Wellbore Storage Effects Research Articles

Evaluation of near wellbore damaged conditions with an injection - falloff tests during transient flow regime in clastic hydrocarbon reservoir

Low or near zero daily oil production from a well below its potential is undesirable and should be addressed. This problem is caused by permeability reduction or impairments in the vicinity of a wellbore and could be due to one or combinations of the following factors; mud filtrate invasion, fines redeposition due to production, microbial growth, fracturing fluid, and enhanced chemical processes. The extent of this problem has to be quantitatively evaluated, using a skin factor, before an appropriate solution can be developed. A set of secondary data was simulated with a commercial software package, for a reservoir undergoing transient flow condition acting infinitely. A water injection well, fully perforated, is placed at the centre of an infinite-acting reservoir, for constant water injection. The wellbore radius of 0.5 ft fully penetrated the entire length of 190 ft, and injected water at 250 bbls per day, with water viscosities of 0.8 cP to 1.2 cP, continuously for 4 days. Water injection pressure stabilized at 1300 psi. Analysis of both injectivity and falloff were performed with an initial assumption of zero wellbore storage effects to evaluate formation permeability and skin factor, S. The result showed that skin factor increases with decreasing water viscosities. At water viscosity of 0.8 cP to 1.2 cP, a constant value of skin factor was obtained. An S value of +0.09 indicated that the near wellbore environment is slightly damaged. Therefore, it requires light acidization.

Pressure Transient and Production Analysis of Fractured Vertical Wells in Tight Sand Gas Reservoirs Considering Threshold Pressure Gradient, Phase-Change Phenomenon, and Stress Sensitivity

The productivity and pressure response of the tight sand gas wells are influenced by multiple flow mechanisms, such as threshold pressure gradient, phase-change phenomena, and stress sensitivity. Understanding the sensitivity of these factors is crucial for the effective development of tight sand gas reservoirs. This study aims to clarify the sensitivity of various factors affecting the productivity and pressure response of tight sand gas wells. Based on the percolation theory of tight sand gas reservoirs, we considered stress sensitivity, threshold pressure gradient, and phase-change phenomena to derive an unsteady mathematical model of a fractured well with an infinite boundary, and a point source solution was obtained. The proposed model was solved using series function properties, variable substitution, perturbation technique, Poisson superposition formula, Laplace transform, and numerical inversion. The influence of several important parameters on pressure response and productivity is discussed in detail. The results show that the threshold pressure gradient, stress sensitivity, and skin factor significantly impact gas well production and pressure response, while the wellbore storage effect and phase-change effect primarily affect the initial production and pressure response, having little effect on the cumulative gas production. The proposed model can estimate the influence of the threshold pressure gradient and stress sensitivity on productivity and pressure, providing a guide for the development of technical measures for fractured wells in tight sand gas reservoirs.

A three-dimensional numerical well-test model for pressure transient analysis in fractured horizontal wells with secondary fractures

During oil and gas reservoir development, multi-stage horizontal wells (MFHWs) and hydraulic fracturing techniques can effectively increase estimated ultimate recovery. However, there still lacks an understanding of the three-dimensional (3D) pressure transient behaviors of multi-stage fractured horizontal wells with secondary fractures. To narrow this gap, a three-dimensional numerical well-test model based on a discrete fracture model and unstructured tetrahedral grids is developed to study the pressure transient behaviors of MFHWs with secondary fractures. The pressure transient solutions of MFHWs with secondary fractures have been demonstrated by model verifications. The results show that the proposed model can accurately capture the complex transient flow around fractures, including early radial flow that is not easily captured by two-dimensional numerical well test models. The proposed model classifies the flow regimes of a MFHW as: wellbore storage and skin effects, early radial flow, bilinear flow, linear flow, elliptical flow, pseudo radial flow, and pseudo-boundary dominated flow. It is found that the fracture geometry has a relatively large effect on the shape of the pressure derivative curve in this work. The hydraulic fracture half-length has the greatest impact on the pressure transient behaviors of the MFHW, followed by fracture height and secondary fracture half-length, as found in this study. Additionally, fracture parameters are evaluated, and actual well testing data are interpreted, taking into account the fracture height. This work is meaningful to understand the three-dimensional pressure transient behaviors of MFHWs with secondary fractures.

