scholarly journals A Seepage mathematical model for fractured wells of coalbed methane reservoirs and the corresponding pressure response feature

2021 ◽  
Vol 714 (2) ◽  
pp. 022017
Author(s):  
Chunchun Liu ◽  
Cong Zhang ◽  
Yanmei Xu ◽  
Xinrui Cui ◽  
Weigang Huang ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Coalbed Methane ◽  
Pressure Response ◽  
Response Feature

A Semi-Analytical Fractal-Fractional Mathematical Model for Multi-Fractured Horizontal Wells in Coalbed Methane Reservoirs

2020 ◽  
Vol 143 (1) ◽  
Author(s):  
Ruizhong Jiang ◽  
Xiuwei Liu ◽  
Xing Wang ◽  
Qiong Wang ◽  
Yongzheng Cui ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Coalbed Methane ◽  
Fractal Theory ◽  
Superposition Principle ◽  
Horizontal Wells ◽  
Clean Energy ◽  
Stress Sensitivity ◽  
Element Discretization ◽  
Proposed Model ◽  
Fractured Horizontal Wells

Abstract Coalbed methane (CBM) which is clean energy has received great emphasis recently, and the multi-fracturing technology is widely applied in the exploitation of CBM. Due to the complexity, the randomness, and the anisotropism of the porous medium and the anomalous diffusion process, the fractal theory and fractional calculus are utilized to establish a semi-analytical fractal-fractional mathematical model considering the stress sensitivity of the cleat system for multi-fractured horizontal wells in CBM reservoirs. Through line-sink theory, Pedrosa transformation, perturbation theory, Laplace transformation, element discretization, superposition principle, and Stehfest numerical inversion, the pressure-transient analysis curves are plotted in the double logarithmic coordinates. By comparing with the existing model, the validation of the proposed model is illustrated. Also, nine flowing stages are identified according to different characteristics. Then, sensitivity analysis is conducted and influence laws are summarized. At last, a field application is introduced to furtherly verify the reliability of the proposed model. The relevant results analysis can provide some new significant guidance for interpreting the field data more precisely.

scholarly journals A Mathematical Model to Study the Coupling Effect of Deformation-Seepage-Heat Transfer on Coalbed Methane Transport and Its Simulative Application

2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Jianlin Xie ◽  
Yangsheng Zhao
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
High Temperature ◽  
Pore Pressure ◽  
Coalbed Methane ◽  
Coupling Effect ◽  
Gas Content ◽  
High Temperature Water ◽  
Heat Injection ◽  
Temperature Water

Injection of high-temperature water or steam into low-permeability coalbed for efficient and rapid extraction of coalbed methane has been studied by our university for many years and will soon be implemented in the field. With comprehensive consideration of coupling of heat transfer, water seepage, desorption of coalbed methane, and coal-rock mass deformation, the paper establishes a more comprehensive mathematical model of the coupling effect of deformation-seepage-heat transfer on coalbed methane transport. Compared with the previous studies, this theoretical model considers the change of adsorbed and free coalbed methane at high temperature and the coalbed methane transport caused by a high-temperature gradient. Using the Tunlan Coal Mine of Shanxi Coking Coal Group to conduct the numerical simulations on the coalbed methane extraction project using heat injection technology, results show that (1) high-temperature water flowed towards the extraction hole along fractured fissures, with seepage towards the coal mass on both sides of the fissure at the same time, gradually heating the coalbed and forming an arcuate distribution of temperature from high to low for an area from the fractured fissure to the coalbed upper and lower boundaries. On the thirtieth day of heat injection, the temperature of the coalbed in the heat injection area ranged from 140°C to 260°C. (2) Under high temperatures, desorption of the coalbed gas was quick, and the adsorption gas content formed an oval funnel from the heat injection hole towards the extraction hole, centered by the fractured fissure, and migrating towards the coalbed upper and lower boundaries. Along with heat injection and extraction, the absorbed gas content rapidly decreased, and on the thirtieth day of injection, the absorbed gas content of the entire heat injection area decreased to 1.5 m3/t, only 7% of the original. (3) During heat injection, the coalbed gas pore pressure rapidly increased and reached 5.5 MPa on the tenth day, about 4.5 times the original, and the pore pressure steadied at 3.5 MPa on the thirtieth day of extraction. Such a high gas pressure gradient promoted the rapid flow and drainage of the gas.

scholarly journals A mathematical model of the blood pressure response to salt intake

2008 ◽  
Vol 22 (S1) ◽  
Author(s):  
Violeta Ivanova Mangourova ◽  
John Ringwood ◽  
Bruce Van Vliet
Keyword(s):  
Blood Pressure ◽  
Mathematical Model ◽  
Salt Intake ◽  
Blood Pressure Response ◽  
Pressure Response

