Dual-porosity Reservoir Research Articles

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.

Incorporating Dynamic Production-Logging Data to the Permeability-Estimation Workflow Using Machine Learning

Summary The objective of this work is to develop and train feedforward artificial neural networks (ANNs) on the forecasting of layer permeability in heterogeneous reservoirs. The results are validated by comparing the model outputs with permeability curves computed from production logging data. Production logs are used as targets to train the model. A flow-profile interpretation method is used to compute continuous permeability curves free of wellbore skin effects. In addition, segmentation techniques are applied to high-resolution ultrasonic image logs. These logs provide not only the image of the mega- and giga-pore system but can also identify the permeable facies along the reservoir. The image segmentation jointly with other borehole logs provides the necessary features for the network training process. The proposed neural network focuses on delivering reliable and validated permeability curves. Its development accounts for formation skin factor, as well as nongeological noise usually found in ultrasonic image logs. The procedure is tested on both synthetic and field data sets. The estimations presented herein demonstrate the model's ability to learn nonlinear relationships between geological input variables and reservoir dynamic data even if the actual physical relationship is complex and not known a priori. Although the preprocessing stages of the procedure involve some expertise in data interpretation, the neural-network structure can be easily coded in any programming language, requiring no assumptions on physics in advance. For the case studies presented in this work, the proposed procedure provides more accurate permeability curves than the ones obtained from conventional methods, which usually fail to predict the permeability measured on drill-stem tests conducted in dual-porosity reservoirs. The novelty of this work is to incorporate dynamic production-logging (PL) data into the permeability-estimation workflow. Correction Notice: The preprint paper was updated from its originally published version to correct Fig. 17 on page 11. An erratum detailing the change is included in the Supporting Information section below.

An intelligent heuristic-clustering algorithm to determine the most probable reservoir model from pressure–time series in underground reservoirs

Precise characterization of underground reservoirs requires accurate calculations of the reservoir’s petrophysical data and accurate selection of the mathematical model governing the reservoir’s dynamic. In this study, we develop a novel heuristic-clustering algorithm, namely GA–DBSCAN–KMEANS, that can be applied over pressure transient data to assess the true reservoir model out of a pool of candidates. In this algorithm, each specific reservoir model is considered a subpopulation in the GA (genetic algorithm). Then, the simultaneous optimization of all the reservoir models is sought using the proposed hybrid algorithm. During the optimization process, the population size of different models will be either decreased, increased, or unchanged based on the average quality match obtained for each model. A combined DBSCAN (density-based spatial clustering of applications with noise)–KMEANS clustering scheme is used to increase the population size for the best reservoir model in each iteration of the GA. The accuracy of the proposed algorithm was verified using several synthetic data and a real field case obtained from the open literature. The tested data were collected from different types of reservoir models, including homogeneous reservoirs, matrix-fracture dual-porosity reservoirs, and fault-limited reservoirs. For uncertainty analyses and to test the performance of the algorithm under large numbers of initializations, Monte Carlo simulations were conducted. Results of the Monte Carlo simulations unveiled high values of P10, P50, and P90 for the probability of the true reservoir model and low values of these statistics for the false reservoir models. This shows that the outcome of the proposed algorithm is not affected by the initial randomization of the solution subspaces; hence, the developed algorithm is a reliable tool in determining the most probable reservoir model from transient well testing data.

Flow Regime Analysis on Pressure Build-up Test Result of Z-01 Well Using Dual Porosity Reservoir Model

Flow regime analysis on the results of pressure build-up Z-01 well test was conducted to determine the type of flow that occurs in each time region section. In the early time stage there is a flow which is dominated by linear flow which is then followed by bilinear flow. At the middle time there is a radial flow where the pressure disturbance has spread towards the reservoir. In the late time flow stage is dominated by steadystate flow where the flow is affected because there is a support pressure caused by the constant pressure boundary. In the analysis of pressure build-up used to determine reservoir parameters can be used in the middle time region. This is used because the plot results between ΔP vs. log HTR (Horner Time Ratio) are straight lines which can be used to calculate reservoir parameter values such as permeability (k), formation damage factor (s). This test was analyzed using the Ecrin software and obtained a dual porosity model with a permeability value of 4.8 md, skin -3.57. From the analyzed model, it is obtained that the well fracture-finite conductivity model means that the Z-01 well has been stimulated to increase production.