Multiphysics Modeling Investigation of Wellbore Storage Effect and Non‐Darcy Flow

AbstractThis study presents a comprehensive investigation of wellbore storage effects and non‐Darcy flow in pumping well systems using a multiphysics numerical model. The model incorporates the Reynolds‐averaged Navier‐Stokes equations coupled with a moving free surface to simulate the flow field and drawdown in the wellbore. Hydraulic behavior of the system, including well and aquifer drawdown, pumped water ratio, aquifer flow nonlinearity, and wellbore flow field, is analyzed and compared with simplified 1‐D models. This study highlights the presence of a vortex in the wellbore flow field induced by large Reynolds number and the uneven stress distribution at the screen. This vortex influences the wellbore drawdown and introduces 2‐D flow in the surrounding aquifer, which further contributes to the longer travel paths for groundwater particles and increased hydraulic pressure consumption. The results show that non‐Darcy flow, coupled with wellbore storage effects, leads to higher drawdown in the pumping well compared to Darcy flow cases. The aquifer drawdown exhibits a similar temporal pattern but with decreasing deviation at larger distances due to the cone of depression. The pumped water ratio indicates the challenge of supplying outflow at the intake from aquifer storage, with nonlinear flow resulting in a smaller ratio compared to linear cases. A nonlinearity ratio is defined to illustrate the expansion of nonlinear flow regions over time, their convergence to a predictable quasi‐steady‐state shape, which is influenced by the Forchheimer parameter, and the gradual transition to Darcy flow away from the wellbore.

Develop an empirical flow rate correlation to model wellbore storage phenomenon for wells produced at a constant wellhead pressure

Well-test operation with a constant flow rate for long-time production is not typical in practice. Therefore, reservoirs frequently produce fluids with constant pressure at the wellhead, into a constant pressure separator or pipeline. During the production under this condition, the pressure drop at the wellbore varies as a function of the rate because of changes in the friction flow; therefore, the wellbore formation pressure is not constant. As a consequence, the wellbore storage effect emerges and should be incorporated in the modeling of fluid flow under production at a constant wellhead pressure. All available methods considering the wellbore storage effect can merely be applied for production under the constant rate condition. Moreover, well-test modeling under these circumstances needs a specific function for production rate, which made this type of well-testing less common. Even though there are exact solutions for production under the constant wellbore pressure in the Laplace domain, their inverse transform is quite complex and cannot be applied for modeling the wellbore storage effect. In this study, a new function is introduced as an approximate solution of the diffusivity equation, for a well that produces at a constant wellbore pressure, using multiple steps of the optimization process. Consequently, an efficient correlation is developed for flow rate about or concerning this condition. Next, the effect of the wellbore storage at constant pressure well-test operation was enumerated for the first time, which was commonly neglected in previous studies. This endeavor concentrated on modeling the two types of well-test operation, producing at constant wellhead pressure and, pressure build-up following the production at a constant wellhead pressure (constant pressure Build-up test). The results were also verified with numerical simulation as well as field data further confirming the excellent accuracy of developed solutions.

Capillary Impact on Tidal Response of Groundwater in Unconfined Aquifers With Finite Thickness, Anisotropy and Wellbore Storage—An Analytical Model

