#
STOMP User Guide

#### Subsurface Transport Over Multiple Phases

STOMP User Guide

#### Subsurface Transport Over Multiple Phases

### STOMP Shortcourse Example Problems

The example application problems provided here are those presented during an introductory STOMP short course. They are intended to provide the student with a general overview of the code's capabilities and diversity. Each application is described through background text material, images of simulation results, and references to more detailed discussions. Additional exercises with solutions are often also provided. The applications have been chosen to demonstrate the simulator's application over a range of scales from laboratory experiments to field scale problems, and vary in complexity and include saturated and unsaturated flow, solute transport, salt-water brine, nonaqueous phase liquid flow, volatile dense nonaqueous phase liquid flow, partition tracers, CO_{2} sequestration, enhanced oil recovery, and nonisothermal coupled thermal and hydrologic transport.

STOMP-W example problems include saturated and unsaturead flow, solute transport, and geochemistry (reactive transport). Problems W-1 through W-4 can be executed with STOMP-W. Problems W-5 and W-6 require the ECKECHEM module to be compiled (STOMP-W-R).

## W-1: Aqueous Flow in Saturated and Unsaturated Porous Media

The user is introduced to the development of input files for successful simulation of flow problems. The first problem is a simple 1D vertical, single-phase aqueous flow system. Through manipulation of input file parameter values and boundary conditions, various saturated and unsaturated systems are obtained.

## W-2: Aqueous Flow to a Well in a Confined Multi-Layer System

This test case illustrates flow to a well in a confined multi-layer system, where two identical aquifers (upper and lower) are separated by an aquitard. The well produces only from the lower aquifer, where it is fully penetrating. This problem is known in the literature as the leaky aquifer problem. The user is introduced to a two-dimensional domain, a cylindrical coordinate system, and Neumann boundary conditions.

## W-3: Solute Transport in a Saturated Porous Media

This test case illustrates transport of a solute within a steady state, uniform flow field. An initial square pulse of solute mass is instantaneously introduced into the flow field and transported downstream. The pulse undergoes advection, dispersion and molecular diffusion. The user is introduced to solute transport input file cards, standard and higher order transport options, and the importance of controlling Peclet and Courant numbers.

## W-4: Solute Transport in a Saturated Porous Media

This test problem illustrates the use of zonation files for specifying both spatially variable material types and inactive nodes, and linked-list x-y-z seepage face and x-y-z hydraulic gradient boundary conditions. When used in combination, these features are useful for representing boundary conditions over irregular surfaces such as undulating surface topography and sloping river shorelines. Furthermore, when large regions of a model domain can be specified as inactive (e.g. the part of the domain representing the river itself and the atmosphere above the ground surface) significant improvements in the computational performance of STOMP can potentially be achieved due to the decreased number of unknowns that are being solved for. Note that the features demonstrated by this test problem also provide an alternative to using curvilinear or boundary-fitted coordinates, or finite element methods, for representing irregular physical boundaries.

## W-5: Transport, kinetic biodegradation, cell growth, and kinetic sorption (STOMP-W-R)

This example problem was developed and published by Parkhurst and Appelo (1999), from an advective-dispersive-reactive transport problem, developed by Tebes-Steven and Valocchi (1998). The transport involves mobile and immobile species; where the immobile species are either bacterial cells or sorbed metals. The chemistry involves speciation, bacterially mediated degradation of an organic substrate, bacterial growth and decay, and kinetic metal sorption, including metal-ligand complexation. In brief the problem involves the steady-flow of an aqueous solution through a 10-m column, initially containing biomass. A pulse of dissolved nitrylotriacetate (Nta) and cobalt (Co) are introduced at the inlet of the column. Nta is defined to degrade in the presence of biomass and oxygen, yielding biomass growth. The equilibrium chemistry in this problem assumes activity coefficients of 1.0. To solve the chemical reactions in this problem, STOMP-W-R is used.

## W-6: Uranium sorption/desorption due to river water/groundwater interactions (STOMP-W-R)

This problem addresses the significance of water chemistry on uranium mobility at the Hanford 300 Area. Laboratory-derived uranium sorption models were used in the simulation. To solve the chemical reactions in this problem, STOMP-W-R is used.

