Geofluids

Volume 2017, Article ID 6803294, 11 pages

https://doi.org/10.1155/2017/6803294

## Application of Numerical Modelling and Genetic Programming in Hydrocarbon Seepage Prediction and Control for Crude Oil Storage Unlined Rock Caverns

^{1}Mineral Industries Research Center, Shahid Bahonar University of Kerman, Kerman, Iran^{2}Mining Engineering Department, Shahid Bahonar University of Kerman, Kerman, Iran^{3}Chemical Engineering Department, Shahid Bahonar University of Kerman, Kerman, Iran

Correspondence should be addressed to Ebrahim Ghotbi Ravandi; moc.oohay@miharbe_ibtohg

Received 23 November 2016; Revised 2 March 2017; Accepted 15 March 2017; Published 14 June 2017

Academic Editor: Micol Todesco

Copyright © 2017 Ebrahim Ghotbi Ravandi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Seepage control is a prerequisite for hydrocarbon storage in unlined rock caverns (URCs) where the seepage of stored products to the surrounding host rock and groundwater can cause serious environmental and financial problems. Practically seepage control is performed by permeability and hydrodynamic control methods. This paper employs numerical modelling and genetic programming (GP) for the purpose of seepage prediction and control method determination for the crude oil storage URCs based on the effective parameters including hydrogeologic characteristic of the rock and physicochemical properties of the hydrocarbons. Several levels for each parameter were considered and all the possible scenarios were modelled numerically for the two-phase mixture model formulation. The corresponding seepage values were evaluated to be used as genetic programming data base to generate representative equations for the hydrocarbon seepage value. The coefficients of determination () and relative percent errors of the proposed equations show their ability in the seepage prediction and permeability or hydrodynamic control method determination and design. The results can be used for crude oil storage URCs worldwide.

#### 1. Introduction

Underground storage of hydrocarbons in unlined rock caverns (URCs) is more secure, safe, and economical than above-ground storage and has several environmental and operational advantages. The main concern associated with URCs is the seepage of stored products, vapor, and VOCs of them to the surrounding host rock and groundwater which can cause serious environmental problems such as groundwater contamination and accumulation of flammable gas near the surface as well as economic and financial losses. Therefore, seepage control is a fundamental prerequisite for URCs where minimum product seepage is required. Practically seepage control from an URC is performed by permeability or hydrodynamic control methods. Permeability control means applying techniques such as grouting or freezing to control and decrease hydrocarbon seepage by maintaining a specified low permeability and sealing of the rock mass. However these techniques are very time-consuming and expensive [1]. By hydrodynamic control, it is meant that there is groundwater in the rock mass with the static head that exceeds the internal storage pressure resulting in positive groundwater gradient towards the cavern to prevent the escape of the stored products [2]. Aberg [3] postulated that no seepage will occur if the water pressure gradient towards the cavern is positive and greater than unity. There is no standard for acceptable seepage value and how much sealing work is required. It depends on the environmental and economic (operational) aspects. As a general rule, 24 m^{3}/24 hr period in a cavern of 100,000 m^{3} is considered to be an acceptable limit [1]. Liquid hydrocarbons (e.g., crude oil and gasoline) are not stored under pressure and their pressure inside caverns is hydrostatic. Hydrocarbons vapors and gases pressure inside caverns varies as a function of the temperature, oil level, and components, usually from 0.5 to 3 bar (10^{5} Pa) [4]. Typically, 75% and 25% of a cavern space are considered for liquid oils and gases, respectively [2].

Hydrocarbons seepage (especially crude oil) from underground unlined rock caverns to the surrounding saturated porous media is barely investigated in the literature [5, 6]. In this paper prediction equations for the hydrocarbons (crude oil and gas) seepage value from the Iranian URCs in terms of m^{3}/24 hr are represented using genetic programming based on the data gathered by numerical modelling of the hydrocarbon seepage for a variety of conditions using COMSOL and the two-phase mixture model formulation (see Supplementary Material available online at https://doi.org/10.1155/2017/6803294). By applying and solving the proposed equations for the seepage values less than the allowable one, prejudgment can be done and the seepage control technique (e.g., permeability or hydrodynamic control) can be selected.

