Rate Transient Analysis of Heterogeneous Unconventional Gas Reservoir Using a Fractional Decline Model

2021 ◽  
Author(s):  
Loc Luong
Keyword(s):  
Gas Flow ◽  
Transient Flow ◽  
Fractured Reservoirs ◽  
Synthetic Data ◽  
Fracture Network ◽  
Hydraulic Fractures ◽  
Curve Matching ◽  
Reservoir Properties ◽  
Type Curve ◽  
Type Curves

Abstract In this study, an extended version of the fractional decline model is analytically developed for gas flow in fracture reservoir using the anomalous diffusion equation incorporated with the fractional calculus and equation of state. The model can represent the heterogeneity of complex fracture networks and can further be used to interpret reservoir properties by performing type-curve matching of flow rate and cumulative production from multi-fractured horizontal wells in unconventional reservoirs. To address the limitations of conventional planar fracture idealization, the hydraulic fractures in this present study are integrated with the fracture network, and the fractional diffusivity is solved for a horizontal wellbore. Upon establishing and solving the governing equation in the Laplace domain, the solutions are converted back to the real-time and space domain by performing numerical Laplace inversion. A set of distinctive type curves is generated on the basis of an infinite conductivity horizontal well model, considering early and middle times, in order to capture the heterogeneity of the fractal network in the reservoir model. Application of this new model is demonstrated through type-curve matching of two synthetic cases of simulation data obtained from commercial software; the cases cover orthogonal evenly and unevenly distributed networks. Results from these examples show an acceptable match between the fractional decline model and synthetic data and, hence, showcase the applicability of this model to capture the transient flow in heterogeneous fractured reservoirs.

Seismic reflectivity of hydraulic fractures approximated by thin fluid layers

Geophysics ◽  
2013 ◽  
Vol 78 (4) ◽  
pp. T79-T87 ◽  
Author(s):  
A. Oelke ◽  
D. Alexandrov ◽  
I. Abakumov ◽  
S. Glubokovskikh ◽  
R. Shigapov ◽  
...  
Keyword(s):  
Analytical Solutions ◽  
Fluid Layer ◽  
Synthetic Data ◽  
P Wave ◽  
Hydraulic Fractures ◽  
Reflection Coefficients ◽  
S Wave ◽  
Reservoir Properties ◽  
Thin Fluid ◽  
Theoretical Results

We have analyzed the angle-dependent reflectivity of microseismic wavefields at a hydraulic fracture, which we modeled as an ideal thin fluid layer embedded in an elastic, isotropic solid rock. We derived full analytical solutions for the reflections of an incident P-wave, the P-P and P-S reflection coefficients, as well as for an incident S-wave, and the S-S and S-P reflection coefficients. The rather complex analytical solutions were then approximated and we found that these zero-thickness limit approximations are in good agreement with the linear slip model, representing a fracture at slip contact. We compared the analytical solutions for the P-P reflections with synthetic data that were derived using finite-difference modeling and found that the modeling confirmed our theoretical results. For typical parameters of microseismic monitoring by hydraulic fracturing, e.g., a layer thickness of [Formula: see text] and frequencies of [Formula: see text], the reflection coefficients depend on the Poisson’s ratio. Furthermore, the reflection coefficients of an incident S-wave are remarkably high. Theoretical results suggested that it is feasible to image hydraulic fractures using microseismic events as a source and to solve the inverse problem, that is, to interpret reflection coefficients extracted from microseismic data in terms of reservoir properties.

Parallel-Simulator Framework for Multipermeability Modeling With Discrete Fractures for Unconventional and Tight Gas Reservoirs

SPE Journal ◽  
2016 ◽  
Vol 21 (04) ◽  
pp. 1370-1385 ◽  
Author(s):  
Larry S. Fung ◽  
Shouhong Du
Keyword(s):  
Organic Matter ◽  
Transient Flow ◽  
Domain Decomposition Method ◽  
Knudsen Diffusion ◽  
Fracture Network ◽  
Simulation System ◽  
Hydraulic Fractures ◽  
Mathematical Framework ◽  
Fine Grid ◽  
Shale Reservoirs