The STOMP-GT example problem simulates the classical natural heat pipe problem.

## GT-1: Simulation of Countercurrent Flow and Heat Transport with Local Evaporation and Condensation (Natural Heat Pipe)

This heat pipe problem demonstrates the simulator’s ability to model countercurrent aqueous and gas flow in variably saturated geologic media, including saturations below residual saturation. As posed, the problem involves one-dimensional horizontal flow and heat transport, but this classic multifluid subsurface flow and transport problem involves complex flow behavior, which is subtle to changes in soil properties. The user will first explore the effects of changes in soil thermal conductivity, specific heat, and enhanced vapor transport on the formation and temperature distribution for a horizontal one-dimensional heat pipe. After completing these investigations, the user is asked to design an input file for a two-dimensional problem involving dynamic heat pipe flow.

STOMP-CO2 example problems include a suite of problems created for the GeoSeq code comparison study (CO2-1, CO2-2, Co2-3, & CO2-5), a demonstration of the coupled well model (CO2-4), viscous fingering with CO2 dissolution (CO2-7) and CO2 injection into a hybrid heterogeneous domain (CO2-8). Problems CO2-6 and CO2-11 simulate geochemical processes and require the ECKEChem module to be compiled.

## CO2-1: Radial Flow of Supercritical CO_{2} from an Injection Well (GeoSeq #3)

Radial flow of injected supercritical CO2 into simplified fresh-water and saline aquifers is compared. This problem is identical to Problem 3 of the code intercomparison problems developed under the GeoSeq Project (Pruess et al. 2002) and addresses two- fluid flow of CO2 and aqueous for a simplified flow geometry and aquifer properties. A constant mass injection rate of CO2 is applied from a line source at the center of the infinite radial domain into an aquifer with homogeneous and isotropic hydrologic properties. Gravity and inertial effects are ignored by using a one-dimensional radial computational domain. The problem has a similarity solution, where dependence on the radial distance (r) and time (t), is replaced by the similarity variable (ξ = r2 /t), (O’Sullivan 1981; Doughty and Pruess 1992).

## CO2-2: Discharge of Sequestered CO2 Along a Fault Zone (GeoSeq #4)

Loss of CO2 from a deep fresh-water aquifer through a leaky fault is investigated. This problem is identical to Problem 4 of the code intercomparison problems developed under the GeoSeq Project (Pruess et al. 2002) and addresses two-fluid flow of CO2 and aqueous for a simplified one-dimensional vertical flow geometry. The problem is designed to investigate the transport of CO2 from the disposal aquifer to another aquifer 500 m above, through an intersecting vertical fault. The vertical fault is idealized using a one-dimensional geometry and constant pressure boundary conditions (Pruess and Garcia 2002).

## CO2-3: CO2 Injection into a 2-Dimensional Layered Brine Formation (GeoSeq #7)

Pressure and buoyancy driven migration of CO2 injected into a layered formation that is representative of the Sleipner Vest field in the Norwegian sector of the North Sea is investigated. This problem is identical to Problem 7 of the code intercomparison problems developed under the GeoSeq Project (Pruess et al. 2002). A key assumption for the problem, as posed, was isothermal conditions at the formation temperature of 37 ̊C; therefore, STOMP-CO2 was executed for these simulations. The problem involves a constant mass rate injection of scCO2 into a layered saline formation comprising sands and shales.

## CO2-4: Contrasting Pressure- and Flow-Controlled CO2 Injection Wells

The rate of CO2 injection into saline reservoirs is often limited by the local fracture pressure gradient in the effort to meet regulatory requirements and to avoid fracturing the reservoir or caprock. This problem demonstrates the use of the coupled well model in STOMP-CO2, in which the user can specify both an injection rate and a maximum injection pressure. CO2 is injected into a layered saline reservoir with layers of varying permeability and scenarios of pressure-controlled and flow-controlled CO2 injection are investigated.

## CO2-6: Mineral Trapping in a Basaltic Formation (STOMP-CO2-R)

This problem presents a simulation of pilot-scale CO2 injection into the flow top of the Slack Canyon #2 basalt flow in the Grande Ronde basalt formation using the STOMP-CO2 simulator with the ECKEChem reactive transport solver. Relative amounts of CO2 sequestration by dissolution and mineral trapping are demonstrated.

