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Reservoir Formation Damage Episode 3 Part 3

Tham khảo tài liệu 'reservoir formation damage episode 3 part 3', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 532 Reservoir Formation Damage Effluent species concentrations versus pore volume injected 9. Output that can be requested Best estimates of the unknown parameters Predicted versus measured data Simulation of pressure various species concentrations in the flowing fluid and the pore surface porosity and permeability as functions of pore volume injected or time Numerical Solution of Formation Damage Models Depending on the level of sophistication of the considerations theoretical approaches mathematical formulations and due applications formation damage models may be formed from algebraic and ordinary and partial differential equations or a combination of such equations. Numerical solutions are sought under certain conditions defined by specific applications. The conditions of solution can be grouped into two classes 1 initial conditions defining the state of the system prior to any or further formation damage and 2 boundary conditions expressing the interactions of the system with its surrounding during formation damage. Typically boundary conditions are required at the surfaces of the system through which fluids enter or leave such as the injection and production wells or ports or that undergo surface processes such as exchange or reaction processes. Algebraic formation damage models are either empirical correlations and or obtained by analytical solution of differential equation models for certain simplified cases. Numerical solution methods for linear and nonlinear algebraic equations are well developed. Ordinary differential equation models describe processes in a single variable such as either time or one space variable. However as demonstrated in the following sections in some special cases special mathematical techniques can be used to transform multi-variable partial differential equations into single-variable ordinary differential equations. Amongst these special techniques are the methods of combination of variables and separation of variables and the .