Material Balance Pseudo-time Research Articles

Application of dynamic material balance to evaluate oil wells in Buzurgan oil field

The Material Balance Equation is a crucial tool utilized in reservoir studies to evaluate fluids and rock properties at static pressures. The Flowing and Dynamic Material Balance methods offer a significant advantage by avoiding the requirement to shut down wells, as they use flowing pressure instead of static pressure under constant or variable flow rates. The concept of "Dynamic Material Balance" involves converting the bottom hole flowing pressure at any point at any given time to the average reservoir pressure at that point. This allows for the use of classical material balance calculations and the development of classical material balance plots. In this study, the Dynamic Material Balance and Agrawal Type Curve techniques were used to estimate average reservoir pressures, initial hydrocarbon in place, and ultimate oil recovery for a well in the Mishrif reservoir, the main reservoir in the Buzurgan oil field. Many wells in this field experience problems such as high-pressure decline or continuous water production, necessitating ongoing evaluation. While the Dynamic Material Balance method focuses on boundary-dominated flow data, the Agrawal-type curve technique analyzes data from both transient and boundary flow periods. Agarwal decline curves were constructed using relationships of pseudo pressure normalized production, material balance pseudo time, and dimensionless variables in well-test analysis. The results from both methods showed comparable results with an absolute percentage error of (0.738) %, (3.07) %, and 5.7% for oil-in-place, drainage area, and average reservoir pressure, respectively. This strong correlation between the Dynamic Material Balance and Type Curve results indicates their accuracy and reliability.

Rate transient analysis methods for water-producing gas wells in tight reservoirs with mobile water

Tight gas reservoirs with mobile water exhibit multi-phase flow and high stress sensitivity. Accurately analyzing the reservoir and well parameters using conventional single-phase rate transient analysis methods proves challenging. This study introduces novel rate transient analysis methods incorporating evaluation processes based on the conventional flowing material balance method and the Blasingame type-curve method to examine fractured gas wells producing water. By positing a gas-water two-phase equivalent homogenous phase that considers characteristics of mobile water, gas, and high stress sensitivity, the conventional single-phase rate transient analysis methods can be applied by integrating the phase's characteristics and defining the phase's normalized parameters and material balance pseudo-time. The rate transient analysis methods based on the equivalent homogenous phase can be used to quantitatively assess the parameters of wells and gas reservoirs, such as original gas-in-place, fracture half-length, reservoir permeability, and well drainage radius. This facilitates the analysis of production dynamics of fractured wells and well-controlled areas, subsequently aiding in locating residual gas and guiding the configuration of well patterns. The specific evaluation processes are detailed. Additionally, a numerical simulation mechanism model was constructed to verify the reliability of the developed methods. The methods introduced have been successfully implemented in field water-producing gas wells within tight gas reservoirs containing mobile water.

Rate transient analysis of wells exhibiting two-phase (gas+water) flowing by use of pseudopressure-based approach

The primary focus of rate transient analysis (RTA) is put on the estimation of the reserves of gas/water reservoirs. RTA based on the single-phase assumption is limited to gas/water two-phase flow in the development of the material-balance time function. This work aims to propose a practical approach for analyzing production data from wells exhibiting gas/water two-phase flow during both infinite-acting flow (IAF) and boundary-dominated flow (BDF) periods. In this work, we present a comprehensive pseudopressure-based solution associated with the constitutive saturation/pressure (Sw/p) relationship. The pseudovariables, namely pseudopressure and β-factor, have the ability of handling the two-phase nonlinearities in the governing flow equations of gas and water phases and generating the required benchmark analytical solutions for liquid flow equation. By integrating the liquid-type solutions with the principle of Duhamel convolution, a set of gas/water-phase productivity equations are recast for wells producing at different operating conditions, including constant bottomhole-pressure, constant rate and steplike change in bottomhole-pressure/rate. The presented solutions provide a theoretical framework for developing two-phase RTA based on two-phase material-balance pseudotime (MBPT). The RTA method is validated against synthetic cases generated from numerical simulation, and the dependability of two-phase MBPT is also corroborated in detail. A field case example is analyzed to demonstrate the practical applicability of this method. The RTA method provided herein accounts for all flowing phases in the reservoir, and serve as an alternative to numerical model history matching for estimating original gas in place (OGIP) and original water in place (OWIP).