AbstractThis study develops a novel, two‐dimensional analytical model to study capillary effects on Earth tidal responses of groundwater in unconfined aquifers. It differs from the previous model by accounting for effects of finite aquifer thickness, anisotropy and wellbore storage. We test the present model against the previous model and numerical simulations and apply it to the field data. Several significant results are obtained: (a) At high conductivity ( m/s), the effect of capillary zones dominates tidal responses of groundwater and causes higher amplitude ratio and smaller phase shift compared with that predicted by the unconfined aquifer model without a capillary zone. At low conductivity ( m/s), the effect of capillary zones on the tidal responses diminishes. (b) The impact of the finite thickness on the tidal response is regulated by the anisotropy. If the anisotropic ratio is small (), the impact of thickness may be negligible; at high anisotropic ratio (), however, the amplitude ratio decreases and the phase shift increases, and the response differs substantially from that of the previous model, which is caused by a change in the flow pattern. (c) Wellbore storage have significant impacts on the tidal response at low conductivity ( 10−5 m/s) but negligible impact at higher conductivity. (d) The present model marginally improved the fit by the half‐space model to the field data from a well in SW China, showing that the remaining misfit to the field data by models with capillarity cannot be due to finite aquifer thickness, anisotropy, or wellbore storage.

Two‐region flow caused by pumping at a partial penetration well in a leaky confined aquifer

AbstractAn analytical model for depicting two‐region flow caused by constant‐rate pumping at a partially penetrating well in a leaky confined aquifer is established. The two‐region flow is described by the radial Izbash non‐Darcy flow in the vicinity of the abstraction well and Darcy flow away from the abstraction well in the pumped aquifer. The model considers the effects of aquitard storage, wellbore storage, and wellbore skin. The semi‐analytical solutions of drawdown are developed by means of a linearization procedure combined with Laplace transform and separation of variables. The time‐domain drawdowns are then obtained by using the Stehfest method for numerical Laplace inversion. The solutions encompass previous solutions for one or two‐region flow to a partially penetrating well in a (non‐)leaky confined aquifer. The drawdown response in the abstraction well, non‐Darcy region, and Darcy region is investigated, and sensitivity analysis is made to assess the impact of various controlling parameters. The results demonstrate that the intermediate and late‐stage drawdowns in the abstraction well and non‐Darcy region for the two‐region flow model are larger than the corresponding values for the non‐Darcy flow model. The drawdown in the Darcy region for the two‐region flow model is larger than that for the Darcy flow model throughout the pumping duration. The results of sensitivity analysis show that the drawdowns in the abstraction well, non‐Darcy region, and Darcy region are most sensitive to the non‐Darcy constant n, and is very sensitive to the well configuration, and horizontal hydraulic conductivity of the Darcy region.

Location estimation of subsurface fluid-filled fractures: Cepstral predominant peak analysis and numerical study

In various subsurface resource development or fluid piping transportation problems, subsurface fluid-filled fractures often appear. Fracture location determination has always been critical in the related fields. Acoustic wave reflection at the junction and boundary in the pipeline can carry information about the property of the system. By using the accompanying acoustic wave information combined with the water hammer effect, the location of subsurface fractures can be estimated. A numerical fluid flow model for instantaneous shut-in is presented based on the water hammer effect. Fluid penetration effects, wellbore storage effect, and fluid inertial effect are considered. A method for determining the locations of subsurface fractures using cepstral predominant peak (CPP) is first proposed. By cepstral, we mean the inverse Fourier transform of the logarithm of the estimated signal spectrum. Also, the relationship between instantaneous shut-in pressure and cepstrum response is investigated in detail. To improve the robustness, CPP analysis based on Kaiser windowed cepstrum is used to identify the impulse period of fracture. Compared with the original cepstrum, Kaiser windowed cepstrum has the better performance for CPP analysis. The proposed flow model is impactful as it can provide pressure data with known fracture locations. Meanwhile, the data can be used to optimize and examine the performance of CPP analysis with Kaiser windowed cepstrum. A field experiment is conducted to validate the analysis about the acoustic wave in a pipeline system with fractures. By installing a high-frequency pressure monitoring device at the pump, the actual instantaneous shut-in pressure for an oil well is obtained. The experiment results show that the CPP analysis can obtain the fracture location efficiently and accurately, which can provide insights for engineering practices.