Reservoir Characterization Constrained to Well-Test Data: A Field Example

2000 ◽  
Vol 3 (04) ◽  
pp. 325-334 ◽  
Author(s):  
J.L. Landa ◽  
R.N. Horne ◽  
M.M. Kamal ◽  
C.D. Jenkins
Keyword(s):  
Mathematical Model ◽  
Test Data ◽  
Pressure Response ◽  
Well Testing ◽  
Pressure Measurements ◽  
Well Test ◽  
Well Test Analysis ◽  
Test Analysis ◽  
Reservoir Description ◽  
Different Sources

Summary In this paper we present a method to integrate well test, production, shut-in pressure, log, core, and geological data to obtain a reservoir description for the Pagerungan field, offshore Indonesia. The method computes spatial distributions of permeability and porosity and generates a pressure response for comparison to field data. This technique produced a good match with well-test data from three wells and seven shut-in pressures. The permeability and porosity distributions also provide a reasonable explanation of the observed effects of a nearby aquifer on individual wells. As a final step, the method is compared to an alternate technique (object modeling) that models the reservoir as a two-dimensional channel. Introduction The Pagerungan field has been under commercial production since 1994. This field was chosen to test a method of integrating dynamic well data and reservoir description data because the reservoir has only produced single phase gas, one zone in the reservoir is responsible for most of the production, and good quality well-test, core, and log data are available for most wells. The method that was used to perform the inversion of the spatial distribution of permeability and porosity uses a parameter estimation technique that calculates the gradients of the calculated reservoir pressure response with respect to the permeability and porosity in each of the cells of a reservoir simulation grid. The method is a derivative of the gradient simulator1 approach and is described in Appendices A and B. The objective is to find sets of distributions of permeability and porosity such that the calculated response of the reservoir closely matches the pressure measurements. In addition, the distributions of permeability and porosity must satisfy certain constraints given by the geological model and by other information known about the reservoir. Statement of Theory and Definitions The process of obtaining a reservoir description involves using a great amount of data from different sources. It is generally agreed that a reservoir description will be more complete and reliable when it is the outcome of a process that can use the maximum possible number of data from different sources. This is usually referred to in the literature as "data Integration." Reservoir data can be classified as "static" or "dynamic" depending on their connection to the movement or flow of fluids in the reservoir. Data that have originated from geology, logs, core analysis, seismic and geostatistics can be generally classified as static; whereas the information originating from well testing and the production performance of the reservoir can be classified as dynamic. So far, most of the success in data integration has been obtained with static information. Remarkably, it has not yet become common to completely or systematically integrate dynamic data with static data. A number of researchers,2–5 are studying this problem at present. This work represents one step in that direction. Well Testing as a Tool for Reservoir Description. Traditional well-test analysis provides good insight into the average properties of the reservoir in the vicinity of a well. Well testing can also identify the major features of relatively simple reservoirs, such as faults, fractures, double porosity, channels, pinchouts, etc. in the near well area. The difficulties with this approach begin when it is necessary to use the well-test data on a larger scale, such as in the context of obtaining a reservoir description. One of the main reasons for these difficulties is that traditional well-test analysis handles transient pressure data collected at a single well at a time, and is restricted to a small time range. As a result, traditional well-test analysis does not make use of "pressure" events separated in historical time. The use of several single and multiple well tests to describe reservoir heterogeneity has been reported in the literature,6 however, this approach is not applied commonly because of the extensive efforts needed to obtain a reservoir description. The method presented in this paper uses a numerical model of the reservoir to overcome these shortcomings. It will be shown that pressure transients can be used effectively to infer reservoir properties at the scale of reservoir description. Well-test data, both complete tests and occasional spot pressure measurements, will be used to this effect. The well-test information allows us to infer properties close to the wells and, when combined with the shut-in pressures (spot pressure), boundary information and permeability-porosity correlations, provides the larger scale description. General Description of the Method The proposed method is similar to other parameter estimation methods and thus consists of the following major items: the mathematical model, the objective function and the minimization algorithm. Mathematical Model. Because of the complexity of the reservoir description, the reservoir response must be computed numerically. Therefore, the pressure response is found using a numerical simulator. The reservoir is discretized into blocks. The objective is to find a suitable permeability-porosity distribution so that values of these parameters can be assigned to each of the blocks.

scholarly journals Mathematical description of a bounded oil reservoir with a horizontal well

2021 ◽  
Vol 2 (1) ◽  
pp. 61-66
Author(s):  
T. N. Nzomo ◽  
S. E Adewole ◽  
K. O Awuor ◽  
D. O. Oyoo
Keyword(s):  
Mathematical Model ◽  
Pressure Distribution ◽  
Mathematical Description ◽  
Horizontal Well ◽  
Horizontal Wells ◽  
Pressure Response ◽  
Oil Reservoir ◽  
Late Time ◽  
State Flow ◽  
Reservoir Geometry

