Interporosity Flow Coefficient Research Articles

Transient Pressure Behavior of CBM Wells during the Injection Fall-Off Test Considering the Quadratic Pressure Gradient.

Conventional coalbed methane (CBM) reservoir models for injection fall-off testing often disregard the quadratic pressure gradient's impact. This omission leads to discrepancies in simulating the transient behavior of formation fluids and extracting critical reservoir properties. Accurate determination of permeability, storability, and other properties is crucial for effective reservoir characterization and production forecasting. Inaccurate estimations can lead to suboptimal well placement, ineffective production strategies, and ultimately, missed economic opportunities. To address this shortcoming, we present a novel analytical model that explicitly incorporates the complexities of the quadratic pressure gradient and dual-permeability flow mechanisms, prevalent in many CBM formations where nanopores are rich, presenting a kind of natural nanomaterial. This model offers significant advantages over traditional approaches. By leveraging variable substitution, it facilitates the derivation of analytical solutions in the Laplace domain, subsequently converted to real-space solutions for practical application. These solutions empower reservoir engineers to generate novel type curves, a valuable tool for analyzing wellbore pressure responses during injection fall-off tests. By identifying distinct flow regimes within the reservoir based on these type curves, engineers gain valuable insights into the dynamic behavior of formation fluids. This model goes beyond traditional approaches by investigating the influence of the quadratic pressure gradient coefficient, inter-porosity flow coefficient, and storability ratio on the pressure response. A quantitative comparison with traditional models further elucidates the key discrepancies caused by neglecting the quadratic pressure gradient. The results demonstrate the proposed model's ability to accurately depict the non-linear flow behavior observed in CBM wells. This translates to more reliable pressure and pressure derivative curves that account for the impact of the quadratic pressure gradient.

Determination of Reservoir Parameter of Naturally Fractured Reservoir at SF Field using Rate Type Curve Analysis

This Naturally Fractured Reservoir (NFR) is become challenging to identify the behavior of performance in fluid flow in producing well at SF oil Field. Generally, this unique of mechanism that cannot be treated as homogenous reservoir, because has two porous media in this reservoir such as matrix and fracture, the dominantly fluid flow comes from the networks of fractures, but for matrix porous media as function of source that transfer fluid to the fractures. This complexity of reservoir needs deepest investigate the characteristic of this reservoir and estimating the reservoir parameter such as permeability fracture, storativity coefficient ratio (omega) and interporosity flow coefficient (lamda) of SF production wells at SF oil Field are the main objective of this study. There are two wells that are analyzed in this study, and the result of this study yields significant interpretation by analyzing the production data in order to approximate the characteristic of dual porosity in naturally fractured oil reservoir by applying the decline rate type curve matching.

Variability of Double-Porosity Flow, Interporosity Flow Coefficient λ and Storage Ratio ω in Dolomites

Seventy-one pumping tests were carried out in various dolomites, revealing two of the less-studied hydrogeological parameters related to double-porosity flow: the interporosity flow coefficient λ and the ratio between storage in the fractures and storage in the whole system (ω). Conceptually, they are both tied to the flow properties of the fractures and matrix and define the communication between these two hydrogeological domains. Five different groups of dolomites were included in this study, with different diagenesis types, crystal sizes, bed thicknesses, fracture intensities and chert contents represented. The results of both parameters reflect variations in the sedimentological and resulting hydrogeological properties of dolomites. The largest values of the interporosity flow coefficient λ (6.53 × 10−1) are found in dolomites formed by late diagenesis, exhibiting the highest degree of fracturing, resulting in fast responses in fractures and large λ values. The values of the storage ratio ω also vary (the range of most values is from 3.32 × 10−4 to 2.14 × 10−1), with the overall range almost completely filling all the theoretical limits from zero to one. The greatest values of ω are found in dolomites with the largest storage, due to the large number of small fractures, and silica diagenesis probably reduces the matrix storage. The correlations among the parameters show some significant relationships, especially between λ and Km, λ and Sf, ω and Sf, and ω and Sm.