Analysis of seepage pressure in dual-porosity reservoir under elastic boundary

In view of the large limitations of the dual-porosity media seepage model established in the early study, the elastic external boundary condition is newly presented in this paper, which can treats the idealized assumption (external boundary constant pressure, closed, infinite) in traditional model as a special case. Based on it, with considering the influence of well-bore storage, skin factors and external boundary radius on reservoir, an unstable seepage model under the elastic boundary is established first. then, the Laplace space solution of seepage model is obtained by using Laplace transform and similar structure theory in turn. Subsequently, by using Stehfest inversion transformation and the corresponding mapping software, the type curves are drawn, and the impacts of the main parameters on them are analyzed. The results indicate that the elastic coefficient has negative affect on the asymptotic rate of the type curve; And the type curves determined by different external boundary radii deviate during the later period of flow; Further more, the elastic coefficient affects the migration trajectory of the curves. Numerical simulation further verifies the scientificalness of introducing elastic external boundary conditions. The model established in this paper and the corresponding data analysis provide a more solid theoretical basis for the scientific analysis of the influence of reservoir parameters on reservoir pressure, and provide a new idea for the design and improvement of related well testing software.

Analysis of seepage pressure in dual-porosity reservoir under elastic boundary

In view of the large limitations of the dual-porosity media seepage model established in the early study, the elastic external boundary condition is newly presented in this paper, which can treats the idealized assumption (external boundary constant pressure, closed, infinite) in traditional model as a special case. Based on it, with considering the influence of well-bore storage, skin factors and external boundary radius on reservoir, an unstable seepage model under the elastic boundary is established first. then, the Laplace space solution of seepage model is obtained by using Laplace transform and similar structure theory in turn. Subsequently, by using Stehfest inversion transformation and the corresponding mapping software, the type curves are drawn, and the impacts of the main parameters on them are analyzed. The results indicate that the elastic coefficient has negative affect on the asymptotic rate of the type curve; And the type curves determined by different external boundary radii deviate during the later period of flow; Further more, the elastic coefficient affects the migration trajectory of the curves. Numerical simulation further verifies the scientificalness of introducing elastic external boundary conditions. The model established in this paper and the corresponding data analysis provide a more solid theoretical basis for the scientific analysis of the influence of reservoir parameters on reservoir pressure, and provide a new idea for the design and improvement of related well testing software.

Mathematical simulation of a pressure field exemplified by dual porosity reservoir

The authors analyze the process of fluid transfer in a formation using the example of a porous fractured reservoir rock. A reservoir of this type has a natural-fracture system and is described by a dual porosity model. The most detailed description of a filtration process is provided by Warren-Root equations which analyze fluid redistribution between the matrix and the natural fracturing pattern. In this paper we develop a numerical model of fluid flow processes for a fractured-porous reservoir. The finite difference method is applied to solve partial differential equations. The problem is approximated by an implicit difference scheme. The system of linear algebraic equations at each time layer is solved by the matrix sweep method.

Semi-analytical solution for productivity evaluation of a multi-fractured horizontal well in a bounded dual-porosity reservoir

Development of horizontal drilling and multi-stage fracturing technologies makes the production of unconventional reservoirs economically and practically feasible. We study the productivity of the multi-fractured horizontal well (MFHW) in a bounded dual-porosity formation. The infinite conductivity fracture case is modeled by combining the Laplace transform (LT) and finite Fourier cosine transform (FFCT). The model is implemented to finite conductivity cases by applying the distributed volumetric sources (DVS) method. The model outputs are verified by comparing them with the results of the separation of variables technique. Different possible flow regimes are observed. The capability of the finite conductivity solution method for optimizing the fracture geometry is approved. The effects of the interporosity coefficient and storativity ratio as the dual-porosity parameters on the productivity of a bounded dual-porosity reservoir are studied by conducting a sensitivity analysis. Similar to single-porosity reservoirs, it is found that the optimum fracture design based on the pseudo-steady state flow regime leads to a higher productivity in the transient flow regimes in the dual-porosity cases. Finally, the proposed approach is used to perform an economic optimization of the hydraulic fracture design. This research study assists researchers and engineers to make better/more accurate fracture design in various applications such as production from unconventional petroleum reservoirs and remediation in fractured underground porous systems.

