The Impact of Deformable Surrounding Rocks on Naturally-Fractured Reservoir Simulation

For the case of a fractured reservoir surrounded by deformable rocks, the appropriateness and applicability of the two common methods of coupling of flow and deformation, explicit (coupled) and implicit (uncoupled) methods are investigated. The explicit formulation is capable of modelling surrounding media;while the implicit coupling is unable to do so as deformation vector does not appear as a primary variable in the formulation. The governing differential equations and the finite element approximation of the governing equations for each of the methods are presented. Spatial discretization is achieved using the Galerkin method, and temporal discretisation using the finite difference technique. In the explicit model, coupling between flow and deformation is captured through volumetric strain compatibility amongst the phases within the system. In the implicit model, this is achieved by defining the pore space storativity as a function of the formation compressibility and the compressibility of the fluid phases within the pore space. The impact of rock deformability on early, intermediate and late time responses of fractured reservoir is investigated through several numerical examples. Salient features of each formulation are discussed and highlighted. It is shown that the implicit model is unable to capture the constraining effects of a non-yielding, surrounding rock, leading to incorrect projections of reservoir production irrespective of the history matching strategy adopted.

Efficient production optimization for naturally fractured reservoir using EDFM

Naturally fractured reservoirs make important contributions to global oil and gas reserves and production.The modeling and simulation of naturally fractured reservoirs are different from conventional reservoirs as the existence of natural fractures.To address the development optimization problem of naturally fractured reservoirs,we propose an optimization workflow by coupling the optimization methods with the embedded discrete fracture model(EDFM).Firstly,the effective and superior performance of the workflow is verified based on the conceptual model.The stochastic simplex approximate gradient(StoSAG)algorithm,the ensemble optimization(EnOpt)algorithm,and the particle swarm optimization(PSO)algorithm are implemented for the production optimization of naturally fractured reservoirs based on the improved versions of the Egg model and the PUNQ-S3 model.The results of the two cases demonstrate the effectiveness of this optimization workflow by finding the optimal well controls which yield the maximum net present value(NPV).Compared to the initial well control guess,the final NPV obtained from the production optimization of fractured reservoirs based on all three optimization algorithms is significantly enhanced.Compared with the optimization results of the PSO algorithm,StoSAG and EnOpt have significant advantages in terms of final NPV and computational efficiency.The results also show that fractures have a significant impact on reservoir production.The economic efficiency of fractured reservoir development can be significantly improved by the optimization workflow.

Modeling flow in naturally fractured reservoirs： effect of fracture aperture distribution on dominant sub-network for flow

Fracture network connectivity and aperture （or conductivity） distribution are two crucial features controlling flow behavior of naturally fractured reservoirs. The effect of connectivity on flow properties is well documented. In this paper, however, we focus here on the influence of fracture aperture distribution. We model a two dimensional fractured reservoir in which the matrix is impermeable and the fractures are well connected. The fractures obey a power-law length distribution, as observed in natural fracture networks. For the aperture distribution, since the information from subsurface fracture networks is limited, we test a number of cases： log-normal distributions （from narrow to broad）, power-law distributions （from narrow to broad）, and one case where the aperture is pro- portional to the fracture length. We find that even a well- connected fracture network can behave like a much sparser network when the aperture distribution is broad enough （c~ 〈 2 for power-law aperture distributions and σ ≥ 0.4 for log-normal aperture distributions）. Specifically, most fractures can be eliminated leaving the remaining dominant sub-network with 90% of the permeability of the original fracture network. We determine how broad the aperture distribution must be to approach this behavior and the dependence of the dominant sub-network on the parameters of the aperture distribution. We also explore whether one can identify the dominant sub-network without doing flow calculations.

Borehole stability in naturally fractured reservoirs luring production tests

Based on the plane of weakness theory, a model for predicting borehole stability in fractured reservoirs under different stress states was estiblisted and the equations for solving borehole stability were developed. The minimum downhole pressures required to maintain borehole stability under different natural fracture occurrences were calculated by using the data from a well in the Tazhong （central Tarim） area, Tarim Basin, west China. Several conclusions were drawn for naturally fractured reservoirs with a dip angle from less than 10° to greater than 30°. Application in three wells in the Tazhong area indicates that this model is practically useful.