Radius of investigation and impact of inter-porosity flow in naturally-fractured reservoirs

The radius of investigation (ROI) is an essential parameter in many reservoir engineering applications. Inconsistencies and ambiguities still exist between different ROI evaluation methods, especially for the dual-porosity (DP) system representing naturally fractured reservoirs. This paper revisited the impact of inter-porosity flow in the DP system and presented ROI equations in the early and late flow periods based on the Laplace space solution of the Warren-Root dual-porosity model. A new comprehensive ROI expression for the DP system is derived which accounts for both storativity ratio () and inter-porosity flow coefficient (). The new method in this paper reveals that the log-log plot of ROI vs. time for DP models exhibits two parallel straight lines linked by a smooth transition curve. The distance of these two straight lines is dependent on and ROI in the intermediate flow period is highly dependent on the value of The new ROI equation for the DP system can degenerate to similar ROI formula for the single-porosity system in early and late flow periods. Comparison analysis of the new method with other approaches is conducted and the validation of the new method is realized by analytical and numerical matching.

Pressuredrop Response Characteristics for Multi-Injection Well Interfered Vertical Well in Heterogeneous Fractured Anticline Reservoirs

AbstractFractured anticline reservoirs are mostly developed by a line production well located at the top position and a line injecting well located at the bottom position. The production well is often interference with by multiple injecting wells, but there is little related research about multiple injecting well interferences. To solve this problem, an extended bottom-hole pressuredrop (BHPD) response model for production well interfered with by multiple injection wells was presented to capture the injection interference and gravity effect. The proposed model's correctness is validated by the software numerical simulation, and low regimes were identified by the BHPD and its derivative curve. Research results show that: (i) the BHPD derivative curve has a one-half slope line, V-shape, and one slope line in reservoir linear flow regime, inter-porosity flow regime, and interference flow regime, respectively; (ii) the drop rate of pressure increases with the increase of formation transmissibility and storability. The bigger the fracture storability, the more obvious the V-shape feature in the derivative curve of BHPD. As the inter-porosity flow coefficient increases, the V-shape feature emerges later; (iii) the beginning time of the interference flow becomes later when the interference distance increases. When the injection rate trends to the production rate, the BHPD curve shows a slight drop and its derivative curve has an intermittent rupture; (iv) the influence of the gravity effect is not ignored. Due to the gravity effect, the BHPD interfered by constant injection well like the BHPD's behavior interfered by the closed boundary. This work provides technical support for capturing the source and degree of interference from well group in the heterogeneous fractured anticline reservoir.

Fluid Flow Behavior Prediction in Naturally Fractured Reservoirs Using Machine Learning Models

The naturally fractured reservoirs are one of the most challenging due to the tectonic movements that are caused to increase the permeability and conductivity of the fractures. The instability of the permeability and conductivity effects on the fluid flow path causes problems during the transfer of the fluids from the matrix to the fractures and fluid losses during production. In addition, these complications made it difficult for engineers to estimate fluid flow during production. The fracture properties’ study is important to model the fluid flow paths such as the fracture porosity, permeability, and the shape factor, which are considered essential in the stability of fluid flow. To examine this, this research introduced new models including decision tree (DT), random forest (RF), K-nearest regression (KNR), ridge regression (RR), and LASSO regression model,. The research studied the fracture properties in naturally fractured reservoirs like the fracture porosity (FP) and the shape factor (SF). The datasets used in this study were collected from previous studies “i.e., Texas oil and gas fields” to build an intelligence-based predictive model for fluid flow characteristics. The prediction process was conducted based on interporosity flow coefficient, storativity ratio, wellbore radius, matrix permeability, and fracture permeability as input data. This study revealed a positive finding for the adopted machine learning (ML) models and was superior in using statistical accuracy metrics. Overall, the research emphasized the implementation of computer-aided models for naturally fractured reservoir analysis, giving more details on the extensive execution techniques, such as injection or the creation of artificial cracks, to minimize hydrocarbon losses or leakage.

