Gas Reservoir Model Research Articles

Production decline analysis of shale gas based on a probability density distribution function

Abstract Production decline analysis is a simple and efficient method to forecast production dynamics of shale gas. The traditional Arps decline model is also widely used in the production decline analysis of shale gas, but an obvious error is often generated. Based on the Weibull and χ2 probability density distribution function, the monotonic decreasing production prediction equations of shale gas are established. It is deduced that recently, the widely used Duong model is essentially a Weibull probability density distribution model. Decline analysis results of production data from actual shale gas well and numerical simulations indicate that the fitting results of the Weibull (Duong) model and χ2 distribution model are better than the Arps model whose deviation of early data is large. For a shale gas reservoir with very low permeability, pressure conformance area is small and it is obviously influenced by fractures. Early shale gas production rate mainly contributed to by fractures declines quickly and the later production rate mainly contributed to by the matrix declines slowly over time. The production decline curve has obvious long-tail distribution characteristics and it is a better fit to the data with a χ2 distribution model. As for the increase of permeability, the fitting accuracy of the Weibull (Duong) model gradually becomes better than the χ2 distribution model. Research results provide theoretical guidance for choosing a reasonable production decline model of a shale gas reservoir with a different permeability.

A productivity prediction method for condensate gas reservoir

At present, multiphase flow productivity calculation requires many parameters, and most of them only consider oil and gas two-phase flow, which is complicated and limited. Therefore, a reasonable productivity formula of condensate gas reservoir with producing water is needed. The three-zone model of condensate gas reservoirs is generally applied to the physical model for inferring productivity. On this basis, an improved model is established, which includes that different seepage characteristics are considered for different zones. Moreover, the effects of inclined angle and water production on gas wells are regarded as pseudo-skin factors and additional-skin factors. In addition, Zone I considers the effects of high-speed nonDarcy effect(HSND), starting pressure gradient, stress sensitivity, inclined angle and water production; Zone II is the same way excepting starting pressure gradient and stress sensitivity ; Zone III only considers the effects of inclined angle and water production. As a result, a productivity equation with multiple factors for condensate gas wells is established. Through analysing cases and influences in H gas reservoir X1 well, the HSND, starting pressure gradient, stress sensitivity and water production have a negative impact on gas well productivity, but the inclined angle is opposite. Founded that the starting pressure gradient impacts on productivity is less than the HSND because of the limited radius of Zone I; the impact of the HSND on productivity increases with the decreasing of bottom hole pressure; the impact of water production on gas well productivity is much higher. When the angle is over 60°, the effect of gas

Application of Heterogeneous Composite Model with Consideration of Stress Sensitive in Low Permeability Gas Reservoir

Stress sensitivity is a key factor affecting the productivity of single wells in low permeability gas reservoirs. A well test model for heterogeneous composite gas reservoirs under the influence of stress-sensitive effects was established. Based on the theoretical model, the well test was designed by gradually increasing the pressure difference. The relationship between abnormal high pressure and reservoir stress sensitivity was analyzed. Theoretical research shows that stress sensitivity will cause permeability damage during the production process, and the pressure drop test curve shows that the physical properties of the reservoir have gradually deteriorated. The pressure recovery test curve shows that the physical properties of the reservoir are getting better. Field practice shows that stress sensitivity is related to the formation of abnormally high pressure in the formation without considering the micro-cracks in the formation. Stress-sensitive reservoirs are generally unbalanced and compacted due to overpressure, for fluid expansion/conduction overpressure in Ledong Area. For these reservoirs, there is almost no stress sensitivity. The research results have significance for guiding the design and data interpretation of stress-sensitive reservoir.

A Flow - Solid Coupling Permeability Model of Shale Gas Reservoir Based on Dual Media

The study of shale gas seepage mechanism can provide theoretical basis for the production capacity evaluation and prediction of shale gas reservoir. The shale gas permeability model is an important part of the theoretical research of shale gas seepage. In this paper, the spring system model is applied to the shale reservoir, and the shale reservoir is simplified as the ideal dual porosity medium model. By analyzing and considering the influence of adsorption layer, diffusion, seepage, matrix deformation and slippage, the dual porosity permeability model of shale gas under various factors is given. In addition, the model is compared with the Civan permeability model and permeability experiment to verify its rationality. The results show that the model proposed in this paper is reasonable and reliable. The model has certain theoretical and practical significance for perfecting the theory of shale gas seepage flow.

