Application Of Volume Balance Equations In The Numerical Simulation

In the numerical reservoir simulation, the core theory is based on the theory ofconservation of mass (molar mass conservation) in the simulation of black oil model,component model and other types of reservoir computing. Base on this theory, a mathematicalmodel is built and is on control of some auxiliary equations and boundary conditions, thepartial differential equation was discretized and constructing matrix Jacob to computingpressure, saturation and other key parameters, their distribution etc. it is helpful for knowingmore information about reservoir description, reservoir performance prediction, mechanismof oil displacement and improving reservoir hydrocarbon recovery.According to this theory, in fact, the Eclipse reservoir simulation software have beenachieved, and played a huge role in the process of reservoir development, and achieved goodeconomic and extensive social benefits.But with the deepening of oilfield development, the old reservoir production continuesdeclining, discovery and development of new reservoirs is becoming increasingly difficult,there need some new techniques or methods urgently to change the existing situation, to get abetter discovery and improve oil recovery.Meanwhile, under the trend of the full reservoir simulation, numerical simulation ofmillions of nodes, fine numerical simulation, and the new challenge is the simulation speed.The conservation of volume theory and volume balance method are different solutions to thesame problem in the reservoir, and it can improve the simulation speed, which is a veryinteresting, very practical approach.Conservation of volume theory can be described as simple: at an isothermal temperaturecondition, in a grid block, rock porosity volume (PV) is equal to the sum of all forms of fluidvolume. It is named as volume balance equation (Volume Balance, subsequent referred VB)which is from Conservation of volume theory.A volume balance formulation works better than a mass balance formulation because thevolume balance is a local error, and does not accumulate over time when doing linear iterativenonlinear coefficient calculation process, and it have a trend of self-correction in thesubsequent step of computing, so by setting loose convergence tolerance range, it isconvergence quickly after only one iteration, this is main reason which can greatly improvingthe speed of operation. whereas the mass balance formulation leads to material balance errors,which do accumulate over time which using mass conservation as a convergence criterion and allowing a very narrow tolerance range, the error will be accumulated in different time steps,it can reach to tolerances range after multiple iterations, if ten million grid nodes are involvedin operations, it needs long time.In subsequent chapters, we will build volume balance equation through conservation ofvolume theoretical studies and describe the why it is faster than other way in the process ofsolving.It can improve simulation speed using VB method, But someone wonder which thesimulation results coincide with the observed data. In the course of this article, we willcompare simulation results to observed data of individual well performance matching, thewhole matching, water cut fraction, gas oil ratio, daily production, cumulative oil production,average pressure etc. then we will continue to compare to the simulation results of Eclipse,VIP software which base on mass conservation theory, meanwhile we will record thecomputing time for comparing.Through testing in the western oil fields, the effect is ideal to achieve the desiredobjectives of the study, the results are coincide with observed data and the simulation resultsof Eclipse and VIP software, meanwhile, the simulation process is faster.The actual value of the contents of this paper is that the volume balance equations cansignificantly improve speed under the same simulation results.