Fractured reservoir modeling by discrete fracture network and seismic modeling in the Tarim Basin,China

Fractured reservoirs are an important target for oil and gas exploration in the Tarim Basin and the prediction of this type of reservoir is challenging.Due to the complicated fracture system in the Tarim Basin,the conventional AVO inversion method based on HTI theory to predict fracture development will result in some errors.Thus,an integrated research concept for fractured reservoir prediction is put forward in this paper.Seismic modeling plays a bridging role in this concept,and the establishment of an anisotropic fracture model by Discrete Fracture Network （DFN） is the key part.Because the fracture system in the Tarim Basin shows complex anisotropic characteristics,it is vital to build an effective anisotropic model.Based on geological,well logging and seismic data,an effective anisotropic model of complex fracture systems can be set up with the DFN method.The effective elastic coefficients,and the input data for seismic modeling can be calculated.Then seismic modeling based on this model is performed,and the seismic response characteristics are analyzed.The modeling results can be used in the following AVO inversion for fracture detection.

Anisotropic characteristics of electrical responses of fractured reservoir with multiple sets of fractures

In fractured reservoirs, the fractures not but also form the main flow channels which connect productivity of reservoirs. However, because of the only provide the storage space for hydrocarbons, the pores of the matrix, so fractures dominate the heterogeneity and randomness of the distribution of fractures, exploration and evaluation of fractured reservoirs is still one of the most difficult problems in the oil industry. In recent years, seismic anisotropy has been applied to the assessment of fractured formations, whereas electrical anisotropy which is more intense in fractured formations than seismic anisotropy has not been studied or used so extensively. In this study, fractured reservoir models which considered multiple sets of fractures with smooth and partly closed, rough surfaces were established based on the fractures and pore network, and the vertical and horizontal electrical resistivities were derived as a function of the matrix and fracture porosities according to Ohm＇s law. By using the anisotropic resistivity equations, variations of the electrical anisotropy of three types of fractured models under the conditions of free pressure and confining pressure were analyzed through the variations of the exerted pressure, matrix porosity, fracture aperture and formation water resistivity. The differences of the vertical and horizontal resistivities and the anisotropy between the connected and non-connected fractures were also analyzed. It is known from the simulated results that an increase of the confining pressure causes a decrease of electrical anisotropy because of the elasticity of the closed fractures and the decrease of the fracture aperture. For a fixed fracture porosity, the higher the matrix porosity, the weaker the electrical anisotropy in the rock formation.

Numerical simulation of high-resolution azimuthal resistivity laterolog response in fractured reservoirs

The high-resolution azimuthal resistivity laterolog response in a fractured formation was numerically simulated using a three-dimensional finite element method. Simulation results show that the azimuthal resistivity is determined by fracture dipping as well as dipping direction, while the amplitude differences between deep and shallow laterolog resistivities are mainly controlled by the former. A linear relationship exists between the corrected apparent conductivities and fracture aperture. With the same fracture aperture, the deep and shallow laterolog resistivities present small values with negative separations for low-angle fractures, while azimuthal resistivities have large variations with positive separations for high-angle fractures that intersect the borehole. For dipping fractures, the variation of the azimuthal resistivity becomes larger when the fracture aperture increases. In addition, for high-angle fractures far from the borehole, a negative separation between the deep and shallow resistivities exists when fracture aperture is large as well as high resistivity contrast exists between bedrock and fracture fluid. The decreasing amplitude of dual laterolog resistivity can indicate the aperture of low-angle fractures, and the variation of the deep azimuthal resistivity can give information of the aperture of high-angle fractures and their position relative to the borehole.

Structural failure mechanism and strengthening method of fracture plugging zone for lost circulation control in deep naturally fractured reservoirs

Focused on the lost circulation control in deep naturally fractured reservoirs, the multiscale structure of fracture plugging zone is proposed based on the theory of granular matter mechanics, and the structural failure pattern of plugging zone is developed to reveal the plugging zone failure mechanisms in deep, high temperature, high pressure, and high in-situ stress environment. Based on the fracture plugging zone strength model, key performance parameters are determined for the optimal selection of loss control material(LCM). Laboratory fracture plugging experiments with new LCM are carried out to evaluate the effect of the key performance parameters of LCM on fracture plugging quality. LCM selection strategy for fractured reservoirs is developed. The results show that the force chain formed by LCMs determines the pressure stabilization of macro-scale fracture plugging zone. Friction failure and shear failure are the two major failure patterns of fracture plugging zone. The strength of force chain depends on the performance of micro-scale LCM, and the LCM key performance parameters include particle size distribution, fiber aspect ratio, friction coefficient, compressive strength, soluble ability and high temperature resistance. Results of lab experiments and field test show that lost circulation control quality can be effectively improved with the optimal material selection based on the extracted key performance parameters of LCMs.

