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This paper provides a new definition to pseudo-time that incorporates the effects of formation compressibility and residual fluid compressibility, as the reservoir depletes, into well test analysis. The new definition of the pseudo-time can be incorporated into the existing system by using a correction factor that is applied to conventionally defined total system compressibility. The new definition of pseudo-time determines the final average reservoir pressure more accurately even at high degree of depletions of the reservoir. This study also addresses the errors in gas reserves estimation when using conventionally defined total system compressibility, which may have a substantial economic effect. Introduction Well test analysis correlates initial reservoir pressure, well flowing pressure, reservoir and fluid characteristics to well flow rate. The transient and pseudo-steady state flow relationships are formulated for constant compressibility and viscosity fluids. Oil and water above bubble point can be approximated to constant compressibility and viscosity fluids, whilst gas or multiphase cannot, making the diffusivity equation non-linear. The introduction of Pseudo-pressure m(p) by Al-Hussaiany et.al2 which takes into account the variation of gas viscosity and z-factor as a function of pressure leads to partial linearization of the gas flow equation. Further, introduction of time function, Pseudo-time by Agarwal R.G.1, considers the variation of the gas viscosity and total compressibility as a function of the pressure enabled the time based correction of the gas properties. The use of above functions made the gas diffusivity equation linear which aided the use of solutions derived for oil to be used for gas wells. On the other hand, reservoir engineers are interested in the material balance calculation to relate the average reservoir pressure to the cumulative off-takes of the fluids and fluid characteristics, instead of using the transient and pseudo-steady state flow relationship. Ensuring that the well test and the material balance approaches tie up correctly is important for confident reserves determination and for forecasting the performance of a well as pressure decline becomes significant and fluid properties start to change to a significant degree. Conventional well test equations for gas flow consider a volumetric reservoir, which assumes that the available pore volume to gas is constant by disregarding the effect of formation compressibility and the expansion of residual fluid during the productive life of the reservoir. Such assumptions may not be correct for long drawdown or where the rock compressibility is contributing considerably towards the total compressibility. If we look into the basics of the theory, the diffusivity equation is derived using continuity and mass balance concept on a small element. Further, when reservoir and fluid properties are changing, we use pseudo-functions to make the diffusivity equation linear. Similarly, material balance works by considering a small element of the reservoir by determining the change in pressure using the same continuity and mass balance concept but here we determine the change in fluid and reservoir properties as we go along. Since the basis of both approaches is very similar, the results from the two approaches should be same; keeping in view, the approximations made during the analysis do not affect the two results considerably.
This paper provides a new definition to pseudo-time that incorporates the effects of formation compressibility and residual fluid compressibility, as the reservoir depletes, into well test analysis. The new definition of the pseudo-time can be incorporated into the existing system by using a correction factor that is applied to conventionally defined total system compressibility. The new definition of pseudo-time determines the final average reservoir pressure more accurately even at high degree of depletions of the reservoir. This study also addresses the errors in gas reserves estimation when using conventionally defined total system compressibility, which may have a substantial economic effect. Introduction Well test analysis correlates initial reservoir pressure, well flowing pressure, reservoir and fluid characteristics to well flow rate. The transient and pseudo-steady state flow relationships are formulated for constant compressibility and viscosity fluids. Oil and water above bubble point can be approximated to constant compressibility and viscosity fluids, whilst gas or multiphase cannot, making the diffusivity equation non-linear. The introduction of Pseudo-pressure m(p) by Al-Hussaiany et.al2 which takes into account the variation of gas viscosity and z-factor as a function of pressure leads to partial linearization of the gas flow equation. Further, introduction of time function, Pseudo-time by Agarwal R.G.1, considers the variation of the gas viscosity and total compressibility as a function of the pressure enabled the time based correction of the gas properties. The use of above functions made the gas diffusivity equation linear which aided the use of solutions derived for oil to be used for gas wells. On the other hand, reservoir engineers are interested in the material balance calculation to relate the average reservoir pressure to the cumulative off-takes of the fluids and fluid characteristics, instead of using the transient and pseudo-steady state flow relationship. Ensuring that the well test and the material balance approaches tie up correctly is important for confident reserves determination and for forecasting the performance of a well as pressure decline becomes significant and fluid properties start to change to a significant degree. Conventional well test equations for gas flow consider a volumetric reservoir, which assumes that the available pore volume to gas is constant by disregarding the effect of formation compressibility and the expansion of residual fluid during the productive life of the reservoir. Such assumptions may not be correct for long drawdown or where the rock compressibility is contributing considerably towards the total compressibility. If we look into the basics of the theory, the diffusivity equation is derived using continuity and mass balance concept on a small element. Further, when reservoir and fluid properties are changing, we use pseudo-functions to make the diffusivity equation linear. Similarly, material balance works by considering a small element of the reservoir by determining the change in pressure using the same continuity and mass balance concept but here we determine the change in fluid and reservoir properties as we go along. Since the basis of both approaches is very similar, the results from the two approaches should be same; keeping in view, the approximations made during the analysis do not affect the two results considerably.