Modeling of Matrix/Fracture Transfer with Nonuniform-Block Distributions in Low-Permeability Fractured Reservoirs

Summary Unconventional shale–gas and tight oil reservoirs are commonly naturally fractured, and developing these kinds of reservoirs requires stimulation by means of hydraulic fracturing to create conductive fluid–flow paths through open–fracture networks for practical exploitation. The presence of the multiscale–fracture network, including hydraulic fractures, stimulated and nonstimulated natural fractures, and microfractures, increases the complexity of the reservoir simulation. The matrix–block sizes are not uniform and can vary in a very wide range, from several tens of centimeters to meters. In such a reservoir, the matrix provides most of the pore volume for storage but makes only a small contribution to the global flow; the fracture supplies the flow, but with negligible contributions to reservoir porosity. The hydrocarbon is mainly produced from matrix/fracture interaction. So, it is essential to accurately model the matrix/fracture transfers with a reservoir simulator. For the fluid–flow simulation in shale–gas and tight oil reservoirs, dual–porosity models are widely used. In a commonly used dual–porosity–reservoir simulator, fractures are homogenized from a discrete–fracture network, and a shape factor based on the homogenized–matrix–block size is applied to model the matrix/fracture transfer. Even for the embedded discrete–fracture model (EDFM), the matrix/fracture interaction is also commonly modeled using the dual–porosity concept with a constant shape factor (or matrix/fracture transmissibility). However, in real cases, the discrete–fracture networks are very complex and nonuniformly distributed. It is difficult to determine an equivalent shape factor to compute matrix/fracture transfer in a multiple–block system. So, a dual–porosity approach might not be accurate for the simulation of shale-gas and tight oil reservoirs because of the presence of complex multiscale–fracture networks. In this paper, we study the multiple–interacting–continua (MINC) method for flow modeling in fractured reservoirs. MINC is commonly considered as an improvement of the dual–porosity model. However, a standard MINC approach, using transmissibilities derived from the MINC proximity function, cannot always correctly handle the matrix/fracture transfers when the matrix–block sizes are not uniformly distributed. To overcome this insufficiency, some new approaches for the MINC subdivision and the transmissibility computations are presented in this paper. Several examples are presented to show that using the new approaches significantly improves the dual–porosity model and the standard MINC method for nonuniform–block–size distributions.

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]

Orthogonal Collocation Method for Solving the Diffusivity Equation: Application on Dual Porosity Reservoirs With Constant Pressure Outer Boundary

Fluid flow inside heterogeneous structure of dual porosity reservoirs is presented by two coupled partial differential equations (PDE). Finding an analytical solution for the diffusivity equations is tedious or even impossible in some circumstances due to the heterogeneity of dual porosity reservoirs. Therefore, in this study, orthogonal collocation method (OCM) is proposed for solving the governing equations in dual porosity reservoirs with constant pressure outer boundary. Since no analytical solution has been proposed for this system, validation is carried out by comparing the OCM-obtained results for “dual porosity reservoirs with circular no-flow outer boundary” with both exact analytical solution and real field data. Sensitivity analyses reveal that the OCM with 13 collocation points is a good candidate for prediction of pressure transient response (PTR) in dual porosity reservoirs. OCM predicts the PTR of a real field draw-down test with an absolute average relative deviation (AARD) of 0.9%. Moreover, OCM shows a good agreement with the analytical solution obtained by Laplace transform (AARD = 0.16%). It is worth noting that OCM requires a smaller computational effort. Thereafter, PTR of dual porosity reservoirs with a constant production rate in the wellbore and constant pressure outer boundary is simulated by OCM for wide ranges of operating conditions. Accuracy of OCM and its low required computational time justifies that this approximate method can be considered as a practical candidate for pressure transient analysis in dual porosity reservoirs.

Semi-analytical solution for pressure transient analysis of a hydraulically fractured vertical well in a bounded dual-porosity reservoir

We study the role of a hydraulic fracture on the pressure transient behavior of a vertical well producing from a bounded (or finite) dual-porosity formation. A combination of Laplace transform (LT) and the finite Fourier cosine transform (FFCT) are used to solve the diffusivity equation. The presented analysis allows identification of five flow regimes, including: 1) early linear flow, 2) volumetric depletion of natural fractures, 3) natural-fracture radial flow, 4) transition from natural-fracture radial flow to total (natural fractures and matrix) radial flow, and 5) pseudo-steady state flow. The results reveal that the interporosity flow coefficient, storativity ratio, natural-fracture permeability anisotropy, and reservoir size play significant roles on the identified flow regimes compared to the hydraulically fractured well location and reservoir shape. The developed solution can be useful for well test analysis by generating a new set of type curves or can be applicable to a forward model for estimating parameters of reservoir. This study presents a new semi-analytical solution which finds application in well testing of hydraulically fractured wells in dual-porosity formations.