When horizontal wells are compared with verticals wells, their production is always higher. If their performance can be improved, they can even be more productive. Considering a horizontal well in a completely bounded oil reservoir, when the well has been producing for some time and the effect of the boundaries is evident on the flow, the pressure distribution can be approximated by considering the effects of the boundaries on the flow. Considering when a pseudosteady state flow is attained this study presents a mathematical model for approximating pressure distribution for late time for a horizontal well in an oil reservoir with sealed boundaries. We use appropriate Source and Green’s functions to develop the model. The model developed show that when the flow reaches all the boundaries a pseudosteady state flow is attained and thus pressure distribution is influenced by the oil reservoir geometry especially its width and length. Considering that the thickness of the oil reservoir will be small compared to the length of the well, the oil reservoir width and length will determine the pressure response. This will influence the flow period occurring. By considering all aspects of the flow, the model can be applied to approximate the pressure distribution for as long as the well can continue producing.

Effects of Non-Darcy Flow and Penetrating Ratio on Performance of Horizontal Wells With Multiple Fractures in a Tight Formation

2017 ◽  
Vol 140 (3) ◽  
Author(s):  
Feng Zhang ◽  
Daoyong Yang
Keyword(s):  
Mathematical Model ◽  
Pressure Drop ◽  
Flow Regime ◽  
Darcy Number ◽  
Pressure Response ◽  
Darcy Flow ◽  
Multiple Fractures ◽  
Linear Flow ◽  
Relative Minimum ◽  
Tight Formation

A novel slab source function has been formulated and successfully applied to examine effects of non-Darcy flow and penetrating ratio on performance of a horizontal well with multiple fractures in a tight formation. The Barree–Conway model is incorporated in the mathematical model to analyze non-Darcy flow behavior in the hydraulic fractures, while the pressure response under non-Darcy flow is determined by two dimensionless numbers (i.e., relative minimum permeability (kmr) and non-Darcy number (FND)). A semi-analytical method is then applied to solve the newly formulated mathematical model by discretizing the fracture into small segments. The newly developed function has been validated with numerical solution obtained from a reservoir simulator. Non-Darcy effect becomes more evident at a smaller relative minimum permeability (kmr < 0.05) and a larger non-Darcy number (FND > 10). The non-Darcy number is found to be more sensitive than the relative minimum permeability, resulting in a larger pressure drop even at a larger kmr. In addition, the non-Darcy flow is found to impose a significant impact on the early-stage bilinear/linear flow regime, resulting in an additional pressure drop that is similar to lowering the fracture conductivity. The pressure response can be classified into two categories by a penetrating ratio of 0.5. When the penetrating ratio is decreased, the early bilinear/linear flow regime occurs, followed by an early radial flow regime.

scholarly journals Determination and application of a reasonable drainage rate of coalbed methane in vertical wells in the single-phase flow stage

2021 ◽  
Vol 233 ◽  
pp. 01039
Author(s):  
Sen Yang ◽  
Xiaoming Ni ◽  
Xuebin Tan ◽  
Zheng Zhao ◽  
Peng Chen
Keyword(s):  
Mathematical Model ◽  
Pressure Drop ◽  
Coalbed Methane ◽  
Single Phase ◽  
Water Pressure ◽  
Phase Flow ◽  
Single Phase Flow ◽  
Vertical Wells ◽  
Drainage Rate ◽  
Flow Stage

The determination of a reasonable drainage rate of coalbed methane (CBM) in vertical wells in the single-phase flow stage can provide maximise the transmission of water pressure over distance. Based on the principle of effective stress and Darcy’s law, a mathematical model for dynamic changes of the permeability in the single-phase flow stage was established; on this basis, the relationship between permeability and threshold pressure gradient was experimentally attained; according to the linkage of changes of the transmission distance of water pressure, permeability, and pressure drop in the wellbore in the drainage process, a mathematical model for a reasonable reduction rate of the working fluid level in the single-phase flow stage taking the change of the permeability into account was established. The accuracy of the mathematical model was verified according to practical drainage data from CBM wells in Daning Block in Qinshui Basin, Shanxi Province, China. The results show that the rate of pressure drop decreases in a negative exponential manner with the increase of the drainage time. Different rates of pressure drop were required in coal reservoirs with different permeabilities; when keeping other conditions constant, the larger the permeability of coal reservoirs, the lower the threshold pressure gradient and the lower the rate of daily pressure drop. The research results provide a theoretical basis and reference for the reasonable drainage system in the single-phase flow stage.

scholarly journals Simulasi difusi dan adsorpsi matriks pada proses enhanced coalbed methane