Naturally fractured-vuggy carbonate gas condensate reservoirs in China have some distinctive characteristics: deep buried depth, multi-scale fractures, vugs and caves developed, poor reservoir connectivity and high production decline rate. It is hard to build effective geological models and run reservoir simulation for production forecasting. So how to properly forecast the performance of this kind of reservoirs is a major challenge. This paper presents a systematic technique of production forecast to solve this problem. The systematic technique mainly involves analytical and numerical production analysis (PA), analytical and numerical pressure transient analysis (PTA) and material balance analysis in combination with the geological analysis results. Firstly, using the analytical PA and PTA can quickly and correctly evaluate reservoir properties. Take Tazhong No.1 carbonate gas condensate reservoir in China for example to elaborate the details of this method. The results show that the systematic method can not only properly calculate the reservoir properties, but also can quickly and properly forecast reservoir performance of fractured vuggy carbonate gas condensate reservoirs. And the calibrated dynamic numerical model can both match well production history data and well pressure data. Examples are presented to show how these material balance analysis, analytical and numerical PA and PTA methods fully integrated and constrained with each other, and how the reliable results can be generated finally. Because of the poor connectivity characteristic of Tazhong No. 1 field, dynamic models for each fractured-caved unit should be built and applied for performance prediction.
Formation test pressure is one of the most important and invaluable surveillance data to understand reservoir dynamic behavior, but usually pressure of different wells are not tested at the same time which limit its function. This paper proposed a simplified material balance equation to convert all tested pressure to the same date, then use converted pressure to assist depositional facies mapping and reservoir connectivity evaluation. Take M1 reservoir for example, all pressure data are converted to the same artificial test date with a simplified material balance equation. The material balance equation is simplified under certain assumptions, which is similar to that of volumetric undersaturated oil reservoirs. Then wells were classified into different groups for each zone according to their converted depletion pressure change behavior, and depositional facies and reservoir lateral connectivity of different groups of wells are analyzed with clear understanding and obvious characteristics. M1 reservoir is a multi-layered sandstone reservoir under primary depletion currently, which have 18 wells conducted formation test from 2010 to 2011. It is found that pressure analysis of these wells have no obvious characteristic. But after all pressures converted to the same date with well production constrained, depletion pressure change has clear trend. Then for each zone, wells were classified into different groups according to pressure change behavior, which indicates pressure depletion is similar in the same group while much different from that of other groups. Converted pressure data were analyzed in detail for each zone and used for depositional facies mapping and reservoir connectivity evaluation. Most are consistent between pressure depletion behavior and geological understanding, but some also have contradictions which helps to revise depositional facies. For reservoir connectivity, similar results of depositional facies are drawn. This paper offers a case study of converting pressure to the same date based on simplified material balance equation, and how to use converted pressure for depositional facies mapping and reservoir connectivity evaluation study are also detailed presented.
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