An Optimization-Based Method for the Explicit Production Data Analysis of Gas Wells

This work aims at the exploration of production data analysis (PDA) methods without iterations. It can overcome limitations of the advanced type curve analysis relying on the iterative calculation of material-balance pseudotime and current explicit methods reckoning on specific production schedule assumptions. The dynamic material balance equation (DMBE) is strictly proved by the integral variable substitution based on the gas flow equation under the boundary dominated flow (BDF) condition and the static material balance equation (SMBE) of a gas reservoir. We introduce the pseudopressure level functionγ(p) and the recovery factor functionR(p) to rewrite the DMBE in terms of observed variableYand estimated variableYe; then the PDA can be transformed into an optimization problem of minimizing the error betweenYandYe. An optimization-based method for the explicit production data analysis of gas wells (OBM-EPDA), therefore, is developed in the paper, capable of determining the BDF constant and gas reserves explicitly and accurately for variable rate and/or variable flowing pressure systems. Three stimulated cases demonstrate the applicability and validity of OBM-EPDA with small errors less than 1% for estimated values of both reserves andY. Not second to previous studies, the field case analysis further proves its practicability. It is shown that the nonlinear relation ofγtoRcan be represented by a polynomial function merely dependent on the inherent properties of the gas production system even before sorting out the production data. The errors of observed variableYprovided by OBM-EPDA facilitate the data quality control, and the elimination of outliers not subject to the BDF condition improves the reliability of the analysis. For various gas systems producing whether at a constant rate, a constant bottomhole pressure (BHP), or under variable rate and variable BHP conditions, the proposed method gives insights into the well-controlled volume and production capacity of the gas well whether in a low-pressure or high-pressure gas reservoir, where the compressibilities of rock and bound water are considered.

An Analytical Method for Parameter Interpretation of Fracture Networks in Shale Gas Reservoirs considering Uneven Support of Fractures

In shale gas reservoirs, the production data analysis method is widely used to invert reservoir and fracture parameter, and productivity prediction. Compared with numerical models and semianalytical models, which have high computational cost, the analytical model is mostly used in the production data analysis method to characterize the complex fracture network formed after fracturing. However, most of the current calculation models ignore the uneven support of fractures, and most of them use a single supported fracture model to describe the flow characteristics, which magnifies the role of supported fracture to a certain extent. Therefore, in this study, firstly, the fractures are divided into supported fractures and unsupported fractures. According to the near-well supported fractures and far-well unsupported fractures, the SRV zone is divided into outer SRV and inner SRV. The four areas are characterized by different seepage models, and the analytical solutions of the models are obtained by Laplace transform and inverse transform. Secondly, the material balance pseudotime is introduced to process the production data under the conditions of variable production and variable pressure. The double logarithmic curves of normalized production rate, rate integration, the derivative of the integration, and material balance pseudotime are established, and the parameters are interpreted by fitting the theoretical curve to the measured data. Then, the accuracy of the method is verified by comparison the parameter interpretation results with well test results, and the influence of parameters such as the half-length and permeability of supported and unsupported fractures on gas production is analyzed. Finally, the proposed method is applied to four field cases in southwest China. This paper mainly establishes an analytical method for parameter interpretation after hydraulic fracturing based on the production data analysis method considering the uneven support of fractures, which is of great significance for understanding the mechanism of fracturing stimulation, optimization of fracturing parameters, and gas production forecast.

Two deterministic methodologies for estimation of OGIP by production dynamics diagnostic of gas-condensate reservoir