2018 ◽  
Vol 12 (1) ◽  
pp. 173
Author(s):  
Ade Nurisman ◽  
Retno Gumilang Dewi ◽  
Ucok W.R. Siagian
Keyword(s):  
Mathematical Model ◽  
Co2 Emissions ◽  
Coalbed Methane ◽  
Carbon Capture ◽  
Co2 Storage ◽  
Carbon Capture And Storage ◽  
Co2 Injection ◽  
The Matrix ◽  
Enhanced Coalbed Methane ◽  
And Storage

Diffusion and matrix adsorption simulations in enhanced coalbed methane process. Carbon capture and storage (CCS) can be considered as one of climate change mitigation efforts, through capturing and injecting of CO2 in underground formations for reducing CO2 emissions. CO2 injection in coalbed methane (CBM) reservoir has potentially attracted for reducing CO2 emissions and enhancing coalbed methane (ECBM) recovery. Diffusion and sorption are phenomenon of gas in the matrix on CO2 injection in CBM reservoir. The objectives of the research are focused on understanding of diffusion and sorption of gas in the coal matrix with mathematical model and estimating of CO2 storage in coalbed and CH4 recovery. In this research, mathematical model is developed to describe the mechanism in the matrix on ECBM process. Mathematical model, which have been valid, is simulated in various variables, i.e. macroprosity (0.001, 0.005, and 0,01), pressure (1, 3, and 6 MPa), temperature (305, 423, and 573 K), and initial fraction of CO2 (0.05, 0.1, 0.3, and 0.5). The results of this research show that preferential sequestration of CO2 and preferential recovery of CH4 in the surface of micropore on macroporosity 0.001, pressure 1 MPa, temperature 305 K, and inital fraction CO2 0,5 conditions are 0.9936 and 0.0064.Keywords: carbon capture and storage (CCS), coalbed methane (CBM), ECBM, diffusion, adsorption Abstrak Carbon capture and storage (CCS) dapat dipertimbangkan sebagai salah satu upaya mitigasi perubahan iklim, yaitu dengan menangkap CO2 dan menginjeksikannya ke dalam formasi bawah permukaan. Injeksi CO2 pada lapangan coalbed methane (CBM) berpotensi mengurangi emisi CO2 dan meningkatkan produksi CBM (ECBM). Pada proses injeksi CO2 di lapangan CBM, fenomena yang terjadi di dalam matriks lapisan batubara (coalbed) adalah difusi dan adsorpsi. Penelitian ini bertujuan memahami fenomena difusi dan adsorpsi pada proses injeksi CO2 untuk ECBM melalui model matematika, dan memperkirakan potensi penyimpanan CO2 di dalam lapangan CBM dan potensi recovery CH4. Pada penelitian dilakukan pengembangan model matematika untuk menjelaskan fenomena di dalam matriks pada proses ECBM. Model matematika, yang telah valid, disimulasikan dengan memvariasikan beberapa variabel, yaitu makroporositas (0,001, 0,005, dan 0,01), tekanan (1, 3, dan 6 MPa), suhu (305, 423, dan 573 K), dan fraksi CO2 awal (0,05, 0,1, 0,3, dan 0,5). Hasil penelitian menunjukkan pada makroporositas 0,001, tekanan 1 Pa, suhu 305 K, dan fraksi CO2 awal 0,5, fraksi CO2 yang teradsorpsi pada permukaan mikropori bernilai 0,9936 dan sisa fraksi CH4 yang teradsorpsi pada permukaan mikropori bernilai 0,0064. Kata kunci: carbon capture and storage (CCS), coalbed methane (CBM), ECBM, difusi, adsorpsi

scholarly journals Simulation of parallel capacitance influence on the hydraulic system dynamics

2019 ◽  
Vol 213 ◽  
pp. 02016
Author(s):  
Dýrr Filip ◽  
Hružík Lumír ◽  
Bureček Adam ◽  
Brzezina Petr
Keyword(s):  
Mathematical Model ◽  
System Dynamics ◽  
Mathematical Simulation ◽  
Experimental Measurement ◽  
Hydraulic System ◽  
Stationary Flow ◽  
Pressure Response ◽  
Hydraulic Circuit

This paper covers with experimental measurement and mathematical simulation of parallel capacitance influence on pressure response for non-stationary flow. The hydraulic circuit for measuring required quantities, which are necessary to determine of parallel capacitance influence on the hydraulic system dynamics. A part of hydraulic system is a long pipe, in which the parallel capacitance created by hydraulic hose is connected. A non-stationary flow is caused by fast closing of the seat valve, which is situated at the end of long pipe. Mathematical model is realized and verified in Matlab SimScape Fluids software for this hydraulic system.

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