## University of Texas at Austin Petrophysical and Well-Log Simulator (UTAPWeLS)

#### Borehole Resistivity Modeling Module©

#### Borehole Sonic Modeling Module©

#### Borehole Nuclear Modeling Module©

#### Formation Evaluation Module©

#### Formation Testing Module©

#### Pore-Level Petrophysics Module©

### Borehole Resistivity Modeling Module©

The Borehole Resistivity Modeling Module© simulates and inverts borehole induction, laterolog, and spontaneous potential (SP) measurements for the case of multiple horizontal layers penetrated by a vertical well. Each horizontal layer can include several radial zones with different values of electrical conductivity. These piston-like radial variations of electrical conductivity are intended to describe the effect of axi-symmetric mud-filtrate invasion.

The forward-modeling capabilities of the Borehole Resistivity Modeling Module© include the simulation of Dual-Induction, Dual-Laterolog, Schlumberger's AIT† logs and SP in a vertical borehole and an isotropic earth. New tools have been added to the current version of the Borehole Resistivity Modeling Module©: 3DEX††, HDIL†† and MPR††, all from Baker-Atlas; ARC†, HALS† and HRLA† from Schlumberger and finally MAI††† from Weatherford. Some of these tools allow modeling in a deviated borehole and anisotropic earth (3DEX††, AIT†, ARC†, HDIL†† and MPR††). In addition the new Dual Laterolog Tool†† (DLL) code from Baker-Atlas supports modeling in a vertical borehole and anisotropic earth.

Numerical simulation of induction measurements is performed with an efficient mode-matching approach (Chew et al, 1984 and Zhang et al, 1995, 1999), whereas the numerical simulation of laterolog and SP measurements is performed with a finite-element method (Zhang, 1986, Zhang and Wang 1997, 1999).

Currently, this module inverts raw AIT† measurements into 2D parametric distributions of shallow and deep resistivity (Wang and Torres-Verdín, 2006), as well as radius of invasion. Likewise, the module can perform separate inversions of SP and raw AIT† measurements to estimate water-zone electrical resistivity properties as well as parametric distributions of shallow and deep resistivity, and radius of invasion (Wang and Torres-Verdín, 2006).

Computer programs include capabilities for 1D simulation along deviated wells, in addition to bed-boundary picking. Software used to simulate induction, laterolog and SP measurements were written in Fortran 90, whereas the graphical user interface (GUI) was written in MATLAB® version 7.0.4.365 (R14). The user-friendly interface operates on any computer furbished with the above MATLAB® version or later.

†Mark of Schlumberger

††Mark of Baker Atlas

†††Mark of Weatherford

### Borehole Sonic Modeling Module©

The Borehole Sonic Modeling Module© simulates full-wave time-domain sonic measurements acquired in axial-symmetric media. Sources and receivers are located along the axis of a vertical well. It is assumed that the vertical well penetrates horizontal layers that consist of multiple radial zones (including a borehole) similar to those of mud-filtrate invaded formations. Sources consist of monopole, dipole, and quadrupole transmitters, whereas point receivers can measure pressure, displacement, or stress depending on the choice of source (Chi et al., 2006, Ma and Torres-Verdín, 2006, Peyret and Torres-Verdín, 2006). Moreover, horizontal layers can exhibit transverse isotropy in their elastic properties.

Numerical simulation is performed with a finite-difference discretization scheme in space and time of the velocity-stress wave equation in cylindrical coordinates. Perfectly matched layer absorbing boundary conditions are used to efficiently truncate the computational domain in space.

The Module includes a variety of options for entering elastic properties of the input media as well as a variety of options to select the location of sources and receivers, the types of source time wavelets, and the time interval for the simulations. In addition, there are several options for post-processing included in the toolbox that allow the user to plot the sonic traces, to normalize them, and to process them with the slowness-time coherence (STC) algorithm to detect propagation modes and to calculate their corresponding speeds (Chi et al, 2006). Finally, a number of options have been included in the toolbox to help the user check the consistency of the input parameters and to design the finite-difference mesh.

Great efforts have been made to include user-friendly commands and menus to guide the user in his/her simulations with this Module. However, the user is required to have some familiarity with the basics of numerical simulations that involve wave-equation phenomena. This knowledge is important to understand the quality, reliability, and stability of the simulations for specific choices of material properties, spatial discretization, time stepping, central frequency, initial simulation time, etc. It is strongly recommended that the user devotes some amount of time to gain familiarity with the sensitivity of the simulations to numerical and media parameters.