## CO2-8: CO_{2} Injection into a Hybrid Heterogeneous Domain

Geophysical field measurements combined with geostatistical techniques can yield complex geological models that have fully heterogeneous distributions of petrophysical properties. Typically only a limited number of parameters are distributed across the domain in a fully heterogeneous manner, such as porosity and intrinsic permeability. Parameters that define the relationships between capillary pressure, phase saturation, and phase relative permeability (ksP functions), are generally determined from measurements on discrete core samples. The STOMP simulator input routines have been designed to handle homogeneous, zoned, heterogeneous, and hybrid heterogeneous distributions of petrophysical properties. This problem considers the injection of CO_{2} into a saline formation whose petrophysical properties of porosity and intrinsic permeability are fully heterogeneous, relative permeability-saturation-capillary pressure (ksP) function parameters are zoned, and all other parameters homogeneous. This is known as the hybrid heterogeneous distribution.

## CO2-10: Hydromechanical Responses During CO_{2} Injection into an Aquifer-Caprock System

The consequences of rock deformation in response to a constant-pressure CO_{2} injection into the bottom of a one-dimensional vertical domain comprising a caprock overlying an aqueous reservoir are addressed in this problem. Deformation of the rock due to the injection of CO_{2} results in changes in porosity and intrinsic permeability, through stress dependent functions. Initial conditions for the geomechanical system are established based on static conditions for stress, fluid pressure and temperature. Simulations of CO_{2} injection over a thirty-year period are then conducted with and without considering hydromechanical effects. Changes in the entry pressure with changes in porosity are ignored for this problem. Simulations are conducted with the nonisothermal version of the geologic sequestration version, STOMP-CO2.

The following problem is based on a problem from the benchmark study presented at the Workshop on Numerical Models for CO_{2} Storage in Geological Formations in Stuttgart, Germany,and require the non-isothermal version of STOMP-CO2 (STOMP-CO2E).

## CO2E-2: : Estimation of the CO_{2} Storage Capacity of a Brine Aquifer (Modified Stuttgart #3)

Estimation of the CO_{2} storage capacity is investigated for CO_{2} injection into a single-layer formation. The processes modeled include advective, multiphase flow, dissolution of CO2 into the ambient brine, and non-isothermal effects due to temperature gradients within the formation. This problem is based on Problem 3 of the benchmark study first presented at the Workshop on Numerical Models for CO_{2} Storage in Geological Formations in Stuttgart, Germany, and focuses on an injection scenario where CO2 injection is located near a fault zone (Class, et al., 2009).

STOMP-EOR example problems demonstrate the nonisothermal capabilities of STOMP-CO2. These must be include saturated and unsaturead flow, solute transport, and geochemistry (reactive transport). Problems W-1 through W-4 can be executed with STOMP-W. Problems W-5 and W-6 require the ECKECHEM module to be compiled (STOMP-W-R).

## EOR-6: Primary, Secondary, and Tertiary Recovery from a Regular Five-Spot Well Pattern in the Farnsworth Unit using the Compositional Option

STOMP-EOR has two principal options for solving problems involving oil and gas production: 1) black-oil and 2) compositional. The compositional option numerically simulates all three stages of oil and gas recovery from a reservoir: 1) primary, 2) secondary, and 3) tertiary. Primary recovery uses the initial pore pressure and pumping to produce oil and gas. During secondary recovery, water is injected into the reservoir to drive oil and gas to the production wells. Tertiary recovery seeks to alter the properties of the unrecovered oil in the reservoir. The particular technique of interest for this problem is the injection of CO2 to yield miscible displacement of the oil toward the production wells. The compositional option solves mass conservation equations for water, CO2 CH4, salt, and a user-specified number of petroleum components. The simulator additionally solves an energy conservation equation, which allows for nonisothermal conditions. This problem is designed to investigate the recovery of oil and gas from a regular five-spot well pattern using geologic and petroleum properties, which are representative of the Farnsworth Unit, Ochiltree County, Texas (in the Anadarko Basin of northern Texas).