A non-isothermal wellbore model for high pressure high temperature natural gas reservoirs and its application in mitigating wax deposition

Correctly estimate pressure drop and temperature distribution along wellbore is crucial for completion design, production optimization and flow assurance in oil and gas well. In places where wax or paraffin deposits along the wellbore is a concern, a non-isothermal wellbore model is needed to analyze the risks of wellbore plugging under various operational/reservoir conditions and design mitigating approaches accordingly. In this study, a non-isothermal wellbore model for high pressure and high temperature (HPHT) natural gas reservoirs is proposed. The mathematical framework laid out in this article can also be used as a template for modeling gas injection in deep wells. Field cases are used to calibrate and validate the presented model, along with discussions on associated uncertainties. Matain well-head temperature above a desired level is critical for mitigating wax/paraffin deposition, and it is found that the most effective methods to minimize temperature drop along the wellbore are: increasing production rate by hydraulic fracturing; selecting an optimal tubing size and applying thermal insulation coating to the production tubing.

Fracability Evaluation of Shale of the Wufeng‐Longmaxi Formation in the Changning Area, Sichuan Basin

The fracturing technology for shale gas reservoir is the key to the development of shale gas industrialization. It makes much sense to study the mechanical properties and deformation characteristics of shale, due to its close relationship with the fracability of shale gas reservoir. This paper took marine shale in the Changning area, southern Sichuan Basin of China as the research object. Based on field profile and hand specimen observation, we analyzed the development of natural fractures and collected samples from Wufeng Formation and Longmaxi Formation. Combining with the indoor experiment, we investigated the macroscopic and microscopic structural features and the remarkable heterogeneity of shale samples. Then we illustrated the mechanics and deformation characteristics of shale, through uniaxial compression test and direct shear test. The shale has two types of fracture modes, which depend on the angular relation between loading direction and the bedding plane. Besides, the Wufeng shale has a higher value of brittleness index than the Longmaxi shale, which was calculated using two methods, mechanical parameters and mineral composition. Given the above results, we proposed a fracability evaluation model for shale gas reservoir using the analytic hierarchy process. Four influence factors, brittleness index, fracture toughness, natural fractures and cohesive force, are considered. Finally, under the control of normalized value and weight coefficient of each influence factor, the calculations results indicate that the fracability index of the Wufeng Formation is higher than that of the Longmaxi Formation in Changning area, southern Sichuan Basin.

Accumulation characteristics of CO2-bearing natural gas reservoir in Xudong area of Xujiaweizi fault depression

In the north of Songliao basin, some high CO2 gas reservoirs have been found while great breakthroughs have been made in hydrocarbon natural gas. Based on the analysis of the reservoir characteristics of CO2 gas reservoirs in Xudong area, this paper clarifies that the Yingcheng formation CO2 is inorganic gas, volcanic rock is the main reservoir, and establishes the differential accumulation model of CO2 gas reservoirs in the study area, which can also guide further research and exploration.

Pore characteristics and evolution of Wufeng–Longmaxi Fms shale gas reservoirs in the basin-margin transition zone of SE Chongqing

At present, researches on the pore evolution of shale reservoir and its evolution mechanism are still at such a groping stage that a consensus has not yet reached. Based on core analysis and thermal simulation experiments, the pore types, pore structures and pore-size change rules of shale gas reservoirs of Upper Ordovician Wufeng–Lower Silurian Longmaxi Fms in the southeastern (SE) Sichuan Basin and its basin-margin transition zone (hereinafter referred to as the basin-margin transition zone of SE Chongqing) were studied by means of argon ion polishing–scanning electron microscopy (SEM) and atomic force microscopy. Then, the evolution characteristics of organic pores were discussed, and the influence of associated minerals on pore evolution was analyzed. Finally, a pore evolution model for the shale gas reservoirs in this area was established. And the following research results were obtained. First, three types of reservoir spaces are mainly developed in the high-quality shale reservoirs of Wufeng–Longmaxi Fms in this area, including fracture, inorganic pore and organic pore. And the organic pores provide the primary reservoir space of shale gas, which can be divided into four categories, i.e., amorphous kerogen pores, structured kerogen pores, asphaltene pores and paleontology fossil pores. Second, organic contracted fractures are related to the contraction of organic matters, first appearing on one side of the organic matters and then becomes wider and wider with the increase of temperatures. Third, organic pores are mostly the “spongy” pores distributed densely inside the organic matters. When Ro is in the range of 1.56–3.50%, macropores and mesopores are dominant. And when Ro exceeds 3.50%, macropores decrease while mesopores and micropores increase. Fourth, the types of organic matters and the content of associated minerals (e.g. clay minerals, siliceous particles and pyrite) play an important role in the development of pores. In conclusion, the pore evolution law of Wufeng–Longmaxi shale in the basin-margin transition zone of SE Chongqing is that with the increase of burial depth, inorganic porosity decreases significantly, organic porosity increases first and then decreases, and the total porosity shows a change trend of decreasing first, then increasing and finally decreasing continuously.

