracture spacing, hydraulic fracture spacing, conductivity of induced fractures, conductivity of hydraulic fracture, and induced fracture spacing.

Well Performance Simulation and Parametric Study for Different Refracturing Scenarios in Shale Reservoir

Refracturing is an encouraging way to uplift gas flow rate and ultimate gas recovery from shale gas wells. A numerical model, considering the stimulated reservoir volume and multiscale gas transport, is applied to simulate the gas production from a refractured shale gas well. The model is verified against field data from a shale gas reservoir in Sichuan Basin. Two refracturing scenarios: refracturing through existing perforation clusters and refracturing through new perforation zones, are included in the simulation work. Three years after production is determined to be the optimum time for refracturing based on the evolution analysis of reservoir pressure, effective stress, fracture permeability, and gas recovery. The role that the hydraulic fracture conductivity and hydraulic fracture half-length play in gas production for different refracturing cases is explored. Pumping parameters of the refracturing job in Sichuan Basin are discussed combining with sensitivity analysis, and suggestions for pumping parameters optimization are proposed.

The workflow to analyze hydraulic fracture effect on hydraulic fractured horizontal well production in composite formation system

Hydraulic fracturing generally leads to highly complex hydraulic networks for tight oil reservoirs. It is significant to understand the hydraulic fracture effect on well performance. As an effective tool, semi-analytical solution for well pressure transient analysis (PTA) and rate transient analysis (RTA) is used in large amount because of higher calculation efficiency than numerical solution. In this paper, the PTA and RTA methods and result of composite formation system (CFS) are shown comprehensively. Firstly, a mathematical model of multistage fractured horizontal well (MsFHW) in CFS was proposed for tight oil reservoir with different regions and formation properties. In the model, two regions with different formation parameters were distinguished. This assumption of two regions, i.e. CFS is a composite tight reservoir formed after hydraulic fracturing. Difference of finite hydraulic fracture conductivity, inclined angle of hydraulic fracture, different shapes of multi-wing fractures in perforating point are considered to make this model powerful to analyze production performance of different MsFHW types. The inner and outer regions were assumed as dual porosity medium but single porosity medium model can also be solved by simplification. Then, the solution of MsFHW performance analysis model is obtained by source function method and the source function superposition principle which are common used in PTA and RTA. PTA for well producing at a constant production rate and RTA for well producing at a constant wellbore pressure were obtained and discussed. Different flow regimes were divided for different fracture geometry situations. The effects of different MsFHW types on PTA and RTA were analyzed. The inflow performance for different hydraulic fractures were presented. Cited as : Yuan, J., Jiang, R., Zhang, W. The workflow to analyze hydraulic fracture effect on hydraulic fractured horizontal well production in composite formation system. Advances in Geo-Energy Research, 2018, 2(3): 319-342, doi: 10.26804/ager.2018.03.09

Hydraulic Conductivity Calibration of Logging NMR in a Granite Aquifer, Laramie Range, Wyoming.

In granite aquifers, fractures can provide both storage volume and conduits for groundwater. Characterization of fracture hydraulic conductivity (K) in such aquifers is important for predicting flow rate and calibrating models. Nuclear magnetic resonance (NMR) well logging is a method to quickly obtain near-borehole hydraulic conductivity (i.e., KNMR ) at high-vertical resolution. On the other hand, FLUTe flexible liner technology can produce a K profile at comparable resolution but requires a fluid driving force between borehole and formation. For three boreholes completed in a fractured granite, we jointly interpreted logging NMR data and FLUTe K estimates to calibrate an empirical equation for translating borehole NMR data to K estimates. For over 90% of the depth intervals investigated from these boreholes, the estimated KNMR are within one order of magnitude of KFLUTe . The empirical parameters obtained from calibrating the NMR data suggest that "intermediate diffusion" and/or "slow diffusion" during the NMR relaxation time may occur in the flowing fractures when hydraulic aperture are sufficiently large. For each borehole, "intermediate diffusion" dominates the relaxation time, therefore assuming "fast diffusion" in the interpretation of NMR data from fractured rock may lead to inaccurate KNMR estimates. We also compare calibrations using inexpensive slug tests that suggest reliable KNMR estimates for fractured rock may be achieved using limited calibration against borehole hydraulic measurements.

