Linking up pressure, chemical potential and thermal gradients

Abstract

Petroleum reservoirs are remarkable illustrations of the impact of a thermal gradient on fluid pressure and composition. This topic has been extensively studied during the last decades to build tools that are required by reservoir engineers to populate their models. However, one can get only a very limited number of representative samples from a given reservoir and assessing connectivity between all sampling points is often a key issue. In some extreme cases, the whole reservoir fluid properties must be derived from a single point to define the field development plan. To do so, available models are usually not satisfactory as they need too many parameters and so cannot be considered as predictive tools. We propose in this work a comprehensive approach based on the irreversible thermodynamics principles to derive the relationships between pressure, chemical potentials and thermal gradients in porous media. It appears that there is no need for additional assumptions, it is just a matter of a making the right choices along theoretical developments. One of the most important steps is to express the full pressure gradient. As a final result, we obtain the chemical potential gradients for all components of the mixtures that can be easily translated in term of compositions through Equation of State modelling. The most important features of the final expressions are: (i) the species relative separation in a thermal field is sensitive to the relative diffusion coefficients at stationary state. In porous media, the separation is sensitive to the permeability when the overall mobility is similar to diffusive mobility; (ii) the magnitude of the separation depends on the residual entropy of the species; (iii) the separation is not simply balanced by the average residual entropy. The balance is modified by the relative diffusion mobility of the components; (iv) in low permeability porous media, the thermal gradient induces a pressure gradient proportional to the fluid residual entropy. As a validation, the proposed approach has been applied on a reservoir fluid subjected to a geothermal gradient and compared with non-equilibrium molecular dynamics simulation results at the stationary state.

Technical Implications of Neglecting Compositional Grading Effects in Petroleum Reservoir Simulation Models

“…The modeling frameworks for the estimation of compositional variation with depth in petroleum reservoirs have been reported in the literature. ,− There are three main categories of these modeling frameworks . The thermodynamic based models (static models) rely on fluid enthalpies to estimate the thermal diffusion coefficient. ,,− The second category is based on activation energy (dynamic models), which is obtained from viscosity correlations. ,− The third category requires a molecular diffusion coefficient and convection term. ,− …”

“…29,[31][32][33] The third category requires molecular diffusion coefficient and convection term. 29,[33][34][35][36][37][38][39][40][41] CG models in the above mentioned second and third categories were not considered in this study because they are not supported by the applied CMG's WinProp simulator. To include these models in this study would require developing separate solution algorithms for each of them,…”

A new approach to thermal segregation in petroleum reservoirs: Algorithm and case studies

“…Pedersen and Lindeloff (2003) assumed a stationary state with an influence of temperature gradient and expressed the change in component compositions in terms of thermodiffusion coefficients depending on partial molar enthalpies of the components. As the gravitational segregation is well quantified, the current practice in the petroleum industry consists of tuning the thermodiffusion parameters to match the available compositional field data (Montel et al, 2019).…”

Thermodynamic Theory of Diffusion and Thermodiffusion Coefficients in Multicomponent Mixtures

“…For diluted gas mixtures, the answers, again, are given by the gas kinetic theory [45]. Recently, a simplified approach to thermodiffusion was suggested specifically for the transport in porous media [46]. The simplification is needed since the experimental determination of the thermodiffusion coefficients in multicomponent mixtures is a difficult task [47,48].…”