This study presents two independent methodologies for estimation of original gas in place (OGIP) by production dynamics diagnostic of gas-condensate reservoir with no-flow outer boundary based on black-oil concept. Classic Blasingame decline-type curves are also extended to apply in gas-condensate reservoir to calculate kh . Both numerically simulated case and field data are used to demonstrate the applicability and validity of proposed methodologies. One method develops a novel analytical model to obtain average reservoir pressure, OGIP and Diatz shape factor at the same time by coupling flow equation of gas-condensate reservoir for boundary dominated flow (BDF) and general material balance equation (GMBE). The two-phase variable-rate flow equation at late time for BDF is clearly and concisely derived in this study in terms of defined two-phase pseodopressure and two-phase material balance pseudotime. In addition, another innovative, simple and effective method for estimation of OGIP is proposed in this study requiring input data of only cumulative production of well and reservoir fluid PVT characteristics of Constant Volume Depletion (CVD) experiment. The fundamental concept of this method suggests that transient cumulative production GOR is determined by only current gas recovery degree and fluid PVT characteristics of the reservoir. Due to the accurate, simple and relaxed data-requiring nature of this method, widespread use in field to estimate OGIP of gas-condensate reservoir is potentially encouraging. On the contrary, if OGIP is already known, an intermediate equation of the method can also be applied to check accuracy of CVD experiment results from laboratory. The first methodology extends OGIP estimation to gas-condensate reservoir from Blasingame and Lee (1988)’s method for dry-gas reservoir. Often used two-phase z factor, which is inconvenient to evaluate and easy to yield error, for gas-condensate reservoir in material balance equation is avoided in this methodology by applying more analytical and accurate Walsh et al. (1994)’s GMBE instead. The second methodology, to the authors’ knowledge, is the first proposed allowing OGIP estimation of gas condensate reservoir without requiring bottom hole flowing pressure (BHFP), pressure tests and complex calculation.

Deviations from transient linear flow behavior: A systematic investigation of possible controls on abnormal reservoir signatures

Observed deviations from classical diffusion (specifically transient linear flow, TLF) for Permian Basin Wolfcamp shale oil wells have been historically attributed to reservoir geometric heterogeneity and consequent anomalous diffusion (AD). Recently, we have suggested that the combination of multiphase flow and variable operating conditions could create similar reservoir signatures (as quantified using classic flow-regime identification techniques). However, there are additional factors, not previously investigated, that could be affecting flow-regime identification (ID). This work aims to systematically investigate all possible causes of deviations from classical diffusion behavior. A general, new semi-analytical oil flow solution is proposed that explicitly accounts for multi-phase flow, stress-sensitive reservoir properties, and variable operational conditions. This is achieved through using the combination of modified oil-phase pseudo-pressure and material balance pseudo-time. Additionally, reservoir geometric heterogeneity and AD are incorporated into the exponent of the power-law relationship between rate-normalized oil-phase pseudo-pressure and material balance pseudo-time. A new workflow is also developed to improve flow regime ID while various reservoir complex behaviors are occurring simultaneously. Using the new workflow, a comprehensive investigation into which parameters are primarily causing deviations from TLF is performed in use of simulated cases with inputs that are similar to those used to history-match a Wolfcamp shale well. Further, errors in the determination of reservoir and fracture properties caused by misdiagnosis of the flow regime are analyzed. Our extensive investigations demonstrate that: 1) multi-phase flow, and in particular the appearance of gas flow (producing gas-oil-ratio ramps up) as flowing bottomhole pressure (FBHP) drops below the bubble point pressure, has the biggest impact on the deviation from TLF; 2) even for cases with high producing water-oil-ratio, water production has relatively minor effects; 3) pressure-dependent permeability has relatively small effects, even for cases when well FBHP changes strongly; 4) deviations from TLF in a Wolfcamp shale oil example may be primarily caused by the combination of multiphase flow and variable FBHP, while the AD effect is likely secondary. Importantly, if log-log flow-regime identification plots are not corrected for complex reservoir behaviors, the reservoir flow regime may become distorted, leading to the selection of incorrect models for production analysis and errors in reservoir/fracture properties estimates.

Comparison of the Methods for Analyzing Rate- and Pressure-Transient Data from Multistage Hydraulically Fractured Unconventional Gas Reservoirs