Role of proppant distribution on the evolution of hydraulic fracture conductivity

The residual opening of fluid-driven fractures is conditioned by proppant distribution and has a significant impact on fracture conductivity - a key parameter to determine fluid production rate and well performance. A 2D model follows the evolution of the residual aperture profile and conductivity of fractures partially/fully filled with proppant packs. The model accommodates the mechanical response of proppant packs in response to closure of arbitrarily rough fractures and the evolution of proppant embedment. The numerical model is validated against existing models and an analytic solution. Proppant may accumulate in a bank at the fracture base during slick water fracturing, and as hydraulic pressure is released, an arched zone forms at the top of the proppant bank as a result of partial closure of the overlaying unpropped fracture. The width and height of the arched zone decreases as the fluid pressure declines, and is further reduced where low concentrations of proppant fill the fracture or where the formation is highly compressible. This high-conductivity arch represents a preferential flow channel and significantly influences the distribution of fluid transport and overall fracture transmissivity. However, elevated compacting stresses and evolving proppant embedment at the top of the settled proppant bed reduce the aperture and diminish the effectiveness of this highly-conductive zone, with time. Two-dimensional analyses are performed on the fractures created by channel fracturing, showing that the open channels formed between proppant pillars dramatically improve fracture transmissivity if they are maintained throughout the lifetime of the fracture. However, for a fixed proppant pillar height, a large proppant pillar spacing results in the premature closure of the flow channels, while a small spacing narrows the existing channels. Such a model provides a rational means to design optimal distribution of the proppant pillars using deformation moduli of the host to control pillar deformation and flexural spans of the fracture wall.

Production-Pressure-Drawdown Management for Fractured Horizontal Wells in Shale-Gas Formations

Summary The development of unconventional shale-gas formations in North America with horizontal multifractured wells is mature enough to identify production malpractices and abnormal productivity declines generally observed within 18–24 months of initial production. The primary objective of this study is to address all known causes of these productivity declines and to develop a fully coupled geomechanical/flow simulation model to simulate these production conditions. This model mimics the effect of depletion-induced in-situ stress variations on short-term and long-term productivity by taking into account several phenomena, such as stress-dependent matrix and natural-fracture permeability as well as reduction in hydraulic-fracture conductivity caused by proppant crushing, deformation, embedment, and fracture-face creep. Matrix-permeability evolutions, considering the conflicting effects of non-Darcy flow and compaction, have also been accounted for in this model. Numerical solutions for simplified hydraulic-fracture planar geometries are then obtained by use of a finite-element-method scheme. A synthetic case was defined to investigate the effects of each individual phenomenon on short-term and long-term production. Results show that the combined effects of permeability alterations in matrix and natural fractures as well as conductivity losses in hydraulic fractures may result in substantial cumulative-gas-production loss. The model also reproduces familiar field-observed trends, with lower long-term production corresponding to higher drawdowns. This behavior is attributed to the stress-dependent evolution of reservoir permeability and hydraulic-fracture conductivity. The results show that ignoring the effects of any of the previous phenomena results in overestimation of ultimate recovery. Furthermore, it is shown that proper management of pressure drawdown and the penalty for lower initial production rates in unconventional shale-gas reservoirs can yield substantially higher ultimate recovery. The model is fully versatile and allows modeling and characterization of all widely differing (on a petrophysical level) shale-gas formations as well as proppant materials used for the stimulation treatments. This integrated model can be used for optimization of key parameters during the hydraulic-fracture design, for fine tuning production history matching, and especially as a predictive tool for pressure-drawdown management.

Simulations of the effects of proppant placement on the conductivity and mechanical stability of hydraulic fractures

We generate a wide range of models of proppant-packed fractures using discrete element simulations, and measure fracture conductivity using finite element flow simulations. This allows for a controlled computational study of proppant structure and its relationship to fracture conductivity and stress in the proppant pack. For homogeneous multi-layered packings, we observe the expected increase in fracture conductivity with increasing fracture aperture, while the stress on the proppant pack remains nearly constant. This is consistent with the expected behavior in conventional proppant-packed fractures, but the present work offers a novel quantitative analysis with an explicit geometric representation of the proppant particles. In single-layered packings (i.e. proppant monolayers), there is a drastic increase in fracture conductivity as the proppant volume fraction decreases and open flow channels form. However, this also corresponds to a sharp increase in the mechanical stress on the proppant pack, as measured by the maximum normal stress relative to the side crushing strength of typical proppant particles. We also generate a variety of computational geometries that resemble highly heterogeneous proppant packings hypothesized to form during channel fracturing. In some cases, these heterogeneous packings show drastic improvements in conductivity with only moderate increase in the stress on the proppant particles, suggesting that in certain applications these structures are indeed optimal. We also compare our computer-generated structures to micro computed tomography imaging of a manually fractured laboratory-scale shale specimen, and find reasonable agreement in the geometric characteristics.

