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.

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.

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.

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.

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.

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.

Comparison of numerical codes for coupled thermo-hydro-mechanical simulations of fractured media

Geo-energy and geo-engineering applications,such as improved oil recovery(IOR),geologic carbon storage,and enhanced geothermal systems(EGSs),involve coupled thermo-hydro-mechanical(THM)processes that result from fluid injection and production.In some cases,reservoirs are highly fractured and the geomechanical response is controlled by fractures.Therefore,fractures should explicitly be included into numerical models to realistically simulate the THM responses of the subsurface.In this study,we perform coupled THM numerical simulations of water injection into naturally fractured reservoirs(NFRs)using CODE_BRIGHT and TOUGH-UDEC codes.CODE_BRIGHT is a finite element method(FEM)code that performs fully coupled THM analysis in geological media and TOUGH-UDEC sequentially solves coupled THM processes by combining a finite volume method(FVM)code that solves nonisothermal multiphase flow(TOUGH2)with a distinct element method(DEM)code that solves the mechanical problem(UDEC).First,we validate the two codes against a semi-analytical solution for water injection into a single deformable fracture considering variable permeability based on the cubic law.Then,we compare simulation results of the two codes in an idealized conceptual model that includes one horizontal fracture and in a more realistic model with multiple fractures.Each code models fractures differently.UDEC calculates fracture deformation from the fracture normal and shear stiffnesses,while CODE_BRIGHT treats fractures as equivalent porous media and uses the equivalent Young’s modulus and Poisson’s ratio of the fracture.Finally,we obtain comparable results of pressure,temperature,stress and displacement distributions and evolutions for the single horizontal fracture model.Despite some similarities,the two codes provide increasingly different results as model complexity increases.These differences highlight the challenging task of accurately modeling coupled THM processes in fractured media given their high nonlinearity.

On the evaluation of steam assisted gravity drainage in naturally fractured oil reservoirs

Steam Assisted Gravity Drainage(SAGD)as a successful enhanced oil recovery(EOR)process has been applied to extract heavy and extra heavy oils.Huge amount of global heavy oil resources exists in carbonate reservoirs which are mostly naturally fractured reservoirs.Unlike clastic reservoirs,few studies were carried out to determine the performance of SAGD in carbonate reservoirs.Even though SAGD is a highly promising technique,several uncertainties and unanswered questions still exist and they should be clarified for expansion of SAGD methods to world wide applications especially in naturally fractured reservoirs.In this communication,the effects of some operational and reservoir parameters on SAGD processes were investigated in a naturally fractured reservoir with oil wet rock using CMG-STARS thermal simulator.The purpose of this study was to investigate the role of fracture properties including fracture orientation,fracture spacing and fracture permeability on the SAGD performance in naturally fractured reservoirs.Moreover,one operational parameter was also studied;one new well configuration,staggered well pair was evaluated.Results indicated that fracture orientation influences steam expansion and oil production from the horizontal well pairs.It was also found that horizontal fractures have unfavorable effects on oil production,while vertical fractures increase the production rate for the horizontal well.Moreover,an increase in fracture spacing results in more oil production,because in higher fracture spacing model,steam will have more time to diffuse into matrices and heat up the entire reservoir.Furthermore,an increase in fracture permeability results in process enhancement and ultimate recovery improvement.Besides,diagonal change in the location of injection wells(staggered model)increases the recovery efficiency in long-term production plan.

Transient flow model and pressure dynamic features of tree-shaped fractal reservoirs

A transient flow model of tree-shaped fractal reservoirs is built by embedding a fracture network simulated by a tree-shaped fractal network into a matrix system. The model can be solved using the Laplace conversion method. The dimensionless bottom hole pressure can be obtained using the Stehfest numerical inversion method. The bi-logarithmic type curves for the trce-shaped fractal reservoirs are thus obtained. The pressure transient responses under different fractal factors are discussed. The factors with a primary effect on the inter-porosity flow regime include the initial branch number N, the length ratio α, and the branch angle θ. The diameter ratio β has a significant effect on the fracture radial flow, the inter-porosity and the total system radial flow regimes. The total branch level M of the network mainly influences the total system radial flow regime. The model presented in this paper provides a new methodology for analyzing and predicting the pressure dynamic characteristics of naturally fractured reservoirs.

Mechanistic simulation of fracture effects on miscible CO_(2)injection

Miscible injection of carbon dioxide(CO_(2))into oil reservoirs as an Enhanced Oil Recovery(EOR)method has proved to be highly advantageous.According to the volume of the world's recoverable oil resides inside the fractured reservoirs,investigation of the controlling parameters in the efficient injection of miscible CO_(2) is of paramount importance,mainly owing to the intricacies and complexities associated with this process.This complexity in fractured reservoirs arises due to the presence of two distinct media for fluid transfer(i.e.,matrix and fracture network)and the corresponding differences in fluid velocities.Accordingly,performance of miscible carbon dioxide injection in these reservoirs was investigated through mechanistic simulation model in the form of dual-porosity(DP),and dual porosity-dual permeability(DPP).Moreover,due to limited supply and high injection costs of this gas in its pure form,performance of the miscible CO_(2) injection combined with C_(1),N_(2),and H_(2)S was also surveyed and compared to pure gas injection case.A sensitivity analysis was also performed based on fracture porosity,fracture horizontal and vertical permeability,matrix horizontal permeability,block height shape factor,matrix capillary pressure,and impure injected components in DP and DPP models,showing that matrix horizontal permeability and capillary pressure have the greatest,and porosity has the lowest impact on miscibility performance and oil recovery in these models.In the end,after investigating the effect of different injection cases on miscibility performance and oil recovery,it was concluded that the highest oil recovery in miscible gas injection obtained through optimization of a gas composition having the lowest minimum miscibility pressure(MMP)and the lowest density.