Summary Economic gas rate from ultralow-permeability shale reservoirs requires the creation of a complex fracture network in a large volume known as the stimulated reservoir volume (SRV). The fracture network connects a large surface area of the reservoir to the well. It is created by injecting low-viscosity fracturing fluid (slickwater) at very high rates in multiple stages along the horizontal wellbore. Numerical simulation is used to evaluate the stimulation designs and completion strategy. Microseismic (MS) -survey fracture mapping can provide a measurement of the overall SRV and an estimate of the fracture patterns. Special core analyses provide estimates of shale-matrix permeability. The extent of the fracture network indicates that there is insufficient proppant volume, and many stimulated fractures may be only partially propped or may be unpropped. Thus, fracture conductivity will vary spatially caused by uneven proppant distribution and temporally caused by stress sensitivity upon pressure decline during production. Because of the vast contrast in conductivity between stimulated/hydraulic fractures (darcy-ft) and shale matrix (nd-ft), the transient response in matrix/fracture flow cannot be captured accurately if the stimulated fractures are approximated with large dual-continuum (DC) gridblocks. The gridding requirement to achieve an accurate solution in fractured shale reservoirs is investigated and discussed. In this work, the stimulated and hydraulic fractures are discretized explicitly to form a discrete fracture network (DFN). This paper discusses the mathematical framework and parallel numerical methods for simulating unconventional reservoirs. The simulation methods incorporate known mechanisms and processes for shale, which include gas sorption in organic matter; combined Knudsen diffusion and viscous flow in nanopores; stress-sensitive fracture permeability; and velocity-dependent flow in the high-conductivity hydraulic fractures. The simulation system is based on a general finite-volume method that includes a multiconnected multicontinuum (MC) representation of the pore system with either a compositional or a black-oil fluid description. The MC model is used to represent the storage and intercommunication among the various porosities in shale (organic matter, inorganic matter, fine unstimulated natural fractures). Unconventional simulation involves many more nonlinearities, and the extreme contrast in permeabilities will make the problems harder to solve. We discuss numerical implementation of the methods for modeling the mechanisms and processes in fractured shale. In addition, we discuss the MC formulation, the discretization method, the unstructured parallel domain-decomposition method, and the solution method for the simulation system. Finally, we explain our efforts in numerical validation of the system with fine-grid single-porosity simulation. We show numerical examples to demonstrate the applications of the simulator and to study the transient flow behavior in shale reservoirs. The effects of the various mechanisms for gas production are also evaluated.

scholarly journals Transient-Flow Modeling of Vertical Fractured Wells with Multiple Hydraulic Fractures in Stress-Sensitive Gas Reservoirs

2019 ◽  
Vol 9 (7) ◽  
pp. 1359 ◽  
Author(s):  
Ping Guo ◽  
Zhen Sun ◽  
Chao Peng ◽  
Hongfei Chen ◽  
Junjie Ren
Keyword(s):  
Hydraulic Fracture ◽  
Transient Flow ◽  
Superposition Principle ◽  
Pressure Profile ◽  
Stress Sensitivity ◽  
Hydraulic Fractures ◽  
Transient Pressure ◽  
Gas Reservoirs ◽  
Type Curves ◽  
Vertical Well

Massive hydraulic fracturing of vertical wells has been extensively employed in the development of low-permeability gas reservoirs. The existence of multiple hydraulic fractures along a vertical well makes the pressure profile around the vertical well complex. This paper studies the pressure dependence of permeability to develop a seepage model of vertical fractured wells with multiple hydraulic fractures. Both transformed pseudo-pressure and perturbation techniques have been employed to linearize the proposed model. The superposition principle and a hybrid analytical-numerical method were used to obtain the bottom-hole pseudo-pressure solution. Type curves for pseudo-pressure are presented and identified. The effects of the relevant parameters (such as dimensionless permeability modulus, fracture conductivity coefficient, hydraulic-fracture length, angle between the two adjacent hydraulic fractures, the difference of the hydraulic-fracture lengths, and hydraulic-fracture number) on the type curve and the error caused by neglecting the stress sensitivity are discussed in detail. The proposed work can enrich the understanding of the influence of the stress sensitivity on the performance of a vertical fractured well with multiple hydraulic fractures and can be used to more accurately interpret and forecast the transient pressure.

