Method and System for Providing Optimal (Steam Assisted Gravity Drainage) SAGD Operation Control and Sensitivity Analysis by Symbolic Differentiation of Implicit Predictive Models
Publication Date: 2016-Apr-06
The IP.com Prior Art Database
A method and system is disclosed for derivation of sensitivity relations associating a change in Steam Assisted Gravity Drainage (SAGD) controls with respective change in quantities of interest. The method and system relies on representation of a predictive model symbolically with respect to the controls, symbolic differentiation of the quantifies of interest with respect to the controls and a numerical evaluation of the sensitivity relations for a given set of controls.
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Operation Control and Sensitivity Analysis by Symbolic Differentiation of Implicit Predictive Models
Steam Assisted Gravity Drainage (SAGD) is a non-conventional oil production methodology in which a steam is injected through injector wells and drained oil is extracted through producer wells. The operation involves several controls, such as, but not limited to, a rate of steam injected, steam allocation to various sites, gas casing pressure, extracted emulsion pressure, etc. In addition, the SAGD apparatus is instrumented with sensors providing partial information regarding the state of the system with respect to certain observables. The observables can be, but need not be limited to, emulsion rate, temperature profile along the well, sub-cool profile, bottom hole pressure, gas blanket pressure, steam injection surface pressure.
In the prior art, a key challenge was to determine optimal set of controls that maximize the yield of the system while honoring operational constraints such as, but not limited to, upper bounds upon bottom hole pressure, minimum temperature, sub-cooling, etc. Due to the complex multi-physics nature (diffusion, advection, heat transfer, etc.) of subsurface dynamics, it is advantageous to form a model that may involve both an explicit component as well as implicit structures such as a hybrid physics based (explicit) and an adaptive data-driven model (implicit). Under such circumstances, derivation of sensitivity relations cannot be performed a-priori and another resolution is required.
Disclosed is a method and system for derivation of sensitivity relations associating a change in Steam Assisted Gravity Drainage (SAGD) controls with respective change in quantities of interest.
The method and system generates a fully / partially implicit predictive model. Following generation of the predictive model, a symbolic representation of the predictive model
with respect to one or more controls as symbolic variables is generated. Consequently,
symbolic differentiation of the quantities of interest with respect to the one or more controls is derived. Whenever evaluation of the predictive model derivatives is required, actual values are assigned to the symbolic parameters and a numerical evaluation of the symbolic expressions is performed. The numerical values of either the objective or constraint gradients are used to guide the non-linear optimization process.
Alternatively, the derivatives can be used for sensitivity analysis for operational or development purposes
In accordance with an embodiment, the method and system performs model generation and training that involves functional forms that are not determined a-priori (implicit) such as, but not limited to, changes in topology of a neural network connectivity-wise, adaptive determination of activation functions (especially when kernel methods are involved), adaptive tune-up of the n...