A novel semi-analytical monitoring model for multi-horizontal well system in large-scale underground natural gas storage: Methodology and case study

Carbon neutrality necessitates cleaner and more efficient use of fossil fuels. The storage of substantial amounts of energy in porous subsurfaces, such as underground natural gas storage (UGS), which is regarded the only long-term energy storage solution, is one of the promising technologies. Appropriate monitoring mechanisms are necessary for the security of UGS with a correctly configured injection-withdrawal capacity. In this research, a semi-analytical model of multi-horizontal well systems is presented and used to large-scale underground natural gas storage. The Laplace transform and Stehfest numerical inversion are used in UGS to solve the radial diffusion equation. We used the line source function and the pressure superposition principle to find a solution for a multi-horizontal well system. To illustrate the reliability of the suggested method, a numerical verification was performed. In UGS, pressure behavior at various phases identifies several types of flow regions, including wellbore storage effect stage, skin effect stage, early radial flow stage, linear flow stage, transitional flow stage, and late radial flow stage. Continuous gas injection and withdrawal from offset wells might result in pressure behavior with rising or dropping features when compared to a single well model. The evaluated permeability is 0.68 mD, the well spacing is 502 m, and the initial pressure is 27.28 MPa, according to field data from China's largest Hutubi UGS. The maximum injection and withdrawal capacities for wells with and without interference with wells are 9.46 × 105 and 1.1 × 106 m3/d/MPa, respectively, according to the productivity index. By continually injecting gas from offsetting wells, the target well's potential gas withdrawal capacity is raised by 16.2 %.

Pressure Transient Behaviors of Discretely Fractured Reservoirs Using a Numerical Discrete Fracture Model

Summary The conventional dual-porosity model (Warren and Root 1963) may not apply to naturally fractured reservoirs (NFRs), which have poorly connected fractures. To narrow this gap, a new discrete fracture model (DFM)-based numerical well-testing model is developed for pressure transient analysis in vertical wells interacting with natural fractures (NFs). The numerical model is based on a DFM and unstructured perpendicular bisector (PEBI) grid system. The accuracy and practicality of the proposed model have been demonstrated by model verifications with a commercial numerical software. The results show that the flow regimes of the vertical well interacting with NFs can be divided into wellbore storage and skin effects, bilinear flow, linear flow, radial flow, NF effect, and boundary-dominated flow. This is the radial flow of the formation before pressure propagates to NFs, which is virtually quite different from that in the conventional dual-porosity model. However, there are no bilinear and linear flow stages in the vertical well interacting with no NFs. It is found that the vertical well interacting with NFs has a lower pressure depletion. It is also found that the “V-shape” caused by the NF effect in the pressure derivative curve becomes deeper when there are more NFs, longer NFs, and higher fracture conductivity. Furthermore, the “V-shape” appears earlier, and the duration of the NF effect is longer as the number of NFs increases. Besides, with the decrease of the distance between the fracture and the well, the impacts of NFs on pressure transient behaviors of the vertical well are more significant. This work provides a meaningful way to understand the pressure transient behaviors of discrete NFs.

Analysis of the transient pressure of fractured wells coupling with irregular flow fracture: Semi-analytical model and case study

A strange phenomenon happens all the time that the obtained permeability by the conventional finite-conductivity model (FC) is much larger than the actual value in tight reservoir. The conventional pressure-transient analysis models of vertical-fractured wells regard fracture as a regularly non-uniform flow rate. However, due to fracture bending, irregular proppant filling, proppant crushing, and inadequate fracturing fluid backflowing, the fracture may show an irregular flow rate in different fracture segments. An additional horizontal line or concave curve appears on the pressure derivative curve by considering the irregular flow rate in the fracture. In the past, the concave curve would be regarded as an error from field data, and the horizontal line on the pressure derivative curve would be regarded as the quasi-radial flow regime. If the horizontal line is recognized as the quasi-radial flow regime in tight reservoir, the interpreted permeability will be magnified many times. In this work, we proposed a multi-segment irregular non-uniform flow model with changing wellbore storage effect (MINFC) to characterize the pressure response of irregular fractures better, making the pressure response in the fracture more realistic. The MINFC model can correct the magnified permeability and diagnose the partial closure fracture location, length, and flow rate. Green function and Newman product method are applied to obtain the bottom-hole pressure behavior. The results demonstrate that the pressure derivative curve is not a line with a slope of 0.5 in the irregular fracture flow regime but a horizontal or concave curve. Sensitivity analysis demonstrates that the location and length of the irregular proppant filling will affect the duration of the horizontal line. In conclusion, the reservoir permeability and fracture half-length obtained by the MINFC model are closer to the actual value. The locations of irregular proppant filling and low flow rete are quantified so that researchers can take steps to improve fracture performance. Finally, the comparison between the MINFC model and the finite-conductivity model verifies the MINFC model's accuracy. The MINFC model matches field data to verify its practicability.