How much stimulated reservoir volume and induced matrix permeability could enhance unconventional reservoir performance

This paper investigates the impacts of stimulated reservoir volume (SRV) on reservoir performance for unconventional hydraulically fractured formations. It focuses also on the effects of different petrophysical properties of SRV as well as different volume and petrophysical properties of unstimulated part of porous media (USRV). The influences of hydraulic fracture conductivity, fracture assymmetricity, and non-Darcy flow permeability in reservoir pressure profile have been substantially studied in this paper. Stimulated reservoir volume represents the volume of porous media where complex network structures formed from naturally induced fractures, multiple hydraulic fractures, and original matrix. SRV is characterized by an induced or a stimulated matrix permeability which is typically greater than the original matrix permeability. The formations of interest, in this study, are considered having either stimulated reservoir volume only or both stimulated and un-stimulated reservoir volumes and depleted by multiple hydraulic fractures controlled by non-Darcy flow.The impacts of SRV and USRV on pressure distributions, flow regimes, and productivity indices have been studied using multi-linear flow regimes approach. A new analytical model has been proposed in this paper for pressure behavior of a horizontal well intersected by multiple hydraulic fractures assuming symmetrical and asymmetrical stimulated reservoir volumes. This model was developed using multi-linear flow regimes approach with an adjustment for variable SRVs and USRVs. The volume of stimulated part in the reservoir is determined by hydraulic fracture half length, number of fractures and spacing between them, and fracture height. The impact of induced or stimulated matrix permeability in the stimulated reservoir volume and fracture conductivity as well as non-Darcy flow impact on pressure behaviors have also been investigated. Several analytical models for flow regimes, expected to develop during the entire production life of reservoir, were also proposed in this study. A set of type-curves was designed for pseudo-pressure normalized rate and pseudo-pressure normalized cumulative rate with production time.The outcomes of this study can be summarized as: 1) Generating an analytical model that describes pressure behavior in unconventional reservoirs and considers variable SRVs and USRVs. This model includes stimulated matrix permeability, non-Darcy flow impact, and hydraulic fracture conductivity. 2) Understanding the impact of asymmetrical stimulated reservoir volumes on reservoir performance. 3) Developing analytical models for different linear flow regimes that could develop during the entire life of reservoir. 4) Comparing the productivity index for different stimulated and un-stimulated reservoir volumes assuming both symmetrical and asymmetrical reservoir volume. The most interesting points in this study are: 1) Productivity index drops significantly for the case of asymmetrical SRVs compared to symmetrical SRVs. 2) The SRV enhances productivity index more than USRV, however, at early production time, there is no impact for both of them on productivity index. 3) The impact of assymmetricity is seen at all production time. 4) Flow regime types are not changed with respect to the assymmetricity.

Unconventional multi-fractured analytical solution using dual porosity model

Five-region linear flow system proved to be a useful model to reproduce the flow behavior for multi-fractured horizontal wells in shale reservoirs. In earlier developments, the model was assumed single-porosity throughout all five regions. However, assumption of single porosity system for stimulated region may promote errors in pressure transient analysis. So by adopting the existing mathematical models for naturally fractured reservoirs (dual-porosity system), one can apply the dual-porosity nature of flow in the stimulated reservoir volume (SRV). In this study the analytical solution for single-porosity model is reproduced and compared with numerical solution. Then the five-region model of previous studies is modified by implementing the dual porosity behavior in Laplace domain and compared to single-porosity solution using the same reservoir properties. Furthermore, a series of type-curves is constructed in this study using dimensionless properties, such as matrix-fracture capacity ratio and storativity ratio, hydraulic fracture conductivity, and hydraulic fracture half-length. Theses curves could provide valuable information to characterize the multi-fractured complex systems.