An integrated multi-scale model for CO2 transport and storage in shale reservoirs

Shale reservoirs have gradually been recognized as promising potential candidates for CO2 geological storage due to their wide geographic distribution and enormous storage potential. CO2 sequestration in shale is a complex multi-scale process with spatial sizes ranging from nano-scale to kilometer-scale. In this study, an integrated multi-scale model, considering CO2 adsorption, dissolution, slip flow, and diffusion, is developed to describe CO2 transport and storage in shale reservoirs with a multi-stage fractured horizontal well. The computationally efficient semi-analytical solution of the multi-scale model is obtained via Laplace transformation and Pedrosa’s substitution. Based on the established model, a workflow for evaluating the CO2 storage capacity of shale reservoirs is proposed. Taking the Longmaxi shale reservoir in the Sichuan Basin as an application case, the results show that the storage capacity can reach up to 29.97 × 108 m3 at a high constrained injection pressure. In addition, sensitivity analysis suggests that CO2 storage capacity is strongly influenced by the adsorption index of clay minerals, kerogen content, solubility coefficient, and inter-porosity flow coefficient of kerogen and inorganic matrix. Most reservoir parameters have negligible effects on storage capacity at low injection pressures, yet significant effects at high injection pressures. More specifically, the CO2 storage capacity can increase by 6.8 folds when the constrained injection pressure is increased from 5.5 to 8.5 MPa. The findings obtained in this study further expand the description of CO2 transport in the shale formation, laying the foundation for highly efficient CO2 sequestration in shale reservoirs.

Genetic Algorithm Optimization of Deep Structured Classifier-Predictor Models for Pressure Transient Analysis

Abstract This research aims to optimize deep learning models constituting long short-term memory and dense neural networks using the genetic algorithm (GA). This novel scenario has been applied to automatically identify reservoir types (homogeneous and natural fracture) and their external boundaries (infinite acting, circularly closed, and constant pressure) and estimate the related parameters. The suggested scenario includes two classifiers and 48 predictors to handle reservoir/boundary model detection and parameter estimation simultaneously. This methodology can recognize the reservoir/boundary models and predict wellbore storage constant, storativity ratio, skin factor (S), CD (dimensionless wellbore storage constant) × e2S, and inter-porosity flow coefficient. The pressure signals required for training the classifier and predictor models have been simulated by solving governing equations with added noise percentages. The hyperparameters of the intelligent models have been carefully tuned using the genetic algorithm to improve their classification/prediction accuracy. The GA-optimized classifier attained 94.79% and 94.29% accuracy over the training and testing groups of the pressure transient signal, respectively. The separately trained 24 optimized predictors converged well to estimate the reservoir parameters. The reliability of the proposed scenario has also been validated using two actual-field well-testing signals. The results indicate that the suggested procedure accurately identifies the reservoir/boundary model and efficiently approximates the associated parameters.

Employing Deep Learning Neural Networks for Characterizing Dual-Porosity Reservoirs Based on Pressure Transient Tests

Abstract The deep learning model constituting two neural network models (i.e., densely connected and long short-term memory) has been applied for automatic characterization of dual-porosity reservoirs with infinite, constant pressure, and no-flow external boundaries. A total of 16 different prediction paradigms have been constructed (one classifier to identify the reservoir models and 15 regressors for predicting the dual-porosity reservoir characteristics). Indeed, wellbore storage coefficient, CDe2S, skin factor, interporosity flow coefficient, and storativity ratio have been estimated. The training pressure signals have been simulated using the analytical solution of the governing equations with varying noise percentages. The pressure drop and derivation of the noisy synthetic signals serve as the input signals to the intelligent scenario. The hyperparameters of the intelligent model have been carefully adjusted to improve its prediction performance. The trained classification model attained 99.48% and 99.32% accuracy over the training and testing datasets. The separately trained 15 regressors converged well to estimate the reservoir parameters. The model performance has been demonstrated with three uniquely simulated and real-field cases. The results indicate that the compiled prediction model can accurately identify the reservoir model and estimate the corresponding characteristics.