Fluid flow in fractured reservoirs: Exact analytical solution for transient dual porosity model with variable rock matrix block size

Dual porosity reservoirs consist of two comparatively independent systems of fractures and matrix blocks with high and low permeability values, respectively. Semi-analytical and numerical studies on naturally fractured reservoirs have been already cited in the literature. The present study focuses on investigation of a linear double porosity model of a semi-infinite-acting naturally fractured reservoir using an exact analytical method. Different matrix block size distributions are embedded into a transient model to consider the effects of heterogeneity in fractured formations. In order to take into account transient fracture-matrix exchange, an analytical method is proposed to solve the coupled fracture and matrix equations. Gauss Legendre quadrature is employed to evaluate the double integral of general transient solution. Moreover, the corresponding shape factor was evaluated in a double porosity transient model coupled with variable matrix block size distribution. Results demonstrated that matrix block size distributions strongly affect the fluid transfer during the early time region. Also, the presented model was employed to generate interference test curves which in turn were studied to investigate the impacts of storativity ratio and matrix block size distributions on the fracture-matrix fluid transfer. Results illustrated that a series of obtained pressure data from an observational well along with the proposed model may be considered a robust method in fracture intensity assessment. Fast sensitivity analysis and very efficient computational cost are the benefit of the derived analytical solutions with respect to previous numerical solutions.

Composite linear flow model for multi-fractured horizontal wells in tight sand reservoirs with the threshold pressure gradient

Multi-stage fracturing is currently the most effective method to exploit tight sand reservoirs. Various analytical models have been proposed to fast and accurately investigate the post-fracturing pressure- and rate-transient behavior, and hence, estimate the key parameters that affect well performance. However, these analytical models mainly consider the 2D flow, neglecting the fluids’ flow from the upper/lower reservoir when the vertical fractures partially penetrate the reservoir. Although for linear flow models, Olarewaju and Lee (1989) and Azari et al. (1990, 1991) have studied the effects of fracture height, they merely used a skin factor. Moreover, the reservoir heterogeneity is seldom included. This paper presents an analytical model for multi-fractured horizontal wells (MFHWs) in tight sand reservoirs, accounting for the upper/lower reservoir contributions, reservoir heterogeneity and threshold-pressure gradient (TPG).The model is extended from the “five-flow-region” model and subdivides the reservoir into seven parts including two upper/lower flow regions, two outer flow regions, two inner flow regions and a hydraulic fracture flow region. Reservoir heterogeneity along the horizontal wellbore is considered, thus, the effects of the fracture pattern in a heterogeneous reservoir are documented. Fracture interference is simulated by locating a virtual no-flow boundary between two adjacent fractures. The exact location of a no-flow boundary is determined based on the boundary's pressure. Thus, the no-flow boundary has a minimum pressure difference between its two sides during the well production, making the no-flow assumption reasonable. The experimentally observed TPG and the pressure drop within the horizontal wellbore are included.Modeling results are compared with those from the well-testing software KAPPA Ecrin, obtaining a good match in most flow regimes. Both the constant-rate and constant-pressure conditions are studied. Results suggest that the fracture penetration ratio dominates the early-mid time pressure responses and the start time of the boundary-dominated flow. For production responses, it determines the initial productivity and the production decline rate. The existence of the TPG results in a higher pressure drop and accelerates the production decline during the middle-late times. But this influence is marginal when the TPG is small (TPG<0.4psi/ft). Effects of other relative parameters, such as the formation permeability, fracture length, conductivity, fracture pattern, wellbore storage, flow-capacity ratio and storativity ratio for dual-porosity reservoir blocks are systematically investigated. Besides, some field data are analyzed and compared graphically, using type curve matching, and reliable results are obtained.Low CPU demands and the minimal data requirement of this model enable the operators to predict well-testing results under different fracture patterns in heterogeneous reservoirs with TPGs in a simple but effective way.