Hydraulic fracture conductivity: effects of rod-shaped proppant from lattice-Boltzmann simulations and lab tests

The goal of this study is to evaluate the conductivity of random close packings of non-spherical, rod-shaped proppant particles under the closure stress using numerical simulation and lab tests, with application to the conductivity of hydraulic fractures created in subterranean formation to stimulate production from oil and gas reservoirs. Numerical simulations of a steady viscous flow through proppant packs are carried out using the lattice Boltzmann method for the Darcy flow regime. The particle packings were generated numerically using the sequential deposition method. The simulations are conducted for packings of spheres, ellipsoids, cylinders, and mixtures of spheres with cylinders at various volumetric concentrations. It is demonstrated that cylinders provide the highest permeability among the proppants studied. The dependence of the nondimensional permeability (scaled by the equivalent particle radius squared) on porosity obtained numerically is well approximated by the power-law function: K/Rv2=0.204ϕ4.58 in a wide range of porosity: 0.3 ≤ ϕ ≤ 0.7. Lattice-Boltzmann simulations are cross-verified against finite-volume simulations using Navier–Stokes equations for inertial flow regime. Correlations for the normalized beta-factor as a function of porosity and normalized permeability are presented as well. These formulae are in a good agreement with the experimental measurements (including packings of rod-shaped particles) and existing laboratory data, available in the porosity range 0.3 ≤ ϕ ≤ 0.5. Comparison with correlations by other authors is also given.

Composite linear flow model for multi-fractured horizontal wells in heterogeneous shale reservoir

Multi-stage fracturing is currently key technique to develop shale reservoirs. Different analytical models have been proposed to fast investigate post-fracturing pressure- and rate-transient behaviors, and hence, estimate key parameters that affect well performance. However, previous analytical models generally neglect reservoir heterogeneity or typical seepage characters of shale, such as adsorption/desorption, gas slippage, and diffusion effects. This paper presents an analytical model for pressure- and rate-transient analysis of multi-stage fractured shale reservoir, considering heterogeneity, typical seepage characters and, specifically, fluids flow from upper/lower reservoir when vertical fractures partially penetrate the formation.This model is similar to five-region-flow model, but subdivides the reservoir into seven parts, namely, two upper/lower-reservoir regions, two outer-reservoir regions, two inner-reservoir regions, and hydraulic fracture region, which are all transient dual porosity media except the hydraulic fracture. As reservoir heterogeneity along the horizontal wellbore is included, the fracture distribution can be various. Fracture interference is simulated by locating a no-flow boundary between two adjacent fractures. The actual locations of these no-flow boundaries of a specific heterogeneous reservoir are determined based on the pressure value which varies with time and space. Thus, the two sides of this boundary has minimum pressure difference, satisfying the no-flow assumption. Adsorption/desorption, gas slippage and diffusion effects are included for rigorous modeling of flow in shale.This model is validated by comparing with commercial well testing software, obtaining a good match in most flow regimes. Log-log dimensionless pressure, pressure derivative and production type curves are generated to conduct sensitivity analysis. Results suggest that larger desorption coefficient causes smaller pressure and its derivative value as a larger proportion of gas is desorbed in formation and contributes to productivity. Solutions from Azari's (1990, 1991) work, where the effect of fracture height is merely treated as a skin factor are investigated as well. Results show that our model is more accurate in partially penetrating cases, and errors of Azari's method become particularly noticeable in early-middle time response. The influence of other parameters, such as matrix permeability, matrix block size, secondary fracture permeability and hydraulic fracture conductivity, are also discussed. Optimal fracture pattern is selected based on cumulative production. Besides, field data are analyzed and compared graphically with modeling solutions, and reliable results are obtained.As numerical and semianalytical methods require extensive computing processing, this model is a practical alternative to predict well-testing results and select optimal well pattern of shale reservoirs. Reservoir heterogeneities in vertical direction can be further added to our model by vertically subdividing the reservoir into more parts.

Pressure Transient Behavior of Horizontal Well with Time-Dependent Fracture Conductivity in Tight Oil Reservoirs

This work presents a discussion on the pressure transient response of multistage fractured horizontal well in tight oil reservoirs. Based on Green’s function, a semianalytical model is put forward to obtain the behavior. Our proposed model accounts for fluid flow in four contiguous regions of the tight formation by using pressure continuity and mass conservation. The time-dependent conductivity of hydraulic fractures, which is ignored in previous models but highlighted by recent experiments, is also taken into account in our proposed model. We also include the effect of pressure drop along a horizontal wellbore. We substantiate the validity of our model and analyze the different flow regimes, as well as the effects of initial conductivity, fracture distribution, and geometry on the pressure transient behavior. Our results suggest that the decrease of fracture conductivity has a tremendous effect on the well performance. Finally, we compare our model results with the field data from a multistage fractured horizontal well in Jimsar sag, Xinjiang oilfield, and a good agreement is obtained.