A New Model for Predicting Flow in Fractured-Vuggy Carbonate Reservoirs under Pseudosteady State Condition

For constant rate production of a single well in a closed boundary fractured-vuggy carbonate reservoir, when the pressure wave propagates to the reservoir boundaries, boundary-dominated flow occurs, and the transient flow period ends, the reservoir will be in a state of pseudoequilibrium (i.e., pseudosteady state flow occurs, and the pressure at any point in the reservoir declines at the same constant rate over time). The characterization of fluid flow in the fractured-vuggy carbonate reservoir under pseudosteady state condition is of significance in describing the productivity index (PI) of the well. However, due to complex mechanisms (e.g., stress dependency of reservoir properties and crossflow between different systems of the reservoirs) during flow in fractured-vuggy carbonate reservoirs, researches on productivity prediction in fractured-vuggy carbonate reservoirs under pseudosteady state are very limited. The present work is aimed at developing a new analytical model for predicting flow in fractured-vuggy carbonate reservoirs under pseudosteady state condition. In the derived model, the crossflow between different systems (i.e., matrix, fracture, and vug) of the reservoirs was taken into account. In addition, based on Hooke’s law, a quantitative model was proposed to study stress-dependent permeability of the fracture system, which connects the reserve spaces. Moreover, the roughness morphology characteristics of fracture surface were taken into account with fractal theory. Finally, with our derived model, influences caused by various related factors on productivity were analyzed. The results show that well productivity during pseudosteady flow will be significantly affected by the morphology of fracture surface (e.g., fracture microstructure parameters) and effective stress. Specifically, due to effective stress, the fracture system in the fractured-vuggy reservoirs will be deformed, and the corresponding properties (e.g., permeability, porosity, and conductivity) will change, leading to the change of well productivity. In addition, there exists a negative relationship between the elastic storage capacity ratio of vugs and well productivity during pseudosteady flow. Moreover, a larger value of matrix-fracture interporosity flow coefficient or vug-fracture interporosity flow coefficient corresponds to a larger value of well productivity during the pseudosteady period. The new derived model is beneficial to improve the productivity prediction accuracy and reduce uncertainty. What is more, the findings of this study can help for providing theoretical reference for the design of efficient development of fractured-vuggy carbonate reservoirs.

A semi-analytical two-phase flow model of fractured horizontal well with complex fracture networks in natural fractured reservoirs

Complex fracture networks are easily developed along the horizontal wellbore during hydraulic fracturing. The water phase increases the seepage resistance of oil in natural fractured reservoir. The flow regimes become more intricate due to the complex fractures and the occurrence of two-phase flow. Therefore, a semi-analytical two-phase flow model is developed based on the assumption of orthogonal fracture networks to describe the complicate flow regimes. The natural micro-fractures are treated as a dual-porosity system and the hydraulic fracture with complex fracture networks are characterized explicitly by discretizing the fracture networks into multiple fracture segments. The model is solved according to Laplace transformation and Duhamel superposition principle. Results show that seven possible flow regimes are described according to the typical curves. The major difference between the vertical fractures and the fracture networks along the horizontal wellbore is the fluid “feed flow” behavior from the secondary fracture to the main fracture. A natural fracture pseudo-radial flow stage is added in the proposed model comparing with the conventional dual-porosity model. The water content has a major effect on the fluid total mobility and flow capacity in dual-porosity system and complex fracture networks. With the increase of the main fracture number, the interference of the fractures increases and the linear flow characteristics in the fracture become more obvious. The secondary fracture number has major influence on the fluid feed capacity from the secondary fracture to the main fracture. The elastic storativity ratio mainly influences the fracture flow period and inter-porosity flow period in the dual-porosity system. The inter-porosity flow coefficient corresponds to the inter-porosity flow period of the pressure curves. This work is significantly important for the hydraulic fracture characterization and performance prediction of the fractured horizontal well with complex fracture networks in natural fractured reservoirs.

Single Well Productivity Prediction Model for Fracture-Vuggy Reservoir Based on Selected Seismic Attributes

Single well productivity is an important index of oilfield production planning and economic evaluation. Due to fracture-vuggy reservoirs being characteristically strongly heterogeneous and having complex fluid distribution, the commonly used single well productivity prediction methods for fracture-vuggy reservoirs have many problems, such as difficulty in obtaining reservoir parameters and producing large errors in the forecast values of single well productivity. In this paper, based on the triple medium model, the Laplace transform and Duhamel principle are used to obtain the productivity equation of a single well in a fracture-vuggy reservoir. Secondly, the seismic attributes affecting the productivity of a single well are selected using the Spearman and Pearson correlation index calculation method. Finally, the selected seismic attributes are introduced into the productivity equation of the triple medium model through the interporosity flow coefficient and the elastic storativity ratio, and the undetermined coefficients under different karst backgrounds are determined using multiple nonlinear regression. From these, a new method for predicting single well productivity of fracture-vuggy reservoir is established. In order to verify the feasibility of the new method, based on the actual production data of a fracture-vuggy reservoir in Xinjiang, the new single well productivity prediction method is used to predict the productivity of 134 oil wells. The results show that the new productivity prediction method not only reduces calculation workload, but also improves the accuracy of productivity prediction, which contributes to a good foundation for future oilfield development.

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

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

Blasingame production decline and production prediction model of inclined well in triple-porosity carbonate gas reservoir

The inclined well is used widely to enhance the single well production of the triple-porosity carbonate gas reservoir. This work presents an analytical solution of the inclined well in triple-porosity carbonate gas reservoir by Laplace transform and pressure drop superposition. According to well deviation well deviation pseudoskin factor of inclined well and the structure of approximations solution for the vertical well during pseudo-steady flow regime, approximations solution of the inclined well during pseudo-steady flow regime is obtained and Blasingame production decline model of inclined well is constructed. Calculation method of production prediction is presented by combining with material balance equation of the closed gas reservoir. The method was verified by comparing with numerical model. According to characteristic of dimensionless pseudo-pressure and production decline integration derivative curves, the seven obvious flow regime can be distinguished and every flowing regime is analyzed. With the increasing of perforated degree and inclination degree, Blasingame production decline curves become larger before pseudo-steady flow regime and constant-rate production time become longer. The larger interporosity flow coefficient and storativity ratio of vug system and naturally fracture system lead to earlier ‘concave’ starting-time and more shallow ‘concave’ of Blasingame production decline integral derivative curve separately. The larger interporosity flow coefficient and storativity ratio of vug system and naturally fracture system can also lead to longer constant-rate production time. The larger of initial rate and constant wellbore pressure is, the longer duration of constant-rate production is. A field example is presented to demonstrate the application of the proposed model and method.

Auto-characterization of naturally fractured reservoirs drilled by horizontal well using multi-output least squares support vector regression

Pressure transient response (PTR) of horizontal well in naturally fractured reservoirs (NFR) has a particular characteristic shape. This PTR is often used to estimate parameters of NFRs and detect their wellbore and boundary regimes. Interporosity flow coefficient (λ) and storativity ratio (ω) are two important parameters of the NFR that often estimated by matching process on the PTR. Since the matching techniques’ results are not often unique, in this study, the multi-output least squares support vector regression (MLS-SVR) is employed for simultaneous estimation of λ and ω. A databank of 500 PTRs for horizontal wells in naturally fractured reservoirs is generated by the finite element method, converted to the pressure derivative (PD) curves, and then used to develop and evaluate this auto-characterization paradigm. The predictive accuracy of the model is checked and validated by both smooth and noisy PTRs. The proposed model predicts ω and λ with overall absolute average relative deviations (AARD) of 0.186% and 3.754%, respectively. The correlation coefficients (R2) of 1 and 0.99992 are obtained for the prediction of ω and λ, respectively. The Leverage outlier detection technique justified that only less than 6% of the predictions are within the suspect region. This MLS-SVR model can be simply integrated with commercial pressure transient analysis (PTA) packages for accurate prediction of ω and λ even from the noisy PTRs.

Application of Pressure Type Curve Matching for Characterizing the Naturally Fractured Reservoir

Naturally fractured reservoirs have an important role in the production and reserves of hydrocarbons, where more than 40% of the oil and gas reservoir production comes from this reservoir type. There are two systems that affect the production mechanism in this reservoir, namely the matrix as a fluid source and fractures as a fluid transfer network to the wellbore. This study discusses the characterization of naturally fractured reservoirs using curve type matching. In this study, the Warren and Root model is applied to create a reservoir model that applies the fluid flow mechanism from the matrix to the fracture with pseudo steady state interporosity flow. Pressure transient analysis is commonly known and widely used by reservoir engineers as a tool to identify reservoir characteristics, where there are two important parameters that influence reservoir productivity, namely the ratio of the storativity coefficient (omega) and the interporosity flow coefficient (lamda). Based on the results of the analysis, it is found that the coefficients are strongly affected by the values of porosity fracture and permeability fracture also the productivity of the reservoir.

A Practical Methodology for Production Data Analysis in Carbonate Reservoirs Using New Decline Type Curves

Carbonate reservoirs typically have complex pore structures, so the production wells typically have high production in the early production stage, but they decline rapidly. It is highly challenging to achieve accurate interpretation results. In this paper, a new and practical methodology for production data analysis of fractured and fractured-vuggy carbonate reservoirs is proposed. Firstly, analytical solutions to characterize the different multipore media and simulate transient production behavior of fractured and fractured-vuggy carbonate reservoirs during the transient flow regime are presented. Then, a new function f q D and f ′ q D that related to the dimensionless production rate is introduced, and a series of new decline type curves are drawn to make a clear observation of different flow regimes. In addition, the effects of the storativity ratio, interporosity flow coefficient, skin factor, and dimensionless radial distance of external boundary on production performance are also analyzed. Finally, two example wells from the fractured and fractured-vuggy carbonate reservoirs are used to perform rate decline analysis with both the Blasingame type curves and the new type curves. The validation of the new method is demonstrated in comparison to the results of well test interpretation. The results show that the curves of 1 / f ′ q D vs. t D are ∧ -shaped for dual-porosity reservoirs and M -shaped for triple porosity reservoirs and also indicate that the interpreted parameters such as permeability, skin factor, storativity ratio, and interporosity flow coefficient using new decline type curves are aligned well test interpretation. In correlation with other traditional well test analysis, this approach effectively reduces the multisolution probability of interpretation.

Transient Pressure Analysis of Inclined Well in Continuous Triple-Porosity Reservoirs With Dual-Permeability Behavior

Inclined wells has recently been adopted to develop fractured-vuggy carbonate hydrocarbon reservoirs (FVCHRs) composed by matrix, fracture and vug system. Therefore, it is significant for us to describe pressure transient of inclined well for FVCHRs. In this paper, it is assumed that vug and fracture system connect with wellbore, and inter-porosity flow from vug to fracture system appears. Therefore, the pressure transient responses model of inclined well with triple-porosity dual-permeability behavior was built. The model is solved by employing Laplace integral transform and finite cosine Fourier transform. Real-domain solution of the model is obtained by Stehfest inversion algorithm. On the basis model of the published paper, the solution of the simplified model of this paper was validated with horizontal and vertical well of FVCHRs with triple-porosity dual-permeability behavior, and results reach a good agreement. Type curve, according to pressure derivative curve characteristic, can be divided into eight flow regimes, which includes wellbore storage, skin reflect, early vertical radial flow, top and bottom boundary reflection, linear flow, inter-porosity flow from vug to fracture, inter-porosity from matrix to vug and fracture and pseudo-radial flow regimes. The influence of some vital parameters (inclination angle, inter-porosity flow coefficient, well length and permeability ratio etc.) on dimensionless pressure and its derivative curves are discussed in detail. The presented model can be used to understand pressure transient response characteristic of inclined wells in FVCHRs with dual-permeability behavior.

Rate and pressure behavior considering the fractal characteristics of structurally disordered fractured reservoirs

The main objective of this paper is to understand the impact of the fractal characteristics of fractured reservoirs on their pressure behavior, flow rate decline, and productivity index. The paper proposes a new methodology for developing several analytical models for describing the wellbore pressure distribution and the flow rate decline trend. The proposed models consider including the fractal characteristics such as the mass fractal dimension, conductivity index of anomalous diffusion flow mechanism, fractal-network parameters, fractional-derivative order, and matrix/fracture-interaction index as well as dual-porosity media characteristics such as the storativity and interporosity flow coefficient in the analytical models of the pressure, rate, and productivity index. The study has found that: (1) Some of the fractal characteristics have a significant impact on reservoir performance, while others may not have a significant impact. (2) Fractal reservoirs exhibit better performance than the standard geometry reservoirs of single and dual-porosity media.

The performance of complex-structure fractured reservoirs considering natural and induced matrix block size, shape, and distribution

This paper introduces an analytical approach for the performance of the fractured reservoir considering the impact of the matrix block size, shape, and distribution. The objective is better understanding the roles of the variable interporosity flow systems, fracture flowing systems, and reservoir matrix heterogeneity in the responses of the wellbore pressure drop, flow rate, cumulative production, and productivity index. This understanding could help to eliminate the uncertainties and increase the accuracy in characterizing the conventional and unconventional reservoirs where very complex structures of a significant disorder in the matrix block size, shape and distribution could be existed in the porous media.The study uses the well documented multilinear flow model to describe the pressure distribution in the naturally fractured reservoirs depleted by multiple hydraulic fractures considering different matrix block sizes, shapes, and distributions. The analytical models of the flow rate, cumulative production, and the productivity index are also developed in this study from the multilinear flow model. The reservoirs of interest are assumed to have stimulated porous media extending between hydraulic fracture and unstimulated volume extending beyond the fracture tips toward the reservoir boundary. The unstimulated reservoir volume is assumed consisting of uniformly distributed single matrix block size and shape because there is no impact for the hydraulic fracturing process. While the stimulated reservoir volume is considered consisting of a variable matrix block size, shape, and distribution because of the impact of hydraulic fracture propagation. The petrophysical properties of the two porous media, as well as the storativity and interporosity flow coefficient, are assumed functions of the matrix characteristics in the two volumes. The matrix block dimensions (radius or length) are correlated exponentially with the distance from the hydraulic fracture face toward the no-flow boundary between these fractures. Three fracture-matrix fluid flux functions are developed for the reservoirs where the matrix blocks could have a spherical, slab, and cylindrical configuration.The study has reached several conclusions. A positive impact on the reservoir performance is seen when the matrix block size becomes small or when the small size matrix blocks control the distribution of the blocks in the porous media. Reservoir performance is enhanced also when there are several matrix block sizes compared to a single size or very few sizes. It is observed that the reservoirs with spherical blocks may give better performance than the reservoir with slab or cylindrical matrix blocks. In terms of matrix block size and distribution, heterogeneous reservoirs may have a higher productivity index than homogenous reservoirs. The variable matrix block size and distribution in the stimulated reservoir volume is more beneficial than the unstimulated volume. The novel point presented in this paper is developing several analytical models for the wellbore pressure drop, flow rate, cumulative production, and productivity index of hydraulically fractured reservoirs with a consideration given to the matrix block size, shape, and distribution.