Flowing Material Balance Equation Research Articles

A Semi-Analytical Model for Production Prediction of Deep CBM Wells Considering Gas-Water Two-Phase Flow

The productivity prediction of deep coalbed methane (CBM) wells is significantly influenced by gas-water two-phase flow characteristics and seepage parameters of the fracture network. While numerical simulations offer a comprehensive approach, analytical models are favored for their faster and broader applicability. However, conventional analytical models often oversimplify the complex problem of two-phase seepage equations, leading to substantial errors in dynamic analysis outcomes. Addressing this shortcoming, we establish a gas-water two-phase productivity prediction model for deep CBM reservoirs. This model takes into account the two-phase flow characteristics within the reservoir and fracture network, as well as the stress sensitivity of the reservoir and fractures. Additionally, a modified trilinear flow model characterizes the fractured modification body. By integrating the flowing material balance equation with the Newton Iteration method, we gradually update the seepage model’s nonlinear parameters using the average formation pressure. We also linearize the gas-water two-phase model through successive iterations to derive a semi-analytical solution. The accuracy of the model was verified through comparison with commercial numerical simulation software results and field application. The model also enabled us to scrutinize the influence of reservoir and fracture network parameters on productivity. Our research findings suggest that the semi-analytical solution approach can efficiently address the nonlinear seepage problem of gas-water two-phase flow, enabling quick and accurate prediction of deep CBM well productivity. Moreover, appropriate fracture network parameters are paramount for enhancing the productivity of deep CBM wells. Lastly, during the development of deep CBM reservoirs, it is crucial to control the production pressure difference appropriately to minimize the stress sensitivity impact on production capacity.

Study on development methods of different types of gas wells in tight sandstone gas reservoirs

Reasonable production allocation of tight sandstone gas reservoirs is an important basis for efficient development of gas wells. Taking Block XX in Ordos Basin as an example, the modified flowing material balance equation was established considering the variation of gas viscosity and compression coefficient, the advantages and disadvantages of the method were discussed, and a reasonable production allocation process for gas wells was developed. The results show that: ① The commonly used flow material balance method ignores the change of natural gas compression coefficient, viscosity and deviation coefficient in the production process. The slope of the relationship curve between bottom hole pressure and cumulative production and the slope of the relationship curve between average formation pressure and cumulative production are not equal After considering this change. Compared with the results calculated by the material balance method, the results calculated by the flow material balance method are smaller. ② The production of 660 gas wells in the study area during stable production period is verified. Compared with the open flow method, the dynamic reserve allocation method is better, with an error of 0.06%. ③ The new method in this paper is used to allocate production for different types of gas wells. The cumulative production of different types of gas wells shows different degrees of increase. The I, II, III and IV types of gas wells increase by 32.26%, 30.29%, 23.58% and 25.07% respectively. This study provides technical support for dynamic reserve calculation and reasonable production allocation of gas wells in the study area, and has important guiding significance for the formulation of reasonable development plan and economic and efficient development of tight sandstone gas reservoirs.

A Semi-Analytical Model for Gas–Water Two-Phase Productivity Prediction of Carbonate Gas Reservoirs

The productivity prediction of gas wells in carbonate gas reservoirs is greatly affected by the characteristics of gas–water two-phase flow and fracture seepage parameters. Compared with numerical simulation, the productivity prediction based on the analytical model is fast and widely used, but the traditional analytical model is fairly simplified while dealing with the nonlinear problem of the two-phase seepage equation, leading to a large discrepancy in the results of dynamic analysis. To solve this problem, this paper considers the characteristics of gas–water two-phase flow in the reservoir and fracture, uses the dual-medium model to characterize the stress sensitivity of the fracture and reservoir, and establishes a gas–water two-phase productivity prediction model for carbonate gas reservoirs. Combining the flowing material balance equation with the Newton iteration method, the nonlinear parameters of the percolation model are updated step by step with the use of average formation pressure, and the gas–water two-phase model is linearized through successive iterations to obtain the semi-analytical solution of the model. The accuracy of the model was verified using a comparison with the results of commercial numerical simulation software and field application, the gas–water two-phase productivity prediction curve was obtained, and the influence of sensitive parameters on productivity was analyzed. The results show that: (1) the semi-analytical solution method can efficiently deal with the gas–water two-phase nonlinear seepage problem and obtain the productivity prediction curve of carbonate gas wells rapidly and (2) the water production of the carbonate gas reservoir seriously affects the productivity of gas wells. During the development process, the production pressure difference should be reasonably controlled to reduce the negative impact of stress sensitivity on productivity performance.

Study on reasonable production allocation method of tight sandstone gas reservoir—A case of XX block in ordos basin

Reasonable production allocation of tight sandstone gas reservoirs is an important basis for efficient development of wells. Combining multiple mathematical models, the modified flowing material balance equation was established considering the variation of viscosity and compressibility, and a reasonable production allocation process was developed. The results show that: ① The flow material balance method ignores the change of compressibility, viscosity and deviation coefficient in the calculation. Compared with the results calculated by the material balance method, the results of the flow material balance method are smaller. ② A modified flowing material balance method is established, verified by the production of 670 wells in the study area during stable period. Compared with the open flow rate method, the error of dynamic reserve allocation method is smaller, with an error of 0.07%. ③ When dynamic reserves are used to allocate production, the initial decline rate of wells is reduced by 74.65% on average, the production on stable period increases by 21.28%, and the time increases by 1.79%. This study provides support for dynamic reserve calculation and reasonable production allocation of gas wells in the study area, and has important guiding significance for the formulation of reasonable development plan and economic and efficient development of tight sandstone gas reservoirs.

A new approach to production data analysis of non-volumetric naturally fractured gas condensate reservoirs

A significant amount of hydrocarbon exists in naturally fractured formations. Due to the limitations of classical reservoir evaluation methods, the ongoing researches have focused on the analysis of production data to describe reservoir dynamic. Among the existing methods, the flowing material balance (FMB) technique brings a straightforward and accurate method of reserve estimation. Often, the same approach as the single porosity reservoirs are utilized for naturally fractured formations and fewer studies have been performed with the dual-porosity model. Regarding the importance of such reservoir types, the purpose of this study is to propose a new production data analysis approach by implication of a modified compressibility parameter to the conventional FMB equations to achieve an accurate estimation of initial gas in place and average reservoir pressure in non-volumetric naturally fractured gas condensate reservoir. In the current study, we applied the aquifer influence on reservoir performance in the FMB equation by a modified isothermal rock compressibility factor, without using complex multi-phase reservoir modeling. Due to inherent uncertainty associated with aquifer parameters, the production data analysis in this study proceeded in two phases. In the first phase with the assumption of known aquifer parameters, output data were obtained. In the second phase, based on the best-fitted aquifer parameters in advance, the impact of variation of aquifer input data on the validity of output results was studied using the Monte-Carlo simulation approach. To validate the proposed method, different simulation models with variable reservoir and fluid properties were defined and the results were compared against a commercial compositional simulator. The obtained results proved the accuracy of the proposed method. Therefore, applying the modified rock compressibility in the conventional FMB method would result in a simple yet accurate method that requires the least input data to estimate initial gas in place and average reservoir pressure.

Modified Flowing Material Balance Equation for Shale Gas Reservoirs

To determine original gas-in-place, this study establishes a flowing material balance equation based on the improved material balance equation for shale gas reservoirs. The method considers the free gas in the matrix and fracture, the dissolved gas in kerogen, and the pore volume occupied by adsorbed phase simultaneously, overcoming the problem of incomplete consideration in the earlier models. It also integrates the material balance method with the flowing material balance method to obtain the average formation pressure, eliminating the problem with the previous method where shutting down of wells was needed to monitor the formation pressure. The volume of the adsorbed gas on the ground is converted into volume of the adsorbed phase in the formation using the volume conservation method to characterize the pore volume occupied by the adsorbed phase, which solves the problem of the previous model that the adsorbed phase was neglected in the pore volume. The model proposed in this study is applied to the Fuling Shale Gas Field in southwest China and compared with other flowing material balance equations, and the results show that the single-well control area calculated by the model proposed in this study is closer to the real value, indicating that the calculations in this study are more accurate. Furthermore, the calculations show that the dissolved gas takes up a large fraction of the total reserves and cannot be ignored. The sensitivity analyses of critical parameters demonstrate that (a) the greater the porosity of the fracture, the greater the free gas storage; (b) the values of Langmuir volume and TOC can significantly affect the results of the reservoir calculation; and (c) the adsorbed phase occupies a smaller pore volume when the Langmuir volume is smaller, the Langmuir pressure is higher, or the adsorbed phase density is higher. The findings of this study can provide better understanding of the necessity to take into account the dissolved gas in the kerogen, the pore volume occupied by the adsorbed phase, and the fracture porosity when evaluating reserves. The method could be applied to the calculation of pressure, recovery of free gas phase and adsorbed phase, original gas-in-place, and production predictions, which could help for better guidance of reserve potential estimations and development strategies of shale gas reservoirs.

Modifying rock compressibility to analyze the production data of non-volumetric gas and gas condensate reservoirs

Production data analysis, particularly the flowing material balance method, has been used for many years as an efficient, practical, and significant method to obtain important reservoir parameters. Many studies have been done to develop the flowing material balance method in different types of reservoirs which in most of them, the main limitation is that the reservoir has been considered to be volumetric. Therefore, despite being widely used, this method has not been well developed for non-volumetric water drive reservoirs. In the present work, an extremely simple yet very accurate method was introduced to obtain an excellent estimation of average pressure and gas in place of non-volumetric dry gas and gas condensate reservoirs. In our proposed method, a modified rock compressibility parameter was presented to modify current flowing material balance equations which have been developed for volumetric dry gas and gas condensate reservoirs previously. Using the proposed compressibility, the modified flowing material balance equations can be used for non-volumetric dry gas and gas condensate reservoirs producing with constant bottomhole pressure during the boundary-dominated flow period. Moreover, the iterative procedures to estimate average pressure and gas in place of these kinds of reservoirs were presented in detailed steps. Also, the validity of the proposed flowing material balance equations was performed using a commercial numerical reservoir simulator. The obtained results prove the efficiency of the proposed method. Furthermore, due to the high amount of uncertainty in aquifer parameters, an uncertainty analysis has been performed on aquifer parameters using Monte-Carlo simulation. The results of the study indicated that the determination of appropriate aquifer parameters has a significant impact on the estimation of reservoir parameters which can be obtained using a combination of uncertainty analysis and the proposed flowing material balance technique.

Applicability of the flowing material balance method to heterogeneous reservoirs

The flowing material balance (FMB) method is widely used to evaluate geological reserves because it does not require shut-in wells and uses daily production data. The original FMB method is based on a homogeneous medium model, but the reservoir is often heterogeneous. In this study, FMB equations are derived for radial composite reservoirs and naturally fractured reservoirs, and the effect of reservoir parameters on the estimation of geological reserves is analyzed. The study found that in order to obtain accurate geological reserves, the average formation total compressibility should be used. Inappropriate total compressibility may cause significant errors. Finally, the proposed method is validated by a case study.

Modification of the Calculation Method for Dynamic Reserves in Tight Sandstone Gas Reservoirs.

The determination of dynamic reserves is important for tight sandstone gas reservoirs in production. Based on the geological and gas data of the Yan’an gas field, the influence of pressure on the properties of natural gas is studied by mathematical methods. At the same time, the modified flowing material balance equation is established considering the changes in gas viscosity and compressibility. The result shows that (1) the viscosity of natural gas increases rapidly with pressure; (2) the deviation factor decreases with pressure (P < 15 MPa) and then increases (P > 15 MPa) with temperature; (3) the compressibility decreases rapidly with pressure and increases with temperature; (4) compared with the results of the material balance method, the average error of the flowing material balance method is 33.95%, and the accuracy of the modified flowing material balance method is higher with an average error of 1.25%; and (5) a large change in the production will affect the accuracy of the modified flowing material balance method, especially a shut-in for a long time before the pressure drop production is calculated at a certain time, so data points that are relatively consistent should be selected as far as possible to calculate the dynamic reserves. The findings of this study can help in the accurate evaluation of dynamic reserves of the tight gas reservoir in the Yan’an gas field and are an important guide for the formulation of a rational plan for the gas reservoir and its economic and efficient development.

Research on optimal production distribution of tight sandstone gas reservoir

The determination of dynamic reserves is an important basis for rational production allocation. Based on the Yan’an Gas Field, the modified flowing material balance equation is established considering the changes of gas viscosity and compressibility. At the same time, a reasonable production allocation method for gas wells is developed. The result shows: ① μgCg decreases with pressure and increases with temperature. ② The error of the modified flowing material balance method is smaller compared with the flow material balance method, and the error is 1.25 %. ③ The great change of the production will affect the accuracy of the modified flow material balance method, especially the shut-in for a long time before the pressure drop production is calculated at a certain time, so the points with relatively constant should be selected as far as possible. ④ When the dynamic reserves are used for allocation, the initial decline rate decreases by 74.65 % on average, and the stable production period increases by 21.28 % and the stable production period increases by 1.79 % compared with the allocation method of open flow rate. ⑤ When there is a large error of dynamic reserves, it will lead to production deviation from the reasonable value. The findings of this study can help for the accurate evaluation of dynamic reserves and reasonable production allocation of tight gas wells in the Yan’an gas field, and is an important guide for the formulation of a rational plan for the gas reservoir and its economic and efficient development.

A transient two-phase flow model for production prediction of tight gas wells with fracturing fluid-induced formation damage

A major concern with hydraulic fracturing in tight formation is the fracturing fluid-induced formation damage (FFIFD) for the high capillary pressure and the presence of water-sensitive clays. Analytical and semi-analytical models are good choices for formation damage evaluation comparing to computationally expensive numerical simulations, particularly in early times when there is limited information about the formation properties. However, the effects of FFIFD and two-phase flow are not addressed in many analytical models. This paper presents a semi-analytical model for this problem with the consideration of both FFIFD and two-phase flow. First, the physical model and mathematical fundamentals of the model are presented. The triple-porosity model is modified to capture the formation damage caused by fracturing fluid. A low permeability fracturing fluid invasion layer (FFIL) is used to characterize leakoff caused clay swelling and polymer adsorption in the matrix pores, and two-phase flow is assumed in the fractures to capture the choking effects. The analytical solution is obtained in the Laplace domain, and a successive iteration is used to update the dynamic parameters by coupling the flowing material balance equations. Then, the commercial numerical simulator Eclipse is used to validate the precision of the semi-analytical model, and several synthetical cases are presented to study the effects of two-phase flow, and the permeability and width of FFIL on gas production rate. Finally, a field case is provided to test the application of the proposed model. The main contribution of this paper is the provision of a simple yet versatile semi-analytical model for production prediction and analysis with the consideration of fracture networks, FFIFD, and two-phase flow. It serves as a good tool for making production prediction and production data analysis for hydraulically fractured tight gas wells.

Production data analysis of gas reservoirs with edge aquifer drive: A semi-analytical approach

Production data analysis is proved to be an efficient reservoir engineering tool that can be utilized to estimate some important reservoir parameters including fluid in place and, average reservoir pressure. Among the available production data methods, flowing material balance is more popular. In spite of the development of this method for volumetric gas and, oil reservoirs over the past years, non-volumetric effect doesn't feature the equations. In this paper, modified flowing material balance equations are proposed for production data analysis of gas reservoirs subjected to finite-extended edge aquifer. The validity of the presented equations is performed using analytical solutions. For the development of analytical solutions, special simplifying assumptions are considered. To evaluate these assumptions, a comparison is performed using a commercial numerical reservoir simulator for some models with different rock and, fluid properties. Moreover, the introduced flowing material balance equation is combined with material balance equation in order to find a simple equation to calculate average reservoir pressure. Detailed steps are presented to determine gas in place of and, average reservoir pressure of this kind of reservoirs. Furthermore, for a better match between analytical and numerical outputs of gas flow rates, a correction coefficient is recommended which depends on the strength of aquifer.

Field trial of a modified DFIT (pump-in/flowback) designed to accelerate estimates of closure pressure, reservoir pressure and well productivity index

A problem with the conventional diagnostic fracture injection test (DFIT) design, which involves analysis of the pressure falloff after the pump is shut-off, is the long test times required to achieve closure pressure (pc), a proxy for minimum in-situ stress, and after-closure flow regimes that can be analyzed for reservoir pressure in (pr) and transmissibility.An alternative approach to DFIT implementation is to flowback the injected fluid immediately after the pump is shutdown. Historically this approach has been to accelerate closure only, but recently the authors have demonstrated that careful design of the flowback procedure can yield accelerated pc estimates and possibly reservoir information. The new DFIT is referred to as ‘DFIT-FBA’, where FBA refers to the flowback analysis component to the test. pc is estimated using a Cartesian plot of flowing pressure versus flowback time. pr is determined through flowback data flow regime identification. The well productivity index for the studied reservoir interval is derived using the flowing material balance method. With constraints applied on created fracture properties, reservoir permeability may be determined.The practical application of the DFIT-FBA method is demonstrated with a field trial performed in a western Canadian tight oil reservoir. The resulting DFIT-FBA data quality is excellent yielding both closure and reservoir pressures due to accurate flow rate measurement. Both pressure estimates are in excellent agreement with a conventional DFIT performed on the same zone in the same area, but were obtained in a fraction of the time. In addition, application of the flowing material balance equation to after-closure data yielded an estimate of well productivity index for the tested interval.The DFIT-FBA demonstrated herein allows estimation of properties of interest to completions and reservoir engineers in a fraction of the time of the conventional DFIT.

Methods for simultaneously evaluating reserve and permeability of undersaturated coalbed methane reservoirs using production data during the dewatering stage

In this work, a flowing material balance equation (FMBE) is established for undersaturated coalbed methane (CBM) reservoirs, which considers immobile free gas expansion effect at the dewatering stage. Based on the established FMBE, five straight-line methods are proposed to determine the control area, initial water reserve, initial free gas reserve, initial adsorbed gas reserve, original gas in place, as well as permeability at the same time. Subsequently, the proposed FMBE methods for undersaturated CBM reservoirs are validated against a reservoir simulation software with and without considering free gas expansion. Finally, the proposed methods are applied in a field case when considering free gas expansion effect. Validation cases show that the straight-line relationships for the proposed five FMBE methods are excellent, and good agreements are obtained among the actual reserves and permeabilities and those evaluated by the proposed five FMBE methods, indicating the proposed five FMBE methods are effective and rational for CBM reservoirs. Results show that a small amount of free gas will result in a great deviation in reserve evaluation; hence, the immobile free gas expansion effect should be considered when establishing the material balance equation of undersaturated CBM reservoirs at the dewatering stage.

A Semi-Analytical Method for Modeling Two-Phase Flow Behavior in Fractured Carbonate Oil Reservoirs

It is quite common for oil/gas two-phase flow in developing fractured carbonate oil reservoirs. Many analytical models proposed for black oil wells in fractured carbonate reservoirs are limited to single-phase flow cases and conventional methods have been the use of numerical simulations for this problem. In this approach, a novel semi-analytical method is proposed to integrate the complexities of phase change, pressure-dependent pressure-volume-temperature (PVT) properties, two-phase flow behavior, and stress-dependent fracture permeability characteristics. A dual-porosity, black oil model considering the phase change and two-phase flow is applied to model the fractured carbonate reservoirs. To linearize the model, only flow equations of oil phase are used to develop the mathematical model. Nonlinear parameters and producing gas–oil ratio (GOR) are updated with coupled flowing material balance equations, followed by a novel proposed procedure for history matching of field production data and making forecasts. The semi-analytical method is validated with a commercial simulator Eclipse. The results show that both of the production rate curves of oil and gas phase using the proposed model coincide with the numerical simulator. The results also show that the effects of pressure-dependent fracture permeability, fracture porosity, and exterior boundary on production rate are significant. Stress sensitivity influences production rate during the whole process, reducing the cumulative production. Fracture porosity influences production rate during the intermediate flow periods. The exterior boundary affects production rate mainly in the early and intermediate production periods. Finally, a field example from the eastern Pre-Caspian basin is used to demonstrate the practicability of the method. Acceptable history match is achieved and the interpreted parameters are all reasonable.

A novel method for interpreting water data during flowback and early-time production of multi-fractured horizontal wells in shale reservoirs

In recent years, analysis of flowback data has provided an early opportunity to evaluate key fracture parameters (e.g. fracture permeability and fracture volume) in unconventional reservoirs. A combination of diagnostic plots, straight-line methods and simulation model history-matching techniques have been used for this purpose. For many shale gas wells, immediate gas and water production occurs on flowback. In this paper, a novel method is developed and demonstrated for analysis of water data during two-phase (gas + water) flowback and early-time production of shale gas wells.In previous studies, it has been demonstrated that, during the late-time water flow period, the water phase exhibits boundary-dominated flow (BDF) characteristics due to the limited volume of water in fractures or surrounding matrix. The gas phase exhibits transient linear flow (TLF) characteristics within matrix, which is one of the first flow-regimes typically observed after flowback during online production. By introducing a new pseudotime with a modified total compressibility, the water flow equation during two-phase (gas + water) flow period is linearized. Accordingly, a modified flowing material balance (FMB) equation is developed for analyzing water boundary-dominated flow which considers water relativity permeability and the saturation- and pressure-dependent total compressibility. Thus, a novel method is developed by combination of the water FMB equation and an iteration technique, to estimate the facture half-length and fracture permeability during flowback of shale gas wells.The approach is validated using several numerically-simulated cases. Results show that the accuracy of the new method is influenced by the pressure and saturation gradient in the fracture. With an increase in fracture permeability, the calculated fracture parameters become very close to the expected values. The calculated fracture half-length starts to deviate from the expected values with an increase in fracture half-length. However, the derived fracture permeability values are in excellent agreement for all cases studied. The matrix permeability has little effect on the calculated fracture parameters (half-length and permeability). Although there are some deviations between the interpreted and excepted values, both the values generally agree within 5%.Finally, practical application of the method is demonstrated using a Marcellus Shale well in northeast US north-east and a Changning Shale well in southwest China. The new techniques demonstrate the importance of accounting for phase relative permeability and correcting total compressibility, even when the gas phase dominates the flowback period.

A Semi-Analytical Method for Simulating Two-Phase Flow Performance of Horizontal Volatile Oil Wells in Fractured Carbonate Reservoirs

Two-phase flow behavior in fractured carbonate reservoirs was investigated due to the importance for geothermal and petroleum resource recovery, such as in this study the phase change of volatile oil. This paper presents a semi-analytical method for accurately modeling two-phase flow behavior and quickly predicting the production performance. The fractured carbonate reservoir was modeled with a dual-porosity model, and the phase change and two-phase flow were modeled using the black oil model. The production of the oil phase was obtained through linearizing and solving the mathematical model. The gas phase production was forecast using the producing gas-oil ratio (GOR), calculated using flowing material balance equations. By comparing the semi-analytical solution to the solution of the commercial numerical simulator and applying it to a field case, the accuracy and practicability of the proposed semi-analytical method could be validated. Based on the semi-analytical model, the influences of several critical parameters on production performance were also analyzed. The proposed model was shown to be efficient in evaluating two-phase production performance of horizontal volatile oil wells. Furthermore, the new technique is able to serve as a useful tool for analyzing two-phase production data and making forecasts for volatile oil wells in fractured carbonate reservoirs.

Determination of pore compressibility and geological reserves using a new form of the flowing material balance method

Pore compressibility is an important parameter in reservoir engineering. However, its variation from laboratory core analysis or logging data can be large. Moreover, laboratory core analysis cannot identify the influence of macroscopic fractures on pore compressibility. The geological reserves obtained with the commonly used flowing material balance (FMB) method are significantly impacted by the accuracy of the pore compressibility. Therefore, a new form of the FMB method is proposed in this study which can determine the pore compressibility and geological reserves at the same time. For gas wells, the new method uses the material balance equation and the FMB equation including the pore compressibility. For oil wells, new forms of the material balance equation and the FMB equation were established which have the same form as the corresponding equations for gas wells. A new linear expression of the material balance equation is employed for the analysis. Simulation results indicate that the new method can provide more precise predictions of both the pore compressibility and the geological reserves. Furthermore, the new method also considers the influence of formation fractures because it uses well production data. Sensitivity analysis indicates that the error in the pore compressibility has a significant influence on the determination of the geological reserves.