An Efficient Method to Predict Compressibility Factor of Natural Gas Streams

The gas compressibility factor, also known as the deviation or Z-factor, is one of the most important parameters in the petroleum and chemical industries involving natural gas, as it is directly related to the density of a gas stream, hence its flow rate and isothermal compressibility. Obtaining accurate values of the Z-factor for gas mixtures of hydrocarbons is challenging due to the fact that natural gas is a multicomponent, non-ideal system. Traditionally, the process of estimating the Z-factor involved simple empirical correlations, which often yielded weak results either due to their limited accuracy or due to calculation convergence difficulties. The purpose of this study is to apply a hybrid modeling technique that combines the kernel ridge regression method, in the form of the recently developed Truncated Regularized Kernel Ridge Regression (TR-KRR) algorithm, in conjunction with a simple linear-quadratic interpolation scheme to estimate the Z-factor. The model is developed using a dataset consisting of 5616 data points taken directly from the Standing–Katz chart and validated using the ten-fold cross-validation technique. Results demonstrate an average absolute relative prediction error of 0.04%, whereas the maximum absolute and relative error at near critical conditions are less than 0.01 and 2%, respectively. Most importantly, the obtained results indicate smooth, physically sound predictions of gas compressibility. The developed model can be utilized for the direct calculation of the Z-factor of any hydrocarbon mixture, even in the presence of impurities, such as N 2 , CO 2 , and H 2 S, at a pressure and temperature range that fully covers all upstream operations and most of the downstream ones. The model accuracy combined with the guaranteed continuity of the Z-factor derivatives with respect to pressure and temperature renders it as the perfect tool to predict gas density in all petroleum engineering applications. Such applications include, but are not limited to, hydrocarbon reserves estimation, oil and gas reservoir modeling, fluid flow in the wellbore, the pipeline system, and the surface processing equipment.

Fuzzy Structure Element Method for Solving Fuzzy Trilinear Seepage Model of Shale Gas Reservoir

The seepage of shale gas reservoir is more complicated than that of the conventional energy because of its unique reservoir forming characteristics and physical properties. Accordingly, to achieve the large-scale exploitation of shale gas reservoir, the internal seepage characteristics of the reservoir should be clarified. Shale reservoirs are often accompanied by extreme heterogeneity and responsible variability. This phenomenon reveals that it is not reasonable to idealize the reservoir permeability as a fixed value. However, the conventional percolation model often idealizes the reservoir permeability to a specific amount. This will obviously lead to a reduction in the accuracy of the model. In the present study, the concept of fuzzy permeability was proposed. In other words, a fuzzy number was used to describe the reservoir permeability. Subsequently, the trilinear fuzzy seepage model was built and solved using the fuzzy structure element. To solve the practical application problem, a single numerical solution corresponding to the fuzzy solution set was found using the technique of defuzzification by the obtained fuzzy solution set. Finally, the fuzzy seepage model and the conventional seepage model were compared and analyzed by the numerical simulation.

Fluids discrimination by ray-path elastic impedance inversion: A successful case from Sulige tight gas field

Existing seismic prediction methods struggle to effectively discriminate between fluids in tight gas reservoirs, such as those in the Sulige gas field in the Ordos Basin, where porosity and permeability are extremely low and the relationship between gas and water is complicated. In this paper, we have proposed a comprehensive seismic fluid identification method that combines ray-path elastic impedance (REI) inversion with fluid substitution for tight reservoirs. This approach is grounded in geophysical theory, forward modeling, and real data applications. We used geophysics experiments in tight gas reservoirs to determine that Brie’s model is better suited to calculate the elastic parameters of mixed fluids than the conventional Wood’s model. This yielded a more reasonable and accurate fluid substitution model for tight gas reservoirs. We developed a forward model and carried out inversion of REI, which reduced the non-uniqueness problem that has plagued elastic impedance inversion in the angle domain. Our well logging forward model in the ray-path domain with different fluid saturations based on a fluid substitution model proved that REI identifies fluids more accurately when the ray parameters are large. The distribution of gas saturation can be distinguished from the crossplot of REI (p= 0.10) and porosity. The inverted ray-path elastic impedance profile was further used to predict the porosity and gas saturation profile. Our new method achieved good results in the application of 2D seismic data in the western Sulige gas field.

Reservoir-forming conditions and key exploration & development techniques for Xushen gas field in Northeast China

Exploration and development of volcanic gas reservoirs is a world-class problem, and less experience can be learned at home and abroad. Through study of reservoir-forming conditions of Xushen gas field, four sets of hydrocarbon source rocks, mainly mudstone and coal seam of Shahezi Formation, are identified in this gas field; its cap rocks are mudstone in Member 2 of Denglouku Formation, and Member 1 and Member 2 of Quantou Formation. By simulating reservoir-forming history, four filling periods of the Xushen gas field are determined, and the most favorable exploration targets are crater areas with structural highs, large thickness and good physical properties. On the basis of diagenetic mechanism study, the criteria of sequence series, lithology identification and reservoir types of gas reservoirs have been established; the volcanic rock bodies have been carefully depicted and the distribution laws of effective reservoirs of gas pools have been figured out. Based on evaluating reservoir-permeability characteristics of reservoirs, the gas well productivity characteristics (mainly type II, III and IV wells) have been identified, and the optimum design technology for volcanic gas reservoir development has been developed. The gas reservoirs in all blocks of Xushen gas field are classified into three types: single-body gas reservoir model, disconnected multi-body gas reservoir model and interconnected multi-body gas reservoir model. Stimulation technologies, including multi-layer fracturing of vertical well, staged fracturing of open-hole horizontal well and volume fracturing, have been developed. According to gas well production performance, pressure change, well-controlled reserves and spatial distribution of volcanic bodies, combined with numerical simulation and prediction of gas reservoirs, the evaluation method of residual potential of volcanic gas reservoirs has been formed. Key technologies for effective exploration and development of complex volcanic gas reservoirs have been established and perfected, and bring good development effect. The research results can provide guidance and reference for exploration and development of similar gas reservoirs.

Hydraulic Fracture Design with a Proxy Model for Unconventional Shale Gas Reservoir with Considering Feasibility Study

Shale gas is a natural gas trapped in shale formation and is being actively developed in North America. Due to the low permeability of a shale gas reservoir in the range from 10−8 to 10−6 Darcy, horizontal drilling and multi-stage hydraulic fracturing are needed for its development. This paper presents a fast and reliable proxy model to forecast shale gas productions and an optimum hydraulic fracturing design for its development. The proxy model uses a robust regression scheme and can replace a commercial reservoir simulator. The proxy model proposed can determine the influence of impact factors on the production at each production time. The calculation speed of the proposed proxy model is about 1.4 million times faster than that of a reservoir simulator compared. The most economical hydraulic fracture design using the proxy model has a length of 168 m at each stage, which is determined by examining a large number of hydraulic fracturing designs considering economic feasibility.

Single Fuzzy Parameter Seepage Model of Oil and Gas Reservoir

In the process of modeling, the reservoir permeability is often regarded as a certain value in the traditional flow model of oil and gas reservoir, but most reservoir areas are uneven and complex and so this idealization will lead to a great decrease in the accuracy of the model. Given this, this paper puts forward fuzzy permeability, which makes the model more in line with the seepage situation, and then improves the accuracy of the model. At the same time, the fuzzy function theory is studied deeply and systematically. On this basis, according to the seepage law and physical property of the oil and gas reservoir, the fuzzy seepage differential equation and the fuzzy boundary value condition of the reservoir are established. Then, the solution of the fuzzy seepage problem of the oil and gas reservoir is achieved. Compared with the traditional seepage model, the fuzzy seepage model can describe the flow in the reservoir more accurately. The definition of fuzzy permeability and the construction of fuzzy seepage equation provide a new method and a novel idea for studying the seepage of the reservoir.

A semi-analytical solution for hydraulically fractured vertical wells in tight gas reservoirs with fracture networks

Massive hydraulic fracturing technology is a key technology for efficient development of tight gas reservoirs. A complicated stimulated reservoir volume (SRV) is created around the wellbore and the major fracture. The fractures are essential to the recovery and performance of tight reservoirs wells. In this paper, a rectangular composite model of a tight gas reservoir was established to describe a fractured well with an SRV. The SRV is characterised by Warren-Root dual-porosity model. The solution is obtained by Green's and source functions. The well testing type curves are obtained by Stehfest's numerical inversion method. The transient gas flow regime and the sensitivity of variable parameters are analysed. Then, the transient production rate and cumulative production curves with different parameters of well-produced constant bottomhole pressure are plotted, and the corresponding parameters' sensitive analyses are done. The results show the seepage resistance was significantly decreased due to the existence of SRV. [Received: October 29, 2016; Accepted: August 10, 2017]