Summary In this study, we provide a detailed review and comparison of the various graphical methods, available in the literature, to interpret/analyze rate- and pressure-transient data acquired from multistage hydraulically fractured horizontal wells (MHFHWs) completed in unconventional gas reservoirs. The methods reviewed in this study do not address complex transport mechanisms and complex fracture networks, but do address transient matrix linear flow (Ibrahim and Wattenbarger 2006; Nobakht and Clarkson 2012a, 2012b; Chen and Raghavan 2013) and boundary-dominated flow (BDF). The methods for BDF are the contacted-volume methods based on the ending times of linear flow (Wattenbarger et al. 1998; Behmanesh et al. 2015) and the flowing material-balance (FMB) methods. The Agarwal-Gardner FMB method (Agarwal et al. 1999) and the conventional FMB method involve plotting rate-normalized pseudopressure vs. material-balance pseudotime. We delineate the advantages and limitations associated with each method and identify the best methods of interpretation and analysis. Three different production modes—constant rate (CR), constant bottomhole pressure (BHP) (CBHP), and variable-rate BHP—are considered. For comparison, various synthetic test data sets generated from a high-resolution spectral gas simulator, which treats nonlinear gas flow rigorously and accurately to simulate rate-transient data, is used. Both synthetic noise-free and noisy-rate pressure-data sets considering wide ranges of initial reservoir pressure and BHP, as well as real-field data sets, are used to compare the methods. For linear flow, the Nobakht-Clarkson method (Nobakht and Clarkson 2012a, 2012b) yields the best results, although its use is tedious because it requires an iterative procedure. The Chen and Raghavan (2013) method for linear flow seems to provide results that are comparable with the Nobakht-Clarkson method (Nobakht and Clarkson 2012b) but does not require an iterative procedure. The Ibrahim-Wattenbarger method (Ibrahim and Wattenbarger 2006) for linear-flow analysis always overestimates flow capacity compared with the other methods. Among the methods that discuss the ending time of linear flow, it was found that the unit-impulse method from Behmanesh et al. (2015) provides the best results for predicting gas in place. For BDF, the results show that the Agarwal-Gardner FMB method (Agarwal et al. 1999) is quite vulnerable to the error in rate/pressure data, whereas the conventional FMB method is more robust to noise and provides more accurate estimates of gas in place.

A New Straight-Line Analysis Method for Estimating Fracture/Reservoir Properties Using Dynamic Fluid-in-Place Calculations

SummaryStraight-line analysis (SLA) methods, which are a subgroup of model-based techniques used for rate-transient analysis (RTA), have proved to be immensely useful for evaluating unconventional reservoirs. Transient data can be analyzed using SLA methods to extract reservoir/hydraulic-fracture information, whereas boundary-dominated-flow (BDF) data can be interpreted for fluid-in-place estimates. Because transient-flow periods might be extensive, it is also advantageous to evaluate the volume of hydrocarbons in place contacted over time to assist with reserves assessment. The new SLA method introduced herein enables reservoir/fracture properties and contacted fluid in place (CFIP) to be estimated from the same plot, which is an advantage over traditional SLA techniques.The new SLA method uses the Agarwal (2010) approach for CFIP estimation, extended to variable-rate/pressure data for low-permeability (unconventional) reservoirs. A log-log plot of CFIP vs. material-balance time (for liquids) or material-balance pseudotime (for gas) is created, which typically exhibits power-law behavior during transient flow, and reaches a constant value [original fluid in place (OFIP)] during BDF. Although CFIP calculations do not assume a flow geometry, the SLA method requires this to extract reservoir/fracture information. Herein, transient linear flow (TLF) is assumed and used for the SLA-method derivation, which allows the linear-flow parameter (LFP) to be extracted from the y-intercept (at material-balance time or material-balance pseudotime = 1 day) of a straight-line fit through transient data. OFIP can also be obtained from the stabilization level of the CFIP plot.Validation of the new SLA method for an undersaturated oil case is performed through application to synthetic data generated with an analytical model. The new SLA results in estimates of LFP and OFIP that are in excellent agreement with model input (within 2%). Further, the results are consistent with the traditional SLA methods used to estimate the LFP (e.g., the square-root-of-time plot) and the OFIP (e.g., the flowing material-balance plot).Practical application of the new SLA method is demonstrated using field cases and experimental data. Field cases studied include online oil production from a multifractured horizontal well (MFHW) completed in a tight oil reservoir, and flowback water production from a second MFHW, also completed in a tight oil reservoir. Experimental (gas) data generated using a recently introduced RTA core-analysis technique were also analyzed using the new SLA method. In all cases, the new SLA-method results are in excellent agreement with traditional SLA methods.The new SLA method introduced herein is an easy to apply, fully analytical RTA technique that can be used for both reservoir/fracture characterization and hydrocarbon-in-place assessment. This method should provide important, complementary information to traditionally used methods, such as square-root-of-time and flowing material-balance plots, which are commonly used by reservoir engineers for evaluating unconventional reservoirs.The method is currently limited to cases exhibiting single-phase flow, the flow-regime sequence of TLF to BDF, and reservoir homogeneity. In future work, these limitations will be resolved.

