Numerical Solution of the Material Balance Equations of Compartmented Gas Reservoirs

1997 ◽  
Author(s):  
Jacques Hagoort ◽  
Rob Hoogstra
Keyword(s):  
Numerical Solution ◽  
Material Balance ◽  
Balance Equations ◽  
Gas Reservoirs

Numerical Solution of the Material Balance Equations of Compartmented Gas Reservoirs

1999 ◽  
Vol 2 (04) ◽  
pp. 385-392 ◽  
Author(s):  
Jacques Hagoort ◽  
Rob Hoogstra
Keyword(s):  
Numerical Solution ◽  
History Matching ◽  
Material Balance ◽  
Integral Form ◽  
Balance Method ◽  
Balance Equations ◽  
Gas Reservoirs ◽  
Balance Analysis ◽  
Material Balance Method ◽  
Gas Properties

Summary This paper presents a robust and rigorous method for the numerical solution of the material balance equations of compartmented gas reservoirs. The method is based on the integral form of the material balance equations and employs an implicit, iterative solution procedure. The proposed method enables extension of traditional p/z analysis of single gas reservoirs to complex, compartmented gas reservoirs. Example calculations of the depletion of a compartmented reservoir show how the p/z is affected by crossflow, reservoir size, and depletion rate. The depletion behavior can be rationalized by the observation that depletion of a compartmented reservoir at a constant rate tends to develop a semisteady state. A field example is presented that illustrates the capabilities of the extended material balance for the analysis of the past performance of compartmented reservoirs. Introduction Material balance analysis is a standard reservoir engineering tool for the analysis of the performance of oil and gas reservoirs. Applied to single, tank-type gas reservoirs, the material balance yields a characteristic relationship between the ratio of pressure to z factor (p/z) and cumulative gas production.1 In the ideal case of volumetric depletion, i.e., no changes in the hydrocarbon pore volume during depletion, this relation simplifies to a straight line. A relatively new development is the application of material balance analysis to more complex, compartmented reservoirs.2–5 A compartmented reservoir is defined here as a reservoir that consists of two or more distinct reservoirs that are in hydraulic communication. A well-known example is a faulted reservoir made up of different fault blocks separated by partially sealing faults. For the purpose of a material balance analysis, a compartmented reservoir may be modeled as an ensemble of individual tank-type reservoirs, which are connected to one another by thin permeable barriers.2 Each compartment is described by its own material balance, which is coupled to the material balance of neighboring compartments through influx or efflux of gas across the common boundaries. Application of the material balance method to compartmented reservoirs requires a fast, robust, and rigorous method for solving the system of coupled material balance equations. This is the subject of the paper. Hower and Collins2 presented analytical solutions of the material balance equations for a compartmented reservoir consisting of just two reservoirs. Their solutions hold good under rather restrictive conditions: constant offtake rate from only one reservoir compartment, volumetric depletion, and constant gas properties. Yet the analytical solutions clearly demonstrated the basic features of the depletion of compartmented reservoirs. Lord and Collins3 generalized the material balance method to multicompartment reservoirs. They solved the material balance equations numerically, without introducing any simplifying assumptions and conditions. They formulated the equations as a system of coupled first-order ordinary differential equations in the pressure. The solution of this system then boils down to numerically solving an initial value problem, for which the authors used the Burlisch-Stoer method. No details were presented on the implementation of this method. Lord et al.4 applied the extended material balance method to the compartmented gas reservoirs in the Frio formation in South Texas. Payne5 applied the multicompartment reservoir model to single, tight gas reservoirs. He solved the material balance equations by means of an explicit method, ignoring changes in the flow across boundaries and gas properties during a timestep. For the calculation of the crossflow between compartments, Payne used the pressure squared formulation. Payne's calculation method is simple and straightforward, and lends itself very well for implementation in a spreadsheet program. However, the explicit calculation scheme and the use of the pressure-squared approximation might give rise to unacceptable errors. In this paper, we present a simple but rigorous numerical method for the solution of the material balance equations for compartmented gas reservoirs. It is based on the integral form of the material balance equation for each individual compartment, expressed in cumulative quantities, instead of the differential form as used by Lord and Collins. The solution method employs an implicit calculation scheme that properly accounts for the pressure dependency of gas properties. For reasons of clarity and brevity, we restrict ourselves to gas reservoirs that consist of two compartments. However, the method can be readily generalized to multi-compartment reservoirs. To illustrate the method we present examples of a compartmented material balance analysis applied in both the prediction mode and in the history-matching mode. The prediction calculations bring out the depletion characteristics of a typical compartmented reservoir. In the history match example, we illustrate the use of the compartmented reservoir model for the analysis of the observed pressure behavior of a real-life compartmented reservoir. The main advantage of the numerical solution method presented here over previous work is its simplicity. The method can be easily incorporated into existing material balance analysis programs, thereby extending the classic "p over z" analysis to more complex, compartmented reservoir systems. In addition, because of its simplicity the method lends itself very well for automatic history matching of observed reservoir performance. The method is recommended for a first analysis of the performance of compartmented gas reservoirs. Depending on the results a more elaborate analysis may be required by means of a more sophisticated 3D, multigridblock reservoir simulator.