Computer programs that execute the sonic measurements are written in Fortran 90.

A flow chart for the Borehole Sonic Modeling Module© is included in the Appendix 5A section, as a quick reference for the modeling process.

### Borehole Nuclear Modeling Module©

The Borehole Nuclear Modeling Module© simulates gamma, neutron and density measurements for the case of multiple horizontal layers penetrated by a vertical well. Each horizontal layer can include several radial zones with different values of electrical conductivity. These piston-like radial variations of electrical conductivity are intended to describe the effect of axi-symmetric mud-filtrate invasion.

The module helps in interactively matching numerical simulations of the model designed and actual field nuclear logs. This helps in validating the earth model. Thus, the simulator gives us an improved assessment of the matrix components, invasion and shoulder bed effects.

The user initially defines generic beds in the model designed with significant variations in mineral/fluid composition. The simulator then uses a degree of randomness for performing simulations. It uses linear iterative refinement approximation which enables the accurate and rapid simulation of nuclear measurements. Thus, we get fast numerical simulation of nuclear logs in vertical wells in the presence of invasion with environmental corrections. The linear iterative refinement method accounts for variations of the response functions due to local perturbations of energy cross-section in the numerical simulation of neutron and density porosity logs.

Numerical simulation is performed with a new linear iterative refinement technique to accurately and rapidly simulate nuclear borehole measurements (Alberto Mendoza, and Carlos Torres-Verdín).

### Formation Evaluation Module©

The Formation Evaluation Module© is a two-dimensional cylindrical, two-phase (oil and water) simulator with visualization capabilities for interactive sensitivity analysis. It allows numerical simulations of water-base and oil-base mud-filtrate invasion, salt mixing, temperature, and well logging tool responses for single and multi-layer rock formations penetrated by a vertical well (Ramirez et al., 2005, Wu et al., 2004, 2005, Salazar et al., 2005, 2006 and 2007 and Malik et al, 2007a and 2007b).

The solution scheme of the finite-difference near-wellbore reservoir simulator is IMPES (implicitly in pressure and explicitly in saturation).

Computer programs that execute the reservoir fluid-flow simulation were written in Fortran 90 and C++.

Once the process of water-based or oil-based mud-filtrate invasion is simulated, the spatial distributions of electrical resistivity and sonic velocities become the input for the simulation of well-logging measurements (Chew et al, 1984, Zhang et al, 1995, 1999 and Wang and Torres-Verdín, 2006). Simulated results are described graphically in both time and space domains.

This measurement-based petrophysics toolbox can be used to validate the petrophysical consistency of standard interpretation methods. It also allows the quantification of the sensitivity of well logs to a variety of petrophysical and mud parameters.

### Formation Testing Module©

The Formation Testing Module© is an interactive, user-friendly software utility to simulate, design and diagnose formation-tester measurements acquired in a vertical well with a dual-packer acquisition configuration. Simulations are performed assuming a sequence of homogeneous and anisotropic horizontal beds subject to two-phase (oil and water) immiscible fluid flow. In addition, the simulations can take into account the process of water-based mud-filtrate invasion prior to the acquisition of formation-tester measurements (Wu et al., 2005 and Salazar et al., 2005, 2006). The user can appraise flexible configurations and dimensions of dual-packer transient measurements acquired with more than one pressure probe located at will (Lee et al., 2004 and Angeles et al., 2005). Likewise, the user can enter variable flow-rate time sequences to excite draw-down, build-up and injection pressure transients at the pressure probes.

Simulations are performed with a time-marching IMPES (implicitly in pressure and explicitly in saturation) finite-difference formulation. The user can enter arbitrary saturation-dependent capillary and relative-permeability curves to simulate both mud-filtrate invasion and fluid withdrawal through the packer section of the formation tester (Wu et al., 2005). Moreover, the simulated pressure transients can be compared to analytical (single-phase) solutions to verify the accuracy of conventional procedures used to estimate absolute permeability.

If desired, the user can choose to simulate the process of water-base mud-filtrate invasion to initialize the initial spatial distribution of fluid saturation and pressure prior to performing the simulation of pressure transients due to fluid withdrawal through the packer section of the formation tester. The module calculates pressure transients and spatial fluid and pressure distributions that are described graphically with conventional and non-conventional formats.