Characterisation of hydrocarbon reservoirs by analysing deconvolved impulse response

Analysing well testing signals provides a practical way to characterise hydrocarbon reservoirs. Since having a perfect constant rate is hardly possible, petroleum engineers often deal with the multi-rate well testing signals. This study describes an application of the coupled deconvolution-wavelet transform scheme for extraction of reservoir impulse response from the multi-rate well testing signals. Performance of the proposed algorithm is validated using a set of smooth, incomplete and noisy simulated examples. Extraction of the impulse response from the incomplete well test signals has not been considered in the literature up to now. The results confirm an excellent performance of the developed algorithm for revealing the wellbore, reservoir and boundary. The parameters of dual porosity reservoir are estimated whit an absolute average relative deviation percent (AARD%) of 4.68%. [Received: February 10, 2016; Accepted: February 6, 2017]

Estimation of characteristics of naturally fractured reservoirs by pressure transient analysis

PurposeThis paper aims to analyze the pressure behavior in dual porosity reservoirs using different techniques in an attempt to correctly characterize reservoir properties. Pressure transient tests in naturally fractured reservoirs often exhibit non-uniform responses.Design/methodology/approachThe pressure transient tests in naturally fractured reservoirs were analyzed using conventional semi-log analysis, type curve matching (using commercial software) and Tiab’s direct synthesis (TDS) technique. In addition, the TDS method was applied in case of a naturally fractured formation with a vertical hydraulic fracture. These techniques were applied to a single-layer, naturally fractured reservoir under pseudosteady state matrix flow. By studying the unique characteristics of the different flow regimes appear on the pressure and pressure derivative curves, various reservoir characteristics can be obtained such as permeability, skin factor and fracture properties.FindingsFor naturally fractured reservoirs, a comparison between the results semi-log analysis, software matching and TDS method is presented. In case of wellbore storage, early time flow regime can be obscured that lead to incomplete semi-log analysis. Furthermore, the type curve matching usually gives a non-uniqueness solution, as it needs all the flow regimes to be observed. However, the direct synthesis method used analytical equation to calculate reservoir and well parameters without type curve matching. For naturally fractured reservoirs with a vertical fracture, the pressure behavior of wells crossed by a uniform flux and infinite conductivity fracture is analyzed using TDS technique. The different flow regimes on the pressure derivative curve were used to calculate the fracture half-length in addition to other reservoir properties.Originality/valueThe results of different field cases showed that TDS technique offers several advantages compared to semi-log analysis and type curve matching. It can be used even if some flow regimes are not observed. Direct synthesis results are accurate compared to the available core data and the software matching results. It can be used to confirm the software matching results and to give reliable reservoir characteristics when there is lack of data.

A new model for calculating permeability of natural fractures in dual-porosity reservoir

During the development of naturally fractured carbonate reservoirs, understanding the change in fracture permeability is the basis for production evaluation and scientific development. The conventional method of analyzing fracture permeability is to take core samples for laboratory experiments. This paper presents a new method to calculate the fracture permeability decrease using actual reservoir pressure data. The mathematical model of fracture permeability change with pressure is established based on material balance in the production process of a fractured reservoir. The model considers crossflow coefficient as well as compression coefficient. According to the results of the model, the fracture permeability decreases with decrease of the formation pressure, but the degree of decline is related to the crossflow coefficient and the compression coefficient. By using this model, the change in fracture permeability can be calculated under different production pressures. This provides a new method for stress sensitivity determination of fractured reservoirs. Cited as : Zhang, T., Li, Z., Adenutsi, C.D., et al. A new model for calculating permeability of natural fractures in dual-porosity reservoir. Advances in Geo-Energy Research, 2017, 1(2): 86-92, doi: 10.26804/ager.2017.02.03

Analyzing of Drill Stem Test (DST) Result for Dual Porosity Limestone Reservoir

The aim of this paper is to discuss and evaluate the result of DST which was conducted in a limestone reservoir of an oil field at the depth interval 3764.29-3903.0 meter in well-1 to evaluate the dynamic characteristics of the reservoirs, for instance: skin effect, permeability, wellbore storage, reservoir boundary and average reservoir pressure. Reservoir Pressure profiles has been recorded for both Buildup and draw down intervals. Semi-log and log-log coordinates have been used to plot the pressure signature date of both buildup period and its derivative to improve diagnostic and Horner plot. In addition, a dual porosity reservoir and infinite acting characteristic was discovered as a result of the well test data interpretation. Wellbore storage, skin factor and transient flow effects have been detected in the DST analysis on the dual porosity behavior due to phase re distribution. Using final buildup sections, the flow parameters of dual porosity reservoir were determined as the flow between fissure and matrix was (7.558 x 10-6) while, the storability ratio between fissure and matrix was calculated as 0.3 and permeability is 102 MD for both matrix and the fissure together. However, negative value of skin factor mostly appears in double porosity limestone reservoirs, positive skin factor of the reservoir has been observed in this study. It can be considered that the positive skin factor can be resulted in either the formation was partially penetrated and /or wells were not cleaned up properly.