Improvements to Reservoir Material-Balance Methods

2002 ◽  
Vol 5 (01) ◽  
pp. 49-59 ◽  
Author(s):  
J.L. Pletcher
Keyword(s):  
Simulation Study ◽  
Diagnostic Tool ◽  
Material Balance ◽  
Correct Solution ◽  
Negative Slope ◽  
Reliable Estimate ◽  
Cole Plot ◽  
Gas Reservoirs ◽  
Balance Study ◽  
Balance Solution

Summary Experience with material-balance data sets from the field and from simulation has revealed some procedures that can be used to improve analysis of both oil and gas reservoirs:Failure to account for a weak waterdrive can result in significant material-balance errors.The assertion of previous authors that weak waterdrive exhibits a negative slope on the Cole (gas) and Campbell (oil) plots has been confirmed. A weak waterdrive is much more unambiguous on these plots than on commonly used plots, such as the p/z plot for gas.A modified version of the Cole plot is proposed to account for formation compressibility.The reservoir drive indices are a useful tool for determining the correctness of the material-balance solution because they must sum to unity. The drive indices should never be normalized to sum to unity because this obscures their usefulness and leads to a false sense of security.A modified version of the Roach plot (for gas) is proposed that improves interpretation in some waterdrive situations.Material balance has not been replaced by reservoir simulation; rather, it is complementary to simulation and can provide valuable insights to reservoir performance that cannot be obtained by simulation. Introduction Classical material balance is one of the fundamental tools of reservoir engineering. Many authors have addressed the difficult problem of solving the material balance in the presence of a waterdrive (Refs. 1 through 5 are just a few of the more significant ones). The emphasis in the literature has been on strong and moderate waterdrives. In this paper, examples of weak waterdrives are shown in which the effects on the material balance are significant. All aquifers studied here are of the "pot aquifer" type, which is time-independent. In gas reservoirs, the plot of p/z vs. cumulative gas production, Gp, is a widely accepted method for solving the gas material balance1 under depletion-drive conditions. Extrapolation of the plot to atmospheric pressure provides a reliable estimate of original gas in place (OGIP). If a waterdrive is present, the plot often appears to be linear, but the extrapolation will give an erroneously high value for OGIP. Many authors have addressed this problem (including those in Refs. 2 and 5 through 8), especially in cases of strong or moderate waterdrives. The p/z plot is actually more ambiguous in weak waterdrives than in strong or moderate ones. The Cole plot7,9 has proven to be a valuable diagnostic tool for distinguishing between depletion-drive gas reservoirs and those that are producing under a waterdrive. The analogous plot for oil reservoirs is the Campbell plot.10 The literature has emphasized strong and moderate waterdrives, the signature shapes of which are a positive slope and a hump-shaped curve, respectively, on these plots. Previous authors have recognized that weak waterdrives can produce negative slopes on these two diagnostic plots, but this author is not aware of any example plots in the literature. This paper shows examples, using simulation and actual field data, wherein a negative slope clearly reveals a weak waterdrive. These plots are much more diagnostic than the p/z plot. Once a weak waterdrive has been diagnosed, the appropriate steps can be taken in the material-balance equations to yield more accurate results. The Cole plot assumes that formation compressibility can be neglected, which is frequently the case with gas. However, in those reservoirs in which formation compressibility is significant, a modification to the Cole plot is presented that incorporates formation compressibility and gives more accurate results. The reservoir drive indices have been used to quantify the relative magnitude of the various energy sources active in a reservoir. It is shown here that the drive indices are also a useful diagnostic tool for determining the correctness of a material balance solution because they must sum to unity. If they do not sum to unity, a correct solution has not been obtained. In some commercial material-balance software, the drive indices are automatically normalized to sum to unity, which not only obscures their usefulness but also leads to the false impression of having achieved a correct solution. The Roach plot has been presented11 as a tool for solving the gas material balance when formation compressibility is unknown, with or without the presence of waterdrive. This paper shows that for waterdrives that fit the small pot aquifer model, incorporating cumulative water production into the x-axis plotting term improves the linearity of the Roach plot and gives more accurate values for OGIP. Finally, it is argued that even in those reservoirs for which a simulation study is performed, classical material-balance evaluation should be performed on a stand-alone basis. Simulation should not be viewed as a replacement for material balance because the latter can yield valuable insights that can be obscured during simulation. Performing a separate material balance study usually will improve overall reservoir understanding and enhance any subsequent simulation study. Material balance should be viewed as a complement to simulation, not as a competing approach. In this paper, formation compressibility, cf, is assumed to be constant and unchanging over the reservoir life under investigation. References are given for recommended methods to be used in those cases in which cf is variable.