Computer programs that simulate fluid-flow and formation-tester measurements were written in Fortran 90, whereas the graphical user interface (GUI) was written in MATLAB® version 7.0.4.365 (R14). The user-friendly interface operates on any computer furbished with the above MATLAB® version.

The Formation Testing Module can be used to validate the petrophysical consistency of standard interpretation methods. It also allows the quantification of the sensitivity of dual-packer formation-tester measurements to a variety of petrophysical and mud parameters.

### Pore-Level Petrophysics Module©

The Pore-Level Petrophysics Module© (PLPM) provides an integrated platform to calculate fundamental macroscopic static and dynamic properties of porous media, including porosity, absolute permeability, formation factor, resistivity index, relative permeability, capillary pressure, and nuclear magnetic resonance (NMR) response. In addition, the Module can be used to construct compacted and cemented spherical-grain aggregates with a given grain-size distribution. Macroscopic petrophysical properties can be calculated from the constructed grain packs or from input high-resolution three dimensional (3D) digital images of actual rocks acquired with X-ray computed tomography (CT). Both CT and computer-generated images of reconstructed reservoir rock samples can be used as input (Jin et al, 2004, Jin, 2006, and Jin et al, 2007b) to the module for the assessment of macroscopic petrophysical properties. The spatial description of the grain pack or CT image is performed with variable-size Cartesian voxels.

Upon constructing the grain pack and determining the corresponding pore-space distribution, two-phase immiscible fluids are geometrically distributed into the pore space of the synthetic rock using percolation algorithms while enforcing capillary equilibrium. Subsequent simulations of petrophysical properties are carried out to calculate macroscopic resistivity index, capillary pressure, and relative permeability. These macroscopic petrophysical properties can be used to improve the interpretation of well-log measurements and the prediction of multiphase flow properties (Jin et al, 2007b, and Torskaya et al, 2007). Spatial distribution of two immiscible fluids in the pore space can also be performed directly on voxelized 3D CT images.

The Pore-Level Petrophysics Module© simulates pore-level single-phase fluid flow and electrical conduction by means of the lattice-Boltzmann method (Jin et al, 2004) and Diffusion Random Walks, respectively (Jin et al, 2007c). Generation of pore-level models and petrophysical calculations are made consistent with thin sections and 3D CT images via the following different simulators:

--DDM3D (Dynamic Depositional Model in 3D)©

--GPackA (Grain Pack Analysis: Discretization and Cementation)©

--VPerSim (Voxel-based Percolation Simulation)©

--GPerSim (Grain-based Percolation Simulation) ©

--LBSim3D (Lattice-Boltzmann Simulation in 3D)©

--RWSim3D (Random-Walk Simulation in 3D)©

--NMRSim (NMR Simulation) ©

--NMRT2 (NMR T2 inversion) ©

Each of these simulators is discussed in detail in this manual.

The DDM3D module generates random spherical grain packs for any given grain-size distribution by simulating the processes of grain sedimentation and compaction using the Distinct Element Method (Jin et al, 2003, and Jin, 2006). The GPackA module discretizes the grain pack and adds cement, thereby changing the grain shape (Jin et al, 2007a). The VPerSim and GPerSim modules determine the geometrical distribution of two immiscible fluids in the rock's pore space by simulating "drainage" and "imbibition" using the Ordinary and Invasion-Percolation algorithms (Silin et al, 2003, and Toumelin, 2006). The LBSim3D module simulates single-phase fluid flow through the pore space using the lattice-Boltzmann method (Jin et al, 2004). The RWSim3D module simulates electrical conduction using a random-walk technique (Jin et al, 2007c). The NMRSim module simulates NMR response in the rock samples (grain-based sample and voxel-based sample) using a random-walk technique (Toumelin, 2006, and Toumelin et al, 2007). Finally, the NMRT2 module inverts magnetization decays into their spectrum of T2 relaxation times based on curvature smoothing regularization (Chen et al, 1999, and Toumelin, 2002).

It is important that the user reads this manual before using the Pore-Level Petrophysics Module©. This chapter contains important information that a user needs to know when operating PLPM©. It introduces the interface and the procedures that should be followed to successfully operate the module.

Computer programs that execute the pore-level calculations of static and dynamic petrophysical properties are written in Fortran 90 (DDM3D, GPackA, LBSim3D and RWSim3D) and Visual C++ 2005 (GPerSim, VPerSim, NMRSim and NMRT2). The graphical user interface (GUI) is written in MATLAB R2007a.