Sparse well pattern and high-efficient development of metamorphic buried hills reservoirs in Bohai Sea area, China

In order to achieve the development objective of fewer wells with higher production of metamorphic buried hill reservoirs in the Bohai Sea area, the JZ251S oilfield at Bohai Bay Basin was taken as an example to carry out elaboration of reservoir fracture, quantitative characterization of water displacing oil mechanism at dual-porosity reservoir, optimization of new well pattern mode, formulation of rational development technology policy, maintaining productivity and controlling water rising based on development experience of similar oil reservoir, thus forming the key high efficiency development technique of sparse well pattern of offshore metamorphic rock reservoir. Based on the characteristics of the JZ251S buried hill reservoir, forward simulation of wave equation for fracture anisotropy was carried out, verifying the effectiveness of narrow azimuth seismic data to fractures detection in work area. Multi-parameters prestack inversion and geostress field simulation were applied to forecast location of fractures and direction of fractures respectively. Based on the large-scale 3D physical model and numerical simulation, a new top-bottom interlaced 3D injection-production well deployment model concerning the horizontal well was presented. Considering the production demand, the reasonable oil production rate of JZ251S oil reservoir shall be controlled at 3%-4%, depletion development until that the formation pressure level maintains at 70% of initial formation pressure can be implemented for the oil field at the initial stage, and then the development mode of water flooding to keep pressure can be carried out. Considering the pilot production data at the work zone, different water breakthrough models of the horizontal well were simulated to form four diagnosis charts, which help to stabilize oil and control water effectively. The field practice shows that these techniques greatly increase the crude oil output and improve the water-injection development effect.

A semi-analytical model for multilateral horizontal wells in low-permeability naturally fractured reservoirs

Multilateral horizontal wells (MLHWs) can significantly increase the reservoir exposure as well as connect high-permeability areas (natural fractures), and thus have been widely adopted in petroleum industry as an effective technique for efficient development of low-permeability reservoirs. Compared to vertical wells and horizontal wells, the flowing problems caused by MLHWs are more complex. In addition, extensive study has revealed that stress sensitivity of permeability in low-permeability reservoirs is obvious which cannot be ignored, especially for naturally fractured dual-porosity reservoirs. The non-linearity caused by stress sensitivity of permeability further complicates the flowing problems of MLHWs; however, so far, little work has been done in literature to simulate pressure transient dynamics of MLHWs with consideration of stress-sensitivity effect of permeability in low-permeability reservoirs.In this paper, a more rigorous analytical model for MLHWs in low-permeability naturally fractured reservoirs is presented. The model can not only consider different combinations of multiple branches, it can also consider the stress-sensitivity effect of reservoir permeability. The non-linear mathematical model can be linearized by Pedrosa transform and perturbation technique, and the final solution thus can be obtained by Laplace transformation method, finite cosine transform, element discretization and matrix theory. The presented model and corresponding solution are first validated by comparison with transient pressure responses calculated with a commercial numerical simulator for a simple case. Then the transient pressure responses are calculated, and flowing patterns and characteristic flowing periods caused by MLHWs are analyzed. A parametric analysis is also conducted to screen the critical parameters affecting the performance of multilateral horizontal wells. Analysis results suggest that stress-sensitivity of reservoir permeability has significant influence on the performance of MLHWs in low-permeability reservoirs; the parameters related to the shape of MLHWs, such as branch length, branch spacing, the angles between branch and horizontal wellbore, also can obviously affect the transient pressure dynamics of MLHWs. The proposed model in this paper can accurately simulate the transient pressure behaviors of MLHWs. It can help better understand the flowing characteristics of MLHWs, provide more accurate dynamic parameters for reservoir development, and give some insight into the design of MLHWs to obtain higher recovery.