A new analysis model for heterogeneous shale gas reservoirs

In this paper, a new analysis model (MNH), which considers the interactions of flow regimes in matrix, natural fractures and hydraulic fractures, is developed for heterogeneous shale gas reservoirs. In this model, the gas flow in shale matrix is described by non-Darcy law and gas desorption is also considered. Gas flow in discrete natural fractures follows the cubic law in each fracture and these natural fractures are described by a discrete fracture model. An equivalent method is put forward to describe the flow regime in hydraulic fractures. This model is used to analyse the flow regimes of shale gas flow within a multi-stage fractured horizontal well. It also investigates the influences of gas desorption, fracture aperture, spacing and number on the gas production rate. The results show that the MNH model can provide insights into flow mechanisms and production prediction for a multi-stage fractured horizontal well in shale gas reservoirs. [Received: November 2, 2017; Accepted: June 19, 2018]

A new analysis model for heterogeneous shale gas reservoirs

A new analysis model for heterogeneous shale gas reservoirs

An Improved Theoretical Nonelectric Water Saturation Method for Organic Shale Reservoirs

The saturation of a shale gas reservoir is used to characterize the fluid content within the pores and to calculate the free gas content and reserves of the reservoir. Thus, accurately evaluating the saturation of a shale gas reservoir is of great significance. However, little research has been performed to quantitatively evaluate the saturation relative to other parameters used for evaluating the gas content. Moreover, because the conductive mechanism of shale gas reservoirs is very complex, the existing electric saturation model is insufficient. In this paper, based on the results of our analysis, we postulate that the organic pores in shale gas reservoirs are full of gas; furthermore, clastic pores also contain some gas. Thus, an improved model based on the original petrophysical model and the theory of shale density characteristics is proposed, and a calculation scheme based on the saturation model of shale gas reservoirs is deduced. The simulation results indicate that the improved model is less sensitive than the original model to changes in the total organic carbon content (TOC), and the water saturation calculated when the TOC is equal to 0 can be less than 100%, which is more consistent with the actual geological conditions of shale gas reservoirs. Because the saturation model incorporates an exceedingly large number of parameters, we propose the use of a genetic algorithm to automatically optimize those parameters. An evaluation of the Longmaxi formation-Wufeng formation shale gas reservoir in the Yongchuan block of the southern Sichuan Basin reveals that the optimized parameters are consistent with the geological conditions. The prediction accuracy of the proposed method is also higher than that of the original method, especially for the Wufeng formation, for which the number of samples is very small. Moreover, the absolute error is reduced by nearly 10%, which reflects a high accuracy. The proposed model can enhance accuracy through further improving the determination of shale gas reservoir characteristics and thus has the potential to be improved further. This method can also partially resolve problems by evaluating the saturation of shale gas reservoirs and hence could be helpful for core and well logging evaluations of the saturation, especially in overmature shales.

A numerical well model considering capillary end effect for the low-permeability gas reservoir

In the recovery of low permeability reservoir, the capillary pressure has an important effect, which may reduce gas production. Due to the capillary end effect, there are two flow patterns in the vicinity of the production well: both water and gas phases can flow into the production well and only gas phase can enter the production well. Based on the analytical equations of one-dimensional radial flow considering the capillary end effect, an alternative numerical well model for low permeability gas reservoir is constructed. Numerical examples show that the proposed model can reflect the dramatic change for saturation and gas-phase pressure in the vicinity of the production well both for two flow patterns, and therefore can predict the gas and water productions accurately at different grid scales. In contrast, the original Peaceman well model for multi-phase flow, which is directly extended from that for single-phase flow, only can provide good prediction under the condition of that the grid size is enough small. Especially, for the original Peaceman well model, this problem is out of control since it is difficult to estimate a suitable grid size.

A semi-analytical solution for hydraulically fractured vertical wells in tight gas reservoirs with fracture networks

Massive hydraulic fracturing technology is a key technology for efficient development of tight gas reservoirs. A complicated stimulated reservoir volume (SRV) is created around the wellbore and the major fracture. The fractures are essential to the recovery and performance of tight reservoirs wells. In this paper, a rectangular composite model of a tight gas reservoir was established to describe a fractured well with an SRV. The SRV is characterised by Warren-Root dual-porosity model. The solution is obtained by Green's and source functions. The well testing type curves are obtained by Stehfest's numerical inversion method. The transient gas flow regime and the sensitivity of variable parameters are analysed. Then, the transient production rate and cumulative production curves with different parameters of well-produced constant bottomhole pressure are plotted, and the corresponding parameters' sensitive analyses are done. The results show the seepage resistance was significantly decreased due to the existence of SRV. [Received: October 29, 2016; Accepted: August 10, 2017]