#### 2. Two-Phase Mixture Model

Two-phase mixture model which was first mentioned by Wang and Beckermann [7] uses mixture variables to reduce the number of partial differential equations (PDEs) of classical two-phase fluid flow formulations in porous media. Therefore, it is more convenient to use the appropriate numerical schemes for the two-phase mixture model [7].

In the mixture model, the two phases are regarded as constituents of a binary mixture and the mixture variables such as mixture density and mixture velocity vector are denoted without index. With introduction of the mixture quantities (see [7]) the conservation of mass with the porosity () is defined asConservation of momentum using Darcy velocity is as follows in which the dynamic viscosity and the pressure are also mixture quantities (see [7]):where is the kinetic mixture density, is the intrinsic permeability, is the saturation and the subscripts of and are related to the wetting and nonwetting phase, respectively, is the relative permeability, is the gravitational acceleration vector, and is the depth.

The diffusive mass flux connects the mixture mean velocity with the velocity of the individual phases:Wang and Beckerman [7] introduced the diffusive flux () as follows:where is the kinematic viscosity, is the hindrance function for phase migration and separation, and is the capillary diffusion coefficient as a function of the wetting phase saturation:where is capillary pressure. The transport equation is as follows, where is the fluid content of the wetting phase:Several scientists have tried to derive a functional correlation for the relative permeability and the capillary pressure () as a function of the wetting phase saturation based on the experimental data. Brooks and Corey (1964) developed an empirical correlation utilizing the entry capillary pressure () and the wetting phase saturation that empirically has been found to be appropriate for the drainage process as follows [8, 9]:where is the pore size distribution index. Its value is usually considered to be 2 for the carbonated rocks [10].

Exact solutions for two-phase fluid flow problems in porous media which involve gravity, capillarity, and fluid flow in two or three dimensions (multidimensional flow) are impossible due to inherent nonlinearity and the need to solve for multiple dependent variables along with a variety of unknowns. Solving practical problems requires a suitable numerical method [7]. A lot of authors have used numerical methods and software tools to model single- or two-phase fluid flow in porous and fractured media [11–15]. In the mentioned literature the effect of gravity, capillary pressures, and multidimensional flow is usually neglected and not considered simultaneously.

#### 3. Validation of Numerical Modelling of Two-Phase Mixture Model by COMSOL

Neglecting the capillary pressure and gravity effects, the five-spot problem is the standard porous media problem where a square computational domain is initially saturated with the nonwetting phase (oil) and the wetting phase (water) is injected through a well at a lower corner of the domain at a constant rate (or pressure) and displaces the oil. The nonwetting phase is produced at the same rate through a well in the opposite upper corner. In order to evaluate the computational efficiency and accuracy of the mixture model formulation numerical modelling with COMSOL, a verification example of the computational domain with the dimensions 300 m × 300 m for the five-spot problem is given to compare the numerical results with the fully coupled (classical) formulation. Boundary and initial conditions are depicted in Figure 1. Dirichlet pressure boundary conditions are 5 m × 5 m injection and production wells. The other boundaries are impermeable and Neumann no-flow boundary conditions. The nonwetting and wetting phase density and viscosity are considered 1000 Kg/m^{3} and 0.001 Pa·m, respectively. Intrinsic permeability, porosity, and pore size distribution index are 10^{−7} m^{2}, 0.2, and 2, respectively. Figure 1 shows the comparative study of the numerical modelling results for the fully coupled [16] and mixture model formulations referring to the time days and time step of 1 day. As it can be seen from Figure 1 the results (wetting phase saturation fronts and contour lines) of the fully coupled and mixture model formulations are in good agreement with each other.