Field Applications of Constrained Multiwell Deconvolution

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 195516, “Field Applications of Constrained Multiwell Deconvolution,” by V. Jaffrezic, SPE, Total, K. Razminia, SPE, Imperial College, J. Cumming, Durham University, and A.C. Gringarten, SPE, Imperial College, prepared for the 2019 SPE Europec featured at the 81st EAGE Annual Conference and Exhibition, London, 3–6 June. The paper has not been peer reviewed. This paper applies a new constrained multiwell deconvolution algorithm to two field cases: a gas reservoir with two producers and an oil reservoir with three producers and one injector. Responses given by the constrained multiwell deconvolution are compared with simulations from history-matched reservoir models. By extraction of well and interwell reservoir signatures, multiwell deconvolution, the theoretical background of which is discussed in detail in the complete paper, allows identification of compartmentalization or unanticipated heterogeneities very early in field life, making adjustments possible for field-development plans and future well locations. Introduction Permanent downhole pressure gauges are installed routinely in most new wells. In theory, they provide invaluable data for monitoring well productivity and formation pressure in real time and for calibrating the reservoir-simulation model. In practice, however, the resulting large data sets are usually underexploited, mainly because extraction of meaningful information from interfering wells with conventional well-test-analysis techniques is nearly impossible. Field Case 1 A sandstone dry gas reservoir has been developed with two horizontal wells (Wells 9 and 10) with lengths of approximately 400 m that are 1.6 km apart. The production data set spans 19,800 hours (approximately 2 years and 3 months). No datum correction was applied because the vertical distance between the pressure gauges in the two wells was only 10 m and the correction would be negligible. Data Selection. Because the field case involves dry gas, pressure was converted into single-phase normalized pseudopressure using pressure/volume/temperature data. Depletion is moderate, so use of material balance pseudotime to account for changes in gas properties was unnecessary. Pressure data to be used for multiwell deconvolution had to be selected with care. Flowing pressures are usually too noisy, so buildup data are preferred. Linearity is enforced by only considering buildups with similar pressure derivatives. If these differ at early times, because of changing wellbore and skin effects, a buildup of reference is selected, with elimination of early-time data in all other buildups. Derivatives of the selected buildups, however, may also differ at late times because of interference between wells. These late-time data must be kept because they contain information on interwell connectivity and are necessary to recover constant rate interference responses from multi-well deconvolution. Multiwell Algorithm Setup. The following parameters were selected for the deconvolution process: The first nodes of the well main responses were set at 0.01 hours. The derivative slopes before that time were considered a regression parameter with no constraint applied. The same procedure was used for the interference derivatives except that the first nodes were set at 0.1 hours. All deconvolved derivatives were constrained to converge to a unit slope straight line at late times because the two wells are in communication and the reservoir is closed. The deconvolved derivatives were extended by 1.5 log cycles beyond the test duration, and the constraint of convergence was applied from 22,000 hours. The interference derivatives were constrained to remain below the deconvolved derivatives of the individual wells. The initial pressure was considered a regression parameter with no constraint applied. As a result, the algorithm returned different initial pressure estimates for each well. Default weight parameters were used except for the curvature, where a weight of 0.001 was applied to the main responses and 0.005 to the interferences. These values were selected by trial and error to limit the contribution of the curvature constraint.

Blasingame decline analysis for variable rate/variable pressure drop: A multiple fractured horizontal well case in shale gas reservoirs

Advanced production decline analysis methods have become more economic and efficient options due to technical and time limitations of well-testing operations in shale gas reservoirs. By normalizing rate with material balance pseudo-time, Blasingame type decline analysis can be applied to variable rate/variable pressure drop system, making the methodology more widely applicable. Blasingame decline analysis of variable rate/variable pressure drop case for multi-fractured horizontal well (MFHW) in shale has been less investigated, because of multi-scale storage spaces and multi-flow mechanisms. This article presents a semi-analytical Blasingame decline analysis model incorporating multi-flow mechanisms with shale's modified material balance pseudo-time. Laplace transformation, point source function, numerical discrete method, perturbation method, and Gaussian elimination method were employed to solve the mathematical problem caused by multi-flow mechanisms. Besides, the material balance pseudo-time was modified by considering adsorption and desorption. In this study, a workflow to investigate the effects of properties of hydraulic fracture (fracture half-length, number of fractures and fracture spacing) and multi-flow mechanisms (diffusion and desorption) on production decline behaviors through diagnostic Blasingame type curves is proposed. The results indicate that productivity is greater with a larger scale of fracture treatment, and better desorption of adsorbed gas is also beneficial to production. The decline rates affected by the fracture treatment scale and supplement capacity show two opposite trends, which is caused by interference between the fractures and boundary, respectively. Except that the data in the diffusion early flow period do not match very well, because the use of diffusion coefficient as a constant, the good fitting results on the whole verifies the model's validity and reliability.