Data-Driven Model Falsification and Uncertainty Quantification for Fractured Reservoirs

Many properties of natural fractures are uncertain,such as their spatial distribution,petrophysical properties,and fluid flow performance.Bayesian theorem provides a framework to quantify the uncertainty in geological modeling and flow simulation,and hence to support reservoir performance predictions.The application of Bayesian methods to fractured reservoirs has mostly been limited to synthetic cases.In field applications,however,one of the main problems is that the Bayesian prior is falsified,because it fails to predict past reservoir production data.In this paper,we show how a global sensitivity analysis(GSA)can be used to identify why the prior is falsified.We then employ an approximate Bayesian computation(ABC)method combined with a tree-based surrogate model to match the production history.We apply these two approaches to a complex fractured oil and gas reservoir where all uncertainties are jointly considered,including the petrophysical properties,rock physics properties,fluid properties,discrete fracture parameters,and dynamics of pressure and transmissibility.We successfully identify several reasons for the falsification.The results show that the methods we propose are effective in quantifying uncertainty in the modeling and flow simulation of a fractured reservoir.The uncertainties of key parameters,such as fracture aperture and fault conductivity,are reduced.

A Numerical Modelling Method of Fractured Reservoirs with Embedded Meshes and Topological Fracture Projection Configurations

Projection-based embedded discrete fracture model(pEDFM)is an effective numerical model to handle the flow in fractured reservoirs,with high efficiency and strong generalization of flow models.However,this paper points out that pEDFM fails to handle flow barriers in most cases,and identifies the physical projection configuration of fractures is a key step in pEDFM.This paper presents and proves the equivalence theorem,which explains the geometric nature of physical projection configurations of fractures,that is,the projection configuration of a fracture being physical is equivalent to it being topologically homeomorphic to the fracture,by analyzing the essence of pEDFM.Physical projection configurations of fractures may be rigorously established based on this theorem,allowing pEDFM to obtain physical numerical results for many flow models,particularly those with flow barriers.Furthermore,a natural idea emerges of employing flow barriers to flexibly‘cut’the formation to quickly handle the flow problems in the formation with complex geological conditions,and several numerical examples are implemented to test this idea and application of the improved pEDFM.

A Method for Identifying Channeling Paths in Low-Permeability Fractured Reservoirs

Often oilfield fractured horizontal wells produce water flowing in multiple directions.In this study,a method to identify such channeling paths is developed.The dual-medium model is based on the principle of inter-well connectivity and considers the flow characteristics and related channeling terms.The Lorentz curve is drawn to qualitatively discern the geological type of the low-permeability fractured reservoir and determine the channeling direction and size.The practical application of such an approach to a sample oilfield shows that it can accurately identify the channeling paths of the considered low-permeability fractured reservoir and predict production performances according to the inter-well connectivity model.As a result,early detection of water channeling becomes possible,paving the way to real-time production system optimization in low-permeability fractured reservoirs.

Experiments on imbibition mechanisms of fractured reservoirs by microfluidic chips

To solve the problems of long experiment period and difficult measurement in core imbibition experiments,fracture-matrix microfluidic chips of different sizes,boundary conditions and wettability regulated by surface property modification were designed to research the imbibition mechanisms of oil-water,oil-surfactant solution and oil-WinsorⅢtype surfactant solution.In the oil-water,and oil-wettability modification system imbibition process,oil was replaced from the matrix through Haines jump,the capillary back pressure was the main resistance blocking the flow of oil,the reduction of interfacial tension caused the weakening of Haines jump,reduction of oil discharge rate,and increase of oil recovery.The imbibition of oil-water or oil-surfactant solution with low interfacial tension was a counter-current imbibition process dominated by capillary force,in which all boundaries had similar contribution to imbibition,and the recovery data obtained from this experiment fit well with the classic imbibition scaling equation.The imbibition of oil and Winsor III type surfactant solution was a co-current imbibition process dominated by gravity under super-low interfacial tension,and is essentially the formation and re-balance of neutral microemulsion.The imbibition dynamics obtained from this experiment fit well with the modified imbibition scaling equation.