Pumping-Induced Non-Darcian Flow in a Finite Confined Aquifer

An analytic model for depicting non-Darcian flow caused by pumping in a finite confined aquifer with an outer barrier boundary is established. The model considers the wellbore storage and skin effect. And the semi-analytical solution is derived with the aid of the Izbash’s law-based non-Darcian flow and the method for linearization procedure combined with the Laplace transformation. The new presented solution can reduce to some available solutions for the confined aquifer of unlimited extension. The drawdowns in abstraction well and aquifer are explored. The results suggest that the presence of the no-flux outer boundary makes no difference to the early-time drawdowns, the late-time drawdowns in the unlimited confined aquifer are smaller than those in the finite confined aquifer with a zero-flux outer boundary, and the flow in this finite confined aquifer cannot approach quasi-steady state, especially to a smaller finite outer boundary distance radius. The change of power index n in the non-Darcian flow equation cannot affect the early-time drawdowns in abstraction well, while the drawdowns in aquifer are underestimated for Darcian flow case at early pumping time. The late-time drawdowns in the pumping well and aquifer are significantly overestimated under the assumption of Darcian flow. The early-time drawdowns in abstraction well and aquifer are significantly affected by wellbore storage, and a larger wellbore storage coefficient leads to a smaller drawdown. The skin factor can impact the intermediate-time drawdowns in abstraction well, while the early and intermediate-time drawdowns in aquifer are influenced by skin effect.

Influence of hydrogeological and operational parameters on well pumping capacity

Numerous studies have analyzed how groundwater levels respond to pumping depending on aquifer and well characteristics. This study investigates how, conversely, the pumping capacity of a well depends on hydrogeological and operational conditions. The analysis is based on an analytical solution that considers wellbore storage and skin effects. The solution depends on aquifer transmissivity, aquifer storativity, well radius, well surface casing radius, skin layer transmissivity, pumping duration, and maximum allowable head change. We first conduct a sensitivity analysis of dimensionless pumping capacity to the three dimensionless parameters on which it depends. The results show strongly nonlinear relationships and an important effect of wellbore storage for small dimensionless pumping durations. Since the primary (dimensional) parameters are the ones that one ultimately needs to characterize or engineer in practice, we also conduct a sensitivity analysis of the primary system. The results show that, besides being trivially linearly related with the maximum allowable head change, pumping capacity (defined as a volume) is almost linearly related with aquifer transmissivity and pumping duration. Given the broad natural range of transmissivity values, transmissivity is the most critical parameter to determine for the estimation of pumping capacity. In contrast, pumping capacity is little sensitive to aquifer storativity and well radius, and so the precise determination of these parameters is less critical. Finally, we investigate the relationship between pumping capacity and specific capacity, the latter being a commonly used indicator of the productivity of wells. Our analysis confirms the previously acknowledged limitation of specific capacity for predicting pumping capacity when the duration of the specific capacity test is much smaller than the operational pumping duration. The theoretical insights gained from this study will assist groundwater scientists and engineers in their research, planning, and design activities.