scholarly journals Solution and type curves for the seepage model of the water-bearing coalbed with leakage recharge

2017 ◽  
Vol 21 (1) ◽  
pp. 17 ◽  
Author(s):  
Wangang Chen ◽  
Yu Yang ◽  
Hansen Sun ◽  
Chengwei Zhang ◽  
Qin Wen ◽  
...  
Keyword(s):  
Coalbed Methane ◽  
Radial Flow ◽  
Curve Matching ◽  
Pressure Derivative ◽  
Type Curve ◽  
Type Curves ◽  
Reservoir Permeability ◽  
Leakage Coefficient ◽  
Seepage Theory ◽  
Seepage Model

To analyze the effects of the leakage recharge of the aquifer on the initial dewatering of coalbed methane wells, the mathematical seepage model of water in the coalbed considering the aquifer leakage was established by using the leakage coefficient according to the unsteady seepage theory. The model was solved after Laplace transform and the Stehfest numerical reverse inversion was used to obtain the solution in right space. Then, the log-log type curves of pressure and pressure derivative were created with new combinations of parameters. Based on the natural seepage mechanism, the influence of aquifer leakage on curve shape was judged. It is found that the radial flow ends earlier as the leakage coefficient increases. Moreover, it was proposed to obtain reservoir permeability, skin factor, and leakage coefficient by using type curve matching. The type curves are useful for quantitatively evaluating the level of leakage, thereby guiding the adjustment of the following production system for CBM wells. Curvas de solución y tipo para el modelo de filtración de capas carboníferas acuíferas con recarga de fugasResumenEste estudio estableció el modelo matemático de filtración de agua en una capa carbonífera al estimar la salida acuífera con el uso del coeficiente de fuga, de acuerdo con la teoría de filtración inestable, para analizar los efectos en la recarga de pérdida de fluidos de un acuífero en el drenado inicial para pozos de gas metano.  El modelo se resolvió tras usar la transformación Laplace y la inversión numérica Stehfest para encontrar la respuesta en el lugar indicado. Luego, se creó la representación algorítmica de la presión y la presión derivativa con nuevas combinaciones de parámetros. Se evaluó la influencia de la pérdida de fluido del acuífero en la forma de la curva con base al mecanismo físico de filtración. Se estableció que el flujo radial finaliza antes de que el coeficiente de pérdida de fluido se incremente. Además, se propone el uso de la curva tipo correspondiente para obtener la permeabilidad del reservorio, el factor de daño y el coeficiente de pérdida de fluido. Las curvas tipo son útiles para evaluar cuantitativamente el nivel de la pérdida de fluido, y de esta manera guiar el ajuste de un sistema de producción consecuente para pozos de gas metano de carbón.

Estimation of characteristics of naturally fractured reservoirs by pressure transient analysis

2017 ◽  
Vol 14 (5) ◽  
pp. 368-380
Author(s):  
Mohamed Gamal Rezk ◽  
A.A. Abdelwaly
Keyword(s):  
Fractured Reservoirs ◽  
Direct Synthesis ◽  
Flow Regimes ◽  
Naturally Fractured Reservoirs ◽  
Log Analysis ◽  
Curve Matching ◽  
Type Curve ◽  
Pressure Transient ◽  
Content Type ◽  
Naturally Fractured

Purpose This 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/approach The 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. Findings For 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/value The 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.

scholarly journals Uji Sensitivitas dan Solusi Analitik Type curves jenis Reservoir Komposit Infinite acting Reservoir pada Laju Alir Produksi Sumur Konstan

PETRO ◽  
2018 ◽  
Vol 6 (1) ◽  
Author(s):  
Wiwiek Jumiati
Keyword(s):  
Curve Matching ◽  
Type Curve ◽  
Type Curves

<p>Metode analisis yang digunakan untuk mengevaluasi kinerja sumur minyak dengan tujuan melakukan analisis dan evaluasi kinerja pada sumur minyak meliputi antara lain metoda empirik, metoda analitik dan metoda numerik atau kombinasi ketiga metoda tersebut yang dapat menghasilkan <em>type curves</em>. Penelitian ini mengangkat permasalahan kondisi reservoir komposit dengan batas sumur yaitu laju alir produksi konstan dan batas luar <em>adalah infinite acting </em>dimana <em>type curves </em>yang terbentuk dihasilkan dari penurunan analitis yang dihasilkan dari persamaan difusivitas. Uji sensivitas dilakukan dengan merubah parameter jari-jari <em>discontinuity</em>, rasio <em>mobility</em>, <em>storativity </em>dan skin pada lubang sumur. <em>Type curves </em>yang dihasilkan dapat digunakan untuk menginterpretasikan log-log <em>type curve matching </em>dari reservoir komposit.</p>

Early-Time 1D Analysis of Shale-Oil and -Gas Flow

SPE Journal ◽  
2016 ◽  
Vol 21 (04) ◽  
pp. 1254-1262 ◽  
Author(s):  
Ali I. Bajwa ◽  
Martin J. Blunt
Keyword(s):  
Diffusion Equation ◽  
Gas Flow ◽  
Oil And Gas ◽  
Mathematical Formulation ◽  
Synthetic Data ◽  
Early Time ◽  
Spontaneous Imbibition ◽  
Reservoir Properties ◽  
Flow Equations ◽  
Fluid Properties

Summary We present a new semianalytic method to solve the nonlinear pressure-diffusion equation at early time, before reservoir boundaries are encountered, and under constant bottomhole pressure (BHP), applicable to the analysis of unconventional reservoirs. We assume that the flow rate is inversely proportional to the square root of time since the beginning of production. The method is an extension of the semianalytic solution proposed by Schmid et al. (2011) for spontaneous imbibition; we replace the solution for saturation with one for pressure, while extending the functional form of the governing diffusion equation. The solution can accommodate arbitrary pressure-dependent nonlinear rock and fluid properties as well as production caused by desorption. The mathematical formulation is presented for a general nonlinear case and tested by use of synthetic data. Field production from the Barnett Shale is then used to estimate effective matrix permeability. The model can be used to predict production if the rock and fluid properties are known, or can be used to constrain reservoir properties from production data. It is a complement to traditional pressure- or rate-transient analysis; if the response of a well for constant-pressure production can be determined, our method can be used to determine reservoir properties, without any approximations inherent in linearizing the flow equations.

An Investigation of Pressure and Production Data Using Decline and Type Curve Analysis

2017 ◽  
Author(s):  
Arifur Rahman ◽  
Fatema Akter Happy ◽  
Mahbub Alam Hira ◽  
M. Enamul Hossain
Keyword(s):  
History Matching ◽  
Fractured Reservoirs ◽  
Curve Analysis ◽  
The Other ◽  
Production Data ◽  
Type Curve ◽  
Type Curves ◽  
Decline Curve Analysis ◽  
Decline Curve ◽  
Analysis Technique

Decline curve analysis is one of the most widely used production data analysis technique for forecasting whilst type curve analysis is a graphical representation technique for history matching and forecasting. The combination of both methods can estimate the reserves and the well/reservoir parameters simultaneously. The purpose of this study is to construct the new production decline curves to analyze the pressure and production data. These curves are constructed by combining decline curve and a type curve analysis technique that can estimate the existing reserves and determine the other well/reservoir parameters for gas wells. The accuracy of these parameter estimations depends on the quality and type of the pressure and production data available. This study illustrates the conventional decline curve that can be used to analyze the gas well performance data with type curves based on pseudo time function. On the other hand, log-log plots are used as a diagnostic tool to identify the appropriate reservoir model and analogous data trend. Pressure derivative and type curves are used to construct a radial model of the reservoir. In addition, Blasingame and Fetkovich type curves analysis are also presented in a convenient way. The decline curve analysis shows steady state production for a long time, then a decline is observed which indicates a boundary dominated flow. The Blasingame type curve matching points is going downward, which indicate the influence of another nearby well. The reservoir parameters that are obtained by using the decline curve and type curves analysis show a similar trend and close match for different approaches. These observations closely match results of different analysis. This analysis improves the likelihood of the results being satisfactory and reliable, though it changes with time until the end of the production period. This analysis technique can be extended to other type of well/reservoir system, including horizontal wells and fractured reservoirs.

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