A Review of the Dynamic Modeling Approaches for Characterizing Fluid Flow in Naturally Fractured Reservoirs

Fluid flow in fractured media has been studied for decades and received considerable attention in the oil and gas industry because of the high productivity of naturally fractured reservoirs.Due to formation complexity and reservoir heterogeneity,characterizing fluid flow with an appropriate reservoir model presents a challenging task that differs relatively from homogeneous conventional reservoirs in many aspects of view,including geological,petrophysical,production,and economics.In most fractured reservoirs,fracture networks create complex pathways that affect hydrocarbon flow,well performance,hence reservoir characterization.A better and comprehensive understanding of the available reservoir modeling approaches is much needed to accurately characterize fluid flow behavior in NFRs.Therefore,in this paper,a perspective review of the available modeling approaches was presented for fluid flow characterization in naturally fractured medium.Modeling methods were evaluated in terms of their description,application,advantages,and disadvantages.This study has also included the applications of these reservoir models in fluid flow characterizing studies and governing equations for fluid flow.Dual continuum models were proved to be better than single continuum models in the presence of large scale fractures.In comparison,discrete models were more appropriate for reservoirs that contain a smaller number of fractures.However,hybrid modeling was the best method to provide accurate and scalable fluid flow modeling.It is our understanding that this paper will bridge the gap between the fundamental understanding and application of NFRs modeling approaches and serve as a useful reference for engineers and researchers for present and future applications.

Prediction of oil recovery in naturally fractured reservoirs subjected to reinfiltration during gravity drainage using a new scaling equation

By comparing numerical simulation results of single-porosity and dual-porosity models,the significant effect of reinfiltration to naturally fractured reservoirs was confirmed.A new governing equation was proposed for oil drainage in a matrix block under the reinfiltration process.Utilizing inspectional analysis,a dimensionless equation suitable for scaling of recovery curves for matrix blocks under reinfiltration has been obtained.By the design of experiments,test cases with different rock and fluid properties were defined to confirm the scope of the presented equation.The defined cases were simulated using a realistic numerical simulation approach.This method can estimate the oil amount getting into the matrix block through reinfiltration,help simulate the oil drainage process in naturally fractured reservoirs accurately,and predict the recovery rate of matrix block in the early to middle periods of production.Using the defined scaling equation in the dual-porosity model can improve the accuracy of the predicted recovery rate.

Experimental Investigation on Condensate Revaporization During Gas Injection Development in Fractured Gas Condensate Reservoirs

The gas field in the Bohai Bay Basin is a fractured metamorphic buried-hill reservoir with dual-media characteristics. The retrograde vaporization mechanism observed in this type of gas condensate reservoir differs significantly from that observed in sand gas condensate reservoirs. However, studies on improving the recovery of fractured gas condensate reservoirs are limited;thus, the impact of retrograde vaporization on condensate within fractured metamorphic buried-hill reservoirs remains unclear. To address this gap, a series of gas injection experiments are conducted in pressure-volume-temperature(PVT) cells and long-cores to investigate the retrograde vaporization effect of condensate using different gas injection media in fractured gas condensate reservoirs. We analyze the variation in condensate volume, gas-to-oil ratio, and condensate recovery during gas injection and examine the influence of various gas injection media(CO_(2), N_(2), and dry gas) under different reservoir properties and varying gas injection times. The results demonstrate that the exchange of components between injected gas and condensate significantly influences condensate retrograde vaporization in the formation. Compared with dry gas injection and N_(2) injection,CO_(2) injection exhibits a superior retrograde vaporization effect. At a CO_(2) injection volume of 1 PV, the percentage shrinkage volume of condensate is 13.82%. Additionally, at the maximum retrograde condensation pressure, CO_(2) injection can increase the recovery of condensate by 22.4%. However, the condensate recovery is notably lower in fractured gas condensate reservoirs than in homogeneous reservoirs, owing to the creation of dominant gas channeling by fractures, which leads to decreased condensate recovery. Regarding gas injection timing, the effect of gas injection at reservoir pressure on improving condensate recovery is superior to that of gas injection at the maximum retrograde condensation pressure. This research provides valuable guidance for designing gas injection development plans and dynamic tracking adjustments for fractured gas condensate reservoirs.

An efficient hybrid model for fractured reservoirs

In this study, an efficient hybrid model is proposed to simulate the fluid flow in the reservoirs with multi-scale fractures, which cannot be easily modeled by neither the continuum models nor the discrete fracture models. In the proposed method, the small fractures are modeled by using an improved Multiple Sub-Region method, which can capture the strongly anisotropy of fracture elements and the effects of border region on the transmissibility and provide more accurate results, on the other hand, the large fractures are modeled explicitly as major fluid conduits by the Embedded Discrete Fracture Model. Then, an efficient numerical algorithm based on the Mimetic Finite Difference method is developed to solve the hybrid method. At the end, several numerical examples are carried out to verify the accuracy and applicability of the proposed numerical model.