The Method of Dynamic Reserves Prediction for a Constant Volume Gas Reservoir

2013 ◽  
Vol 275-277 ◽  
pp. 456-461
Author(s):  
Lei Zhang ◽  
Lai Bing Zhang ◽  
Bin Quan Jiang ◽  
Huan Liu
Keyword(s):  
Pressure Drop ◽  
Material Balance ◽  
Production Method ◽  
Gas Production ◽  
Constant Volume ◽  
Phase Method ◽  
Gas Reservoirs ◽  
Two Phase ◽  
Material Balance Method ◽  
Unit Pressure

The accurate prediction of the dynamic reserves of gas reservoirs is the important research content of the development of dynamic analysis of gas reservoirs. It is of great significance to the stable and safe production and the formulation of scientific and rational development programs of gas reservoirs. The production methods of dynamic reserves of gas reservoirs mainly include material balance method, unit pressure drop of gas production method and elastic two-phase method. To clarify the characteristics of these methods better, in this paper, we took two typeⅠwells of a constant volume gas reservoir as an example, the dynamic reserves of single well controlled were respectively calculated, and the results show that the order of the calculated volume of the dynamic reserves by using different methods is material balance method> unit pressure drop of gas production method >elastic two-phase method. Because the material balance method is a static method, unit pressure drop of gas production method and elastic two-phase method are dynamic methods, therefore, for typeⅠwells of constant volume gas reservoirs, when the gas wells reached the quasi-steady state, the elastic two-phase method is used to calculate the dynamic reserves, and when the gas wells didn’t reach the quasi-steady state, unit pressure drop of gas production method is used to calculate the dynamic reserves. The conclusion has some certain theoretical value for the prediction of dynamic reserves for constant volume gas reservoirs.

A Dynamic Workflow of Well Health Issue Prediction – Sulfur Deposition

2021 ◽  
Author(s):  
Bashirul Haq
Keyword(s):  
Material Balance ◽  
Gas Production ◽  
Health Issue ◽  
Sulfur Deposition ◽  
Gas Reservoirs ◽  
Gas Field ◽  
Actual Performance ◽  
Sulphur Deposition ◽  
Balance Analysis ◽  
Sour Gas

Abstract Sour gas reservoirs are vital sources for natural gas production. Sulphur deposition in the reservoir reduces a considerable amount of gas production due to permeability reduction. Consequently, well health monitoring and early prediction of Sulphur deposition are crucial for effective gas production from a sour gas reservoir. Dynamic gas material balance analysis is a useful technique in calculating gas initially in place utilizing the flowing wellhead or bottom hole pressures and rates during the well's lifetime. The approach did not apply to monitor a producing gas's health well and detect Sulphur deposition. This work aims to (i) modify dynamic gas material balance equation by adding the Sulphur deposition term, (ii) build a model to predict and validate the issue utilizing the modified equation. A unique form of the flowing material balance is developed by including Sulphur residue term. The curve fitting tool and modified flowing gas material balance are applied to predict well-expected behaviour. The variation between expected and actual performance indicates the health issue of a well. Initial, individual components of the model are tested. Then the model is validated with the known values. The workflow is applied to active gas field and correctly detected the health issue. The novel workflow can accurately predict Sulphur evidence. Besides,the workflow can notify the production engineers to take corrective measures about the subject. Keywords: Sulfur deposition, Dynamic gas material balance analysis, Workflow

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

Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Shijun Huang ◽  
Jiaojiao Zhang ◽  
Sidong Fang ◽  
Xifeng Wang
Keyword(s):  
Data Analysis ◽  
Shale Gas ◽  
Analytical Method ◽  
Material Balance ◽  
Gas Production ◽  
Production Data ◽  
Analysis Method ◽  
Gas Reservoirs ◽  
Data Analysis Method ◽  
Parameter Interpretation

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.

Reserves Determination Using Type Curve Matching and Extended Material Balance Methods in the Medicine Hat Shallow Gas Field

1994 ◽  
Author(s):  
S. L. West ◽  
P. J. R. Cochrane
Keyword(s):  
Material Balance ◽  
Poor Quality ◽  
Curve Matching ◽  
Pressure Data ◽  
Gas Reservoirs ◽  
Shallow Gas ◽  
Gas Field ◽  
Type Curve ◽  
Balance Analysis ◽  
Diffusivity Equation

Tight shallow gas reservoirs in the Western Canada Basin present a number of unique challenges in accurately determining reserves. Traditional methods such as decline analysis and material balance are inaccurate due to the formations' low permeabilities and poor pressure data. The low permeabilities cause long transient periods not easily separable from production decline using conventional decline analysis. The result is lower confidence in selecting the appropriate decline characteristics (exponential or harmonic) which significantly impacts recovery factors and remaining reserves. Limited, poor quality pressure data and commingled production from the three producing zones results in non representative pressure data and hence inaccurate material balance analysis. This paper presents the merit of two new methods of reserve evaluation which address the problems described above for tight shallow gas in the Medicine Hat field. The first method applies type curve matching which combines the analytical pressure solutions of the diffusivity equation (transient) with the empirical decline equation. The second method is an extended material balance which incorporates the gas deliverability theory to allow the selection of appropriate p/z derivatives without relying on pressure data. Excellent results were obtained by applying these two methodologies to ten properties which gather gas from 2300 wells. The two independent techniques resulted in similar production forecasts and reserves, confirming their validity. They proved to be valuable, practical tools in overcoming the various challenges of tight shallow gas and in improving the accuracy in gas reserves determination in the Medicine Hat field.

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