Production data analysis of gas condensate reservoirs using two-phase viscosity and two-phase compressibility

Due to the occurrence of multi-phase flow in gas condensate reservoirs, production data of such reservoirs cannot be accurately analyzed using single-phase, dry gas models. In this work, we established a new semi-analytical method for rate-transient analysis of gas condensate reservoirs producing during boundary-dominated flow. In particular, the single-phase flow assumption in the development of the material-balance pseudotime function for dry gas reservoirs is alleviated by incorporating two-phase viscosity and two-phase compressibility into a modified two-phase pseudotime function. Introducing the definition of two-phase pseudotime achieves the goal of (approximately) linearizing the governing diffusivity equation. Using the principle of superposition applied to the constant rate solution, this methodology is extended for wells with dynamic changes in well operating conditions (i.e. rates and pressures).Original gas-in-place (OGIP) can also be quantified through a specialized plotting technique. To validate the developed method, synthetic production data using fine grid compositional simulations for both lean and rich gas condensate fluids are analyzed. In all cases, the proposed approach provides reasonable estimates of simulator input reservoir properties (e.g. OGIP). The presented technique is successfully applied to the analysis of field cases. This work provides a practical and simple engineering workflow for production data analysis of conventional gas condensate reservoirs with multi-phase flow during boundary-dominated flow.

Decline curve analysis using rate normalized pseudo-cumulative function in a boundary dominated gas reservoir

This paper presents a new and mathematically rigorous method to analyze declining gas production and pressure data using type curve. This method incorporates the pseudo parameters such as pseudo-cumulative production, real gas pseudopressure and a new pseudotime function for the first time to analyze rate-time curve.The pseudotime function provides a convenient approach to handle variations in viscosity-compressibility values more rigorously with pressure since viscosity-compressibility ratio is a function of cumulative production.The proposed method is based on the use of the new material balance pseudotime (Ta), called the rate normalized pseudo-cumulative function. A new algorithm is presented to compute the gas-in-place, and reservoir properties such as permeability, reservoir drainage area, and the pseudosteady sate constant.This method is also capable to analyze the behavior of production data more rigorously for constant bottomhole pressure, variable rate/variable pressure drop, and strong depleted reservoir condition. The proposed method is a direct application of pseudosteady state relation that avoids iterations and extrapolation of data during analysis.Finally, detail analysis and interpretation strategies are presented for both simulated and field data. The results obtained are in good agreement with previously reported results. The proposed method is strictly valid for boundary-dominated flow regime in gas reservoirs.

Blasingame decline type curves with material balance pseudo-time modified for multi-fractured horizontal wells in shale gas reservoirs

Production decline analysis has been considered as a robust method to obtain the flow parameters, reservoir properties and original gas in place. Although advanced Blasingame production decline analysis methods for vertical wells, fractured wells and horizontal wells in conventional reservoirs are widely used, there is no Blasingame production decline type curves for multi-fractured horizontal wells (MFHW) with considering stimulated reservoir volume (SRV) in shale gas reservoirs yet. Compared with conventional gas reservoirs, multi-flow mechanisms (such as Darcy flow, diffusion and adsorption/desorption) and complex flow behaviors of MFHW exist in shale gas reservoirs, bringing a big challenge for analyzing the rate decline performance of the wells. Thus, in this paper based on the material balance equation in consideration of adsorption/desorption, the material balance pseudo-time of Blasingame decline type curves is modified so as to extend the theory of Blasingame production decline analysis to shale gas reservoirs. Considering the nonlinearity caused by gas desorption and diffusion, and the complex flow of MFHW, a numerical method is applied in this paper to obtain Blasingame type curves. Based on the perpendicular bisection (PEBI) grids, a numerical model considered SRV is developed and the solution is obtained using control volume finite element method and the fully implicit method. Further Blasingame type curve is validated by a simplify model, and Blasingame production decline type curves of the MFHW considering SRV in a shale gas reservoir are plotted through computer programming. Five flow regimes, including early formation linear flow, early radial flow, compound linear flow, the second radial flow and pseudo-steady flow, are recognized. Compared with the modified Blasingame type curves presented in this paper, the ones with traditional pseudo-time have a tendency to underestimate the value of normalized rate, normalized cumulative production, normalized integral derivative cumulative production and the reserve. The effects of relevant parameters including SRV radius, outer region radius, permeability in SRV region and outer region, Langmuir pressure, Langmuir volume and diffusion coefficient on type curves are analyzed as well. This work expands our understanding of a MFHW flow behaviors in shale gas reservoirs, which can be used to estimate with reservoir properties, SRV, and reserves in these types of reservoirs.