Naturally fractured hydrocarbon reservoir simulation by elastic fracture modeling

Accurate fluid flow simulation in geologically complex reservoirs is of particular importance in construction of reservoir simulators.General approaches in naturally fractured reservoir simulation involve use of unstructured grids or a structured grid coupled with locally unstructured grids and discrete fracture models.These methods suffer from drawbacks such as lack of flexibility and of ease of updating.In this study,I combined fracture modeling by elastic gridding which improves flexibility,especially in complex reservoirs.The proposed model revises conventional modeling fractures by hard rigid planes that do not change through production.This is a dubious assumption,especially in reservoirs with a high production rate in the beginning.The proposed elastic fracture modeling considers changes in fracture properties,shape and aperture through the simulation.This strategy is only reliable for naturally fractured reservoirs with high fracture permeability and less permeable matrix and parallel fractures with less cross-connections.Comparison of elastic fracture modeling results with conventional modeling showed that these assumptions will cause production pressure to enlarge fracture apertures and change fracture shapes,which consequently results in lower production compared with what was previously assumed.It is concluded that an elastic gridded model could better simulate reservoir performance.

Estimating the Properties of Naturally Fractured Reservoirs Using Rate Transient Decline Curve Analysis

Transient rate decline curve analysis for constant pressure production is presented in this pa- per for a naturally fractured reservoir. This approach is based on exponential and constant bottom-hole pressure solution. Based on this method, when In （flow rate） is plotted versus time, two straight lines are ob- tained which can be used for estimating different parameters of a naturally fractured reservoir. Parameters such as storage capacity ratio （co）, reservoir drainage area （A）, reservoir shape factor （CA）, fracture per- meability （ky）, interporosity flow parameter （,~） and the other parameters can be determined by this ap- proach. The equations are based on a model originally presented by Warren and Root and extended by Da Prat et al. and Mavor and Cinco-Ley. The proposed method has been developed to be used for naturally fractured reservoirs with different geometries. This method does not involve the use of any chart and by us- ing the pseudo steady state flow regime, the influence of wellbore storage on the value of the parameters ob- tained from this technique is negligible. In this technique, all the parameters can be obtained directly while in conventional approaches like type curve matching method, parameters such as co and g should be ob- tained by other methods like build-up test analysis and this is one of the most important advantages of this method that could save time during reservoir analyses. Different simulated and field examples were used for testing the proposed technique. Comparison between the obtained results by this approach and the results of type curve matching method shows a high performance of decline curves in well testing.

Numerical Fluid Flow Modelling in Multiple Fractured Porous Reservoirs

This paper compares the fluid flow phenomena occurring within a fractured reservoir for three different fracture models using computational fluid dynamics.The effect of the fracture-matrix interface condition is studied on the pressure and velocity distribution.The fracture models were compared based on the variation in pressure and permeability conditions.The model was developed for isotropic and anisotropic permeability conditions.The results suggest that the fracture aperture can have a drastic effect on fluid flow.The porous fracture-matrix interface condition produces more realistic transport of fluids.By increasing the permeability in the isotropic porous matrix,the pressure drop was significantly higher in both the fracture and reservoir region.Under anisotropic conditions in the 3D fractured reservoir,the effect of the higher longitudinal permeability was found to lower the pressure in the fractured reservoir.Depending on the properties of the fractured reservoir,this study can enhance the understanding of fracture-matrix fluid interaction and provide a method for production optimisation.

Distribution of gas hydrate in fractured reservoirs:Insights from anisotropic seismic measurements

Seismic properties of hydrate-bearing reservoirs that are affected significantly by the hydrate distribution are key for quantitative assessment of the reservoir.The knowledge of hydrate distribution in fractured reservoirs remains poorly understood.To obtain such knowledge,we measured and analyzed five anisotropic velocities needed to fully characterize the seismic anisotropy in an artificial sandstone with aligned fractures during hydrate formation associated with varying distribution.We showed that while the formation of hydrate improved the velocities,the improvement was more significant for hydrate saturation above 10%.We also showed that the increasing trends varied among the anisotropic velocities when hydrate saturation was above 10%.Specifically,the compressional wave velocity travelling vertical to the bedding plane and the shear wave velocity with polarization perpendicular to the bedding plane increased more rapidly than the other compressional and shear wave velocities,respectively.Interpretation of the anisotropic seismic results suggested that the hydrate tends to bind to the grains in the fractures at low hydrate saturation,and becomes to bridge the fracture surfaces when the hydrate saturation exceeds 10%.The results have provided new insights into the hydrate distribution and its resulting anisotropic seismic properties in fractured reservoirs.This will pave the way for the successful assessment of hydrate in fractured reservoirs.