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.
An online real-time production optimization and monitoring system for the Greater Ekofisk Area of Norway was installed in 2006. The system has evolved significantly since installation; changes driven by multi-disciplinary teams in coordination with the ConocoPhillips Production Optimization Centre (POC).The POC, Subsurface Production Delivery and Reservoir Optimization teams are tasked with assessing real time data from nominally 160 active producers and injectors in order to minimize losses and thereby maximize field production. This online system integrates data from the complete production system: reservoir to export meters. The system realises the importance of visualisation with respect to monitoring field performance, streamlined decisions, and reduced man hours mining data and analysis. The system allows real time monitoring of all wells and associated instrumentation parameters along with field three phase production allocated to the well level. The system alerts an engineer's attention when a well's performance is outside predefined tolerances thereby enabling continuous optimization of the combined field network. This paper demonstrates how the online system addresses the following challenges:• Real-time monitoring of separator loadings, production/injection well performance • Daily production/injection volume losses allocation • Quick screening and allocation issues • Generation of updated well models with the latest well test data for further analysis (nodal analysis, lift performance analysis) • Generation of updated network models for what-if studiesThe tool has an open architecture that allows information to be shared with other software packages. It is also capable of controlling and using results from other software that have open access. The tool is used daily by the POC to review the overall performance of the Greater Ekofisk Area.
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