Research on the Water Production Tracking Method of Horizontal Well in Heavy Oil Reservoir with Bottom Water

Abstract At present, the model of heterogeneous fluid production in horizontal wells in bottom water reservoirs does not comprehensively consider the influence of parameters such as flow, length, and position of each production section, resulting in the distortion of interpretation results. Using the Green function and the Newman product method, this paper derives heterogeneous fluid production in horizontal wells in the bottom water heavy oil reservoir. The Stehfest numerical inversion algorithm was used to obtain the bottom fluid pressure solution of the horizontal well production in the bottom water heavy oil reservoir with the wellbore storage effect and skin effect. By drawing the typical chart of horizontal well test in sections, the new model can be divided into five typical flow stages: wellbore storage stage, transition stage, radial flow stage, linear flow stage, and late stable flow stage. Based on the interpretation of conventional parameters, such as permeability, well storage, and skin effect, the new model can further diagnose the parameters such as liquid production length, liquid production position, and liquid production volume of each horizontal section. The field application examples verify the validity of the research results and broad application prospects.

Wellbore storage removal in pressure transient analysis for gas wells

Wellbore storage (WBS) occurs due to fluid loading/unloading in the wellbore, when a well starts production or is shut-in. This phenomenon creates variable sandface rate and time lag between the surface production rate and the stable sandface rate. Wellbore storage effects can sometimes conceal important information and complicate well test analysis and interpretation. In well tests that suffer from long WBS, removal of WBS effects can usually recover important features in the reservoir signal and lead to significant improvement in identifying the reservoir model and calculating reservoir parameters. Until recently, WBS removal relied on direct deconvolution techniques that require accurate well test data. Presence of noise in the pressure and rate data usually makes direct deconvolution methods unstable. Well test pressure and rate data usually suffer from some noise, and therefore, application of direct deconvolution methods may not work.

Application of a constructive method in solving the composite reservoir model of dual-porosity media with fractal characteristics

In this paper, we apply a constructive method to solve the extended Bessel differential equations with boundary value problem(BVP). Considering wellbore storage and skin effects, a dual-porosity composite reservoir model with fractal characteristics and three typical exterior boundary conditions is established. After symbolic comparison, the reservoir model is identical to the BVP proposed above, and the solving of the reservoir model is naturally reduced to the solving of the BVP. Based on the Laplace transform and a constructive method, the Laplacian space solutions of fracture system pressure and wellbore pressure in the two zones are obtained. The type curves of wellbore pressure and the pressure derivative are plotted with the aid of the Stehfest numerical inversion technique, the flow regimes are identified, and the effects of fractal and reservoir parameters on the type curves are analyzed. Compared with the traditional method, the similar constructive method is more efficient and fast in solving complex reservoir models, which is of great value in designing and implementing well-test analysis algorithms for complex reservoirs.

Pressure transient behavior in a multilayer reservoir with formation crossflow

This study proposes a new solution to the pressure transient behavior for a uniform-flux with a fully penetrating vertical well in a multilayer reservoir with formation crossflow. The general problem of pressure transient in multilayer reservoirs, in which any two adjacent layers are crossflowing in the formation, is solved analytically. The solution is presented for an infinite-acting system with no wellbore storage or skin factor effects. This analytical solution is obtained using Laplace transform, double Fourier transform, and Green's functions method. This solution provides an accurate and fast tool to: evaluate a vertical well performance in a multilayer reservoir, and estimate the effects of formation properties on pressure behavior at locations both far away from and around the well. Based on the solution, the pressure of the vertical well, which produces with a constant rate in the multilayer reservoir, can be examined in detail. An expression of dimensionless crossflow coefficient is obtained by solving a symmetric tri-angular matrix equation. Based on the solution, it is verified that the dimensionless crossflow coefficient is not constant but behavies as a function of the time and distance away from the wellbore. When producing time is sufficiently long, crossflow will cease to exist and crossflow coefficients are equal to zero, which means there are no effects of adjacent layers on the pressure drop of each layer. These findings indicate that each layer produces independently. • Pressure equation for a multilayer reservoir with crossflow is solved analytically. • Crossflow coefficient is obtained by solving a tri-angular matrix equation. • Crossflow coefficient is a function of time and distance away from the wellbore.