A new approach for analysis of production data from constant production rate wells in gas condensate reservoirs

Production data analysis provides key parameters to a series of reservoir engineering calculations such as reserve estimation, inflow performance calculations, and well production forecast. Although techniques of production data analysis for oil and dry gas reservoirs have advanced significantly over the past few decades, application of these techniques for analyzing production data of gas condensate reservoirs has not been fully studied despite its great practical importance. In this work, a simple yet accurate methodology is presented for reliable estimation of initial gas in place and average reservoir pressure in gas condensate reservoirs. We define new pseudopressure and material balance time functions suitable for gas condensate systems. According to our observations, a Cartesian plot of modified normalized pseudopressure versus modified material balance pseudotime of gas condensate production data yields three distinct regions. In this study we will show that the middle region is unusable and should be distinguished and removed from the analysis. The required input data are bottom hole flowing pressures, gas and condensate production rates, and constant volume depletion (CVD) test data. This study provides example analyses and establishes guidelines for the analysis and interpretation of long term production data in gas condensate reservoirs using developed Cartesian plot.

Gas-Production-Data Analysis of Variable-Pressure-Drawdown/Variable-Rate Systems: A Density-Based Approach

Summary This study demonstrates that production-data analysis of variable-bottomhole-flowing-pressure/variable-rate gas wells under boundary-dominated flow (BDF) is possible by use of a density-based approach. In this approach, governing equations are expressed in terms of density variables and dimensionless viscosity/compressibility ratios. Previously, the methodology was successfully used to derive rescaled exponential models for gas-rate-decline analysis of wells primarily producing at constant bottomhole pressure (Ayala and Ye 2013a, b; Ayala and Zhang 2013; Ye and Ayala 2013; Zhang and Ayala 2014). For the case of natural-gas systems experiencing BDF, gas-well-performance analysis has been made largely possible by invoking the concepts of pseudotime, normalized pseudotime, or material-balance pseudotime. The density-based methodology rigorously derived in this study, however, does not use any type of pseudotime calculations, even for variable-rate/variable-pressure-drawdown cases. The methodology enables straightforward original-gas-in-place calculations and gas-well-performance forecasting by means of type curves or straight-line analysis. A number of field and numerical case studies are presented to showcase the capabilities of the proposed approach.

Analytical modeling of flow behavior in non-volumetric reservoirs

Material balance has long been used in reservoir engineering practice as a simple yet powerful tool to determine the original hydrocarbon in place. Traditional material balance methods incorporate shut-in pressure data. However, adequate shut-in pressure data is not available in some reservoirs. Integration of time variable functions and pressure transient analysis into material balance equation (MBE) provides us the flowing material balance technique. Evaluation of the initial hydrocarbon and average reservoir pressure are typical findings of such methods. Although this method is widely used in oil and gas reservoirs, it has not been implemented in water drive reservoirs so far. The objective of this study is to develop a water drive model of dynamic MBE in oil and gas reservoirs. To do so, the average reservoir pressure and water influx are calculated by a newly proposed approach which is applicable for variable rate case as well. In order to incorporate the effect of water encroachment, a novel relationship is derived for material balance pseudo-time. Even though the concept is used practically in gas reservoirs, it has not been applied in oil reservoirs yet. A numerical model was also constructed to verify the presented approach. The findings revealed that there was a high agreement between analytical and numerical schemes. • The amount of water influx can be calculated through flowing wellbore pressure. • The verification of the proposed methodology for variable rate oil and gas reservoirs was accomplished. • A new definition of pseudo-time is introduced to compensate the “non-volumetric effect”. • The proposed model is applicable to either volumetric systems or non-volumetric systems.