The modified gas-water two phase version flowing material balance equation for low permeability CBM reservoirs

The flowing material balance (FMB) equation is a frequently-utilized engineering tool to extract reservoir information according to production performance of producing wells. At present, it is still significantly challenging to adapt the FMB equation to CBM reservoirs due to the existence of gas-water two phase flow, stress dependence, matrix shrinkage and gas desorption. With all my respect to previous FMB equations for CBM reservoirs, a great deal of attention has been drawn to the single water/gas flow, which can only be applied for early production stage or cannot capture the gas-water two phase flow features of general CBM reservoirs. The most recent and comprehensive research effort of FMB equation for CBM reservoirs is performed by Clarkson and Salmachi (2017), which takes the aforementioned characteristics into account. However, suffering the limitation that the pressure-saturation relationship is not available, Clarkson and Salmachi (2017) assume the saturation and pressure gradients in coal seams are negligible, i.e., the relative permeability is not incorporated in the pseudo-pressure calculation, which will inevitably lead to large deviation compared with the precise results. Notably, during the depressurization development process of low-permeability CBM reservoirs, the pressure and saturation gradients are large enough and cannot be overlooked. Thus, a robust FMB equation for gas-water two phase flow in low-permeability CBM reservoirs is still lacking in the petroleum industry and is significantly necessary to be developed. In this study, the important pressure-saturation relationship is rigorously derived in terms of the conservation of mass and momentum equations, in which the gas desorption, matrix shrinkage and stress dependence are fully coupled. Next, the developed relationship is used to calculate the gas/water phase pseudo-pressure and subsequently the previous FMB equation for CBM reservoirs is modified. Finally, reliability of proposed FMB equation is successfully verified against the numerical simulation with excellent agreements compared with the input reservoir properties. In addition, with the intent of further solidifying the field applicability of the modified FMB equation, the production performance of an actual low-permeability CBM well in Hancheng field, China is analyzed through the proposed FMB equation and desirable interpretation results are achieved. Incorporating the pressure-saturation relationship for the first time, the modified FMB equation can serve as a practical and robust tool to extract valuable information regarding the low-permeability CBM reservoirs.

Rate-transient analysis of an undersaturated CBM reservoir in Australia: Accounting for effective permeability changes above and below desorption pressure

Rate-transient analysis (RTA) of coalbed methane (CBM) wells is an on-going reservoir engineering challenge because of the dynamic nature of coal reservoirs. During their lifetime, producing CBM wells completed in initially undersaturated reservoirs (flowing above desorption pressure) experience a change from single-phase water to two-phase (gas + water) production as desorption pressure is reached, and the production characteristics of these wells are affected by a multitude of dynamic CBM reservoir properties. Amongst the most important dynamic properties influencing production is absolute permeability of the natural fracture (cleat) network.Prolific coalbed methane wells in the Fairview Field, central Queensland, eastern Australia, exhibit stress-dependent permeability changes during early dewatering, followed by strong desorption-dependent permeability effects below desorption pressure. These effects, combined with the switch from single-phase to two-phase flow at desorption pressure, make quantitative production data analysis for reservoir properties (e.g. permeability and original gas-in-place) particularly challenging.In this study, a combination of flowing material balance (FMB) equations for gas and water, modified for dynamic changes in effective permeability, and analytical simulation is used to analyze a Fairview Field CBM well completed in coals of the Bandanna Formation using the cavitation technique. The subject well exhibits strong permeability changes for the first several years after desorption pressure is reached, after which permeability changes appear to occur more gradually. Single-phase water production data above desorption pressure is analyzed using an FMB method modified for stress-dependent permeability; gas production data below desorption pressure is analyzed using an FMB method modified to account for relative permeability and desorption-dependent permeability. Because of uncertainty in below-desorption pressure FMB model inputs, the FMB equations and analytical simulation are linked. This approach allows for a consistent, if not unique, analysis.The RTA approach outlined herein provides a reasonable starting point for more rigorous numerical simulation, which in turn can be used for reserves forecasting and development planning. Because of the multitude of reservoir properties (several of the key properties being dynamic) affecting the production characteristics of CBM wells such as those in the Fairview Field, it is important to advance RTA methods to constrain numerical model inputs.