Production Analysis for Fractured Vertical Well in Coal Seam Reservoirs with Stimulated Reservoir Volume

The development and utilization of coalbed methane is of great significance to reduce carbon dioxide emission. Through the research, this paper presents a fast analytical solution method for the productivity of coalbed methane reservoir with finite-conductivity fractured well and stimulated reservoir volume region. Based on the dual-porosity flowing mechanism, combined with the Langmuir adsorb equation, Fick diffusion law, and Darcy law, a mathematical model considering diffusion in matrix and transport in natural fracture system is established, using spherical matrix to describe the transient steady-state sorption, and using cubic matrix to describe the pseudosteady-state sorption. Then, combined with the inner system and outer system, the analytical solution was obtained. Furthermore, the accuracy of the solution was validated against a numerical simulation. According to the Duhamel principle, the effect of wellbore storage and skin factor was got. Due to the SRV region, the linear flow and radial flow will appear before the pressure wave reach the outer region. And then, based on the pressure analysis result, we will have made the sensitivity analysis with different influence parameter. The result reveals that storage coefficient and conductivity factor mainly influence the early time; the permeability ratio and dimensionless SRV region radius mainly influence the property of SRV region. Finally, the analytical solution of the new model was applied to field history match. This model takes into account the adsorption and desorption characteristics of coalbed methane, as well as the SRV zones generated during fracturing. The calculation speed of the new model is increased while the calculation accuracy is retained, and the intensity of software application is reached. The model achieves the purpose of rapid evaluation and accurate prediction of gas well productivity and obtains a set of productivity evaluation method suitable for coalbed methane reservoir with fractured vertical well, which provides a basis for the development and productivity evaluation of coalbed methane reservoir in domestic and international cooperation.

A Mathematical Model for Fracture Networks with Considering Fracture Propagation and Closure in Shale

This study develops a semi-analytical model for fracture networks with considering fracture propagation and closure. To consider the volumetric fracturing, Warren-Root dual-porosity model is used to divide the reservoir into a fracture system and a matrix system. In addition, the discrete secondary fractures connected by hydraulic fractures are also taken into account. After model solution, it is found that flow stages of the theoretical well test curve of the multi-stage fractured horizontal well in shale reservoirs can be divided into: stage before the fracture closes, stage after the fracture closes, supply flow stage between secondary fractures and hydraulic fractures, linear flow stage, early dual radial flow stage, interporosity flow stage, late dual radial flow, and pseudo radial flow. The pressure and pressure conduction curves coincide with a straight line with a slope of 1 at stage before the fracture closes, which is similar to the wellbore storage effect. The shape of the derivative curve of dimensionless pressure and dimensionless pressure is similar to the behaviour of variable well-storage, during stage after the fracture closes. At the supply flow stage, there is a slight “dip”, which means that the reservoir fluid is supplied from the secondary fractures activated by fracturing to the main hydraulic fractures.

New technique revives direct deconvolution methods for Wellbore storage removal in pressure transient analysis

Eliminating wellbore storage (WBS) effects inherent in pressure transient data is one of the challenges in well test analysis. The available WBS-removal techniques are either direct or time-consuming approaches. The direct methods are mostly unstable and require accurate data with almost no noise. However, well test data often have noise in both rate and pressure measurements.This work discusses the development of a stable technique to overcome the shortcomings in the available WBS-removal methods. The technique presented here takes advantage of the recently developed stable deconvolution algorithms (e.g. von Schroeter algorithm) to achieve a stable WBS-removal process. The developed approach provides longer WBS-free reservoir response signal (extended over the entire test duration) than the previous methods. In addition, the approach introduced here can remove WBS-effects in noisy data and does not require sandface rate measurements.Different simulated and field examples were used to validate the proposed approach. The examples included data with different levels of rate and pressure measurement errors and covered wide variety of well/reservoir models. The available approaches were implemented to the same examples. A comparison of the results shows the superiority of the approach presented in this paper.