A New Model for Modern Production-Decline Analysis of Gas/Condensate Reservoirs

Summary Modern production-decline analysis is a robust technique for analysis of production data from a well under variable operating conditions. It uses production rates and flowing pressures to provide reliable estimates of recoverable reserves and fluid in place. The mathematics behind this technique is similar to that of pressure-transient theory; however, the focus is different. It deals with long-term variable production data instead of short-term constant-rate transient data. Using modern decline analysis for two-phase-flow conditions (e.g., gas/condensate reservoirs) is under question because of the single-phase-flow assumption in the development of a "material-balance time" function. This is a time function that converts any decline (e.g., exponential decline) to harmonic decline to account for variable operating conditions. The purpose of this work is to develop a model to use the concepts of modern techniques for analyzing production data of single-porosity gas/condensate reservoirs. For this purpose, the governing flow equation is linearized, using appropriately defined pseudopressure and pseudotime functions. Then, the solution is obtained for constant-well-rate condition. This is followed by employing the superposition theorem to account for variable well pressure/rate conditions, resulting in definition of two-phase material-balance pseudotime. The solution developed here is coupled with an appropriate material-balance equation and used to estimate the average reservoir pressure and original gas in place from analyzing production data. The dependency of relative permeability on capillary number and non-Darcy flow is included in the formulation. Verification of the proposed method is obtained with the analysis of synthetic production data using a series of fine-grid compositional numerical simulations over a typical range of gas/condensate-reservoir parameters.

Type Curves for Dry CBM Reservoirs With Equilibrium Desorption

Abstract The purpose of this work is to model the single-phase radial gas flow in coalbed methane including equilibrium sorption phenomena in the coal matrix and Darcy flow in the natural fracture network. Considering a control volume, the gas desorption rate as a function of time and space is incorporated into the radial continuity equation as a source term. Using a Langmuir-type sorption isotherm, the gas desorption rate is determined at any radius of the reservoir. Introducing the definition of pseudo-pressure and pseudo-time, the resulting continuity equation is converted into the linearized diffusivity equation by modification of total gas compressibility. It is shown how the traditional definition of the material balance pseudo-time is modified for dry CBM reservoirs. With the help of these transformations, the traditional (PTA and RTA) type curves can be employed for analysis of production data of dry CBM reservoirs. The model developed here is validated against Fekete's numerical CBM simulator over a wide range of reservoir parameters. In addition, one set of field data from Horseshoe Canyon coals of the Western Canadian Sedimentary Basin is analyzed using the solution procedure presented in this paper. Introduction Coalbed methane (CBM) is natural gas produced from coal seams. Coal is both the source rock and the reservoir for methane production. The world total CBM resource potential is evaluated at about 143.2 trillion cubic metres(1). CBM reservoirs are naturally fractured reservoirs that are characterized by two distinct porosity systems including:micropores (matrix) with extremely low permeability andmacropores (natural fractures or cleats). Due to the small pore diameter of less than 10 Å, the coal matrix has a large internal surface area of 100 to 300 m(2)/g(2, 3). As a result, substantial quantities of gas can be adsorbed on the surface of the coal grains. Micropores are impermeable to gas and inaccessible to water. However, the desorbed gas can be transported through the primary porosity system by diffusion. The macropores act as a sink to the micropores and provide permeability to fluid flow. In porous media with larger pore size distributions, mass transfer is driven by pressure gradients, whereas in coal, mass transfer is driven by concentration gradients(4, 5). The diffusion through the micropores can be the result of three distinct mechanisms that may act individually or simultaneously(6):bulk diffusion, where molecule/molecule interactions dominate;Knudsen diffusion, where molecule/surface interactions dominate; andtwo-dimensional surface diffusion of the adsorbed gas layer. The steady state diffusion coefficient of methane for most coals is on the order of 10−4 to 10−5 cm(2)/s(6). These experimentally determined diffusion coefficients represent averaged values including the contributions of the bulk, Knudsen and surface diffusion processes. Diffusion effects can be quantified by determining a sorption time. The sorption time is equal to the time required to desorb 63.2% of the initial gas volume. It is determined from whole core canister desorption test. This time is related to fracture spacing and the diffusion coefficient(7). Gas production from the CBM reservoirs is controlled by a four-step process that includes: