Petrophysical inversion of borehole array-induction logs: Part I — Numerical examples

Geophysics ◽  
2006 ◽  
Vol 71 (4) ◽  
pp. F101-F119 ◽  
Author(s):  
Faruk O. Alpak ◽  
Carlos Torres-Verdín ◽  
Tarek M. Habashy
Keyword(s):  
Salt Concentration ◽  
Sensitivity Study ◽  
Absolute Permeability ◽  
Spatial Distributions ◽  
Layer By Layer ◽  
Fluid Saturation ◽  
Phase Saturation ◽  
Porosity And Permeability ◽  
Mud Filtrate ◽  
Induction Logs

We have developed a new methodology for the quantitative petrophysical evaluation of borehole array-induction measurements. The methodology is based on the time evolution of the spatial distributions of fluid saturation and salt concentration attributed to mud-filtrate invasion. We use a rigorous formulation to account for the physics of fluid displacement in porous media resulting from water-base mud filtrate invading hydrocarbon-bearing rock formations. Borehole array-induction measurements are simulated in a coupled mode with the physics of fluid flow. We use inversion to estimate parametric 1D distributions of permeability and porosity that honor the measured array-induction logs. As a byproduct, the inversion yields 2D (axial-symmetric) spatial distributions of aqueous phase saturation, salt concentration, and electrical resistivity. We conduct numerical inversion experiments using noisy synthetic wireline logs. The inversion requires a priori knowledge of several mud, petrophys-ical, and fluid parameters. We perform a systematic study of the accuracy and reliability of the estimated values of porosity and permeability when knowledge of such parameters is uncertain. For the numerical cases considered in this paper, inversion results indicate that borehole electromagnetic-induction logs with multiple radial lengths of investigation (array-induction logs) enable the accurate and reliable estimation of layer-by-layer absolute permeability and porosity. The accuracy of the estimated values of porosity and permeability is higher than 95% in the presence of 5% measurement noise and 10% uncertainty in rock-fluid and mud parameters. However, for cases of deep invasion beyond the radial length of investigation of array-induction logging tools, the estimation of permeability becomes unreliable. We emphasize the importance of a sensitivity study prior to inversion to rule out potential biases in estimating permeability resulting from uncertain knowledge about rock-fluid and mud properties.

Petrophysical inversion of borehole array-induction logs: Part II — Field data examples

Geophysics ◽  
2006 ◽  
Vol 71 (5) ◽  
pp. G261-G268 ◽  
Author(s):  
Carlos Torres-Verdín ◽  
Faruk O. Alpak ◽  
Tarek M. Habashy
Keyword(s):  
Electromagnetic Induction ◽  
Layer By Layer ◽  
Laboratory Measurements ◽  
Inversion Algorithm ◽  
Vertical Wells ◽  
Gas Field ◽  
Rock Formations ◽  
Resistivity Logs ◽  
Porosity And Permeability ◽  
Induction Logs

We describe the application of Alpak et al.’s (2006) petrophysical inversion algorithm to the interpretation of borehole array induction logs acquired in an active North American gas field. Layer-by-layer values of porosity and permeability were estimated in two closely spaced vertical wells that penetrated the same horizontal rock formation. The wells were drilled with different muds and overbalance pressures, and the corresponding electromagnetic induction logs were acquired with different tools. Rock-core laboratory measurements available in one of the two wells were used to constrain the efficiency of gas displacement by water-based mud during the process of invasion. Estimated values of porosity and permeability agree well with measurements performed on rock-core samples. In addition to estimating porosity and permeability, the petrophysical inversion algorithm provided accurate spatial distributions of gas saturation in the invaded rock formations that were not possible to obtain with conventional procedures based solely on the use of density and resistivity logs.

Effects of Surfactant-Emulsified Oil-Based Mud on Borehole Resistivity Measurements

SPE Journal ◽  
2011 ◽  
Vol 16 (03) ◽  
pp. 608-624 ◽  
Author(s):  
Jesús M. Salazar ◽  
Carlos Torres-Verdín ◽  
Gong Li Wang
Keyword(s):  
Electrical Resistivity ◽  
Spatial Distribution ◽  
Sensitivity Analyses ◽  
High Resistivity ◽  
Reliable Estimate ◽  
Spatial Distributions ◽  
Oil Viscosity ◽  
Resistivity Measurements ◽  
Fluid Saturation ◽  
Mud Filtrate

Summary We quantify the influence of oil-based mud (OBM)-filtrate invasion and formation-fluid properties on the spatial distribution of fluid saturation and electrical resistivity in the near-wellbore region. The objective is to appraise the sensitivity of borehole resistivity measurements to the spatial distribution of fluid saturation resulting from the compositional mixing of OBM and in-situ hydrocarbons. First, we consider a simple two-component formulation for the oil phase (OBM and reservoir oil) wherein the components are first-contact miscible. A second approach consists of adding water and surfactant to a multicomponent OBM invading a formation saturated with multiple hydrocarbon components. Simulations also include presence of irreducible, capillary-bound, and movable water. The dynamic process of OBM invasion causes component concentrations to vary with space and time. In addition, the relative mobility of the oil phase varies during the process of invasion because oil viscosity and oil density are both dependent on component concentrations. Presence of surfactants in the OBM is simulated with a commercial adaptive implicit compositional formulation that models the flow of three-phase multicomponent fluids in porous media. Simulations of the process of OBM invasion yield 2D spatial distributions of water and oil saturation that are transformed into spatial distributions of electrical resistivity. Subsequently, we simulate the corresponding array-induction measurements assuming axial-symmetric variations of electrical resistivity. We perform sensitivity analyses on field measurements acquired in a well that penetrates a clastic formation and that includes different values of density and viscosity for mud filtrate and formation hydrocarbon. These analyses provide evidence of the presence of a high-resistivity region near the borehole wall followed by a low-resistivity annulus close to the noninvaded resistivity region. Such an abnormal resistivity annulus is predominantly caused by high viscosity contrasts between mud filtrate and formation oil. The combined simulation of invasion and array-induction logs in the presence of OBM invasion provides a more reliable estimate of water saturation, which improves the assessment of in-place hydrocarbon reserves.

scholarly journals Fluid Saturation Predictions in a “Transition Zone” Carbonate Reservoir, Abu Dhabi

GeoArabia ◽  
1996 ◽  
Vol 1 (4) ◽  
pp. 551-566
Author(s):  
Anthony Kirkham ◽  
Mohamed Bin Juma ◽  
Tilden A.M. McKean ◽  
Anthony F. Palmer ◽  
Michael J. Smith ◽  
...  
Keyword(s):  
Transition Zone ◽  
Free Water ◽  
Analysis Data ◽  
Carbonate Reservoir ◽  
Rock Types ◽  
Fluid Saturation ◽  
Porosity And Permeability ◽  
Capillary Pressures ◽  
Seismic Amplitudes ◽  
Low Amplitude

ABSTRACT The field is a low amplitude structure with a chalky, Lower Cretaceous, Thamama reservoir characterised by a large hydrocarbon transition zone. Porosity generally decreases with depth within the trap although porosity versus depth trends are skewed by tilting. Porosity and permeability mapping was therefore achieved using templates based on seismic amplitudes. Special core analysis data were used to construct algorithms of Leverett J functions versus saturation for a variety of rock types mapped throughout the 3-D geological model of the field. The templated poroperms were then combined with capillary pressures to predict fluid saturations from these algorithms. The modelling of fluid distributions was therefore dependent upon heterogeneities imposed by the rock fabrics. Calibrating the model-predicted saturations against log-derived saturations at the wells involved regression techniques which were complicated by: notional structural tilting of the free water level, imbibition, hysteresis and permeability averaging procedures. Filtered “stick displays” proved useful in assessing the quality of the calibrations and were invaluable tools for highlighting and investigating data anomalies.

Quantitative comparison of processes of oil- and water-based mud-filtrate invasion and corresponding effects on borehole resistivity measurements

Geophysics ◽  
2009 ◽  
Vol 74 (1) ◽  
pp. E57-E73 ◽  
Author(s):  
Jesús M. Salazar ◽  
Carlos Torres-Verdín
Keyword(s):  
Electrical Resistivity ◽  
Flow Rate ◽  
Water Saturation ◽  
Base Case ◽  
Petrophysical Properties ◽  
Resistivity Measurements ◽  
Fluid Saturation ◽  
Mud Cake ◽  
Water Based ◽  
Mud Filtrate

Some laboratory and qualitative studies have documented the influence of water-based mud(WBM)-filtrate invasion on borehole resistivity measurements. Negligible work, however, has been devoted to studying the effects of oil-based mud(OBM)-filtrate invasion on well logs and the corresponding impact on the estimation of petrophysical properties. We quantitatively compare the effects of WBM- and OBM-filtrate invasion on borehole resistivity measurements. We simulate the process of mud-filtrate invasion into a porous and permeable rock formation assuming 1D radial distributions of fluid saturation and fluid properties while other petrophysical properties remain constant. To simulate the process of mud-filtrate invasion, we calculate a time-dependent flow rate of OBM-filtrate invasion by adapting the available formulation of the physics of WBM-filtrate invasion. This approach includes the dynamically coupled effects of mud-cake growth and multiphase filtrate invasion. Simulations are performed with a commercial adaptive-implicit compositional formulation that enables the quantification of effects caused by additional components of mud-filtrate and native fluids. The formation under analysis is 100% water saturated (base case) andis invaded with a single-component OBM. Subsequently, we perform simulations of WBM filtrate invading the same formation assuming that it is hydrocarbon bearing, and compare the results to those obtained in the presence of OBM. At the end of this process, we invoke Archie’s equation to calculate the radial distribution of electrical resistivity from the simulated radial distributions of water saturation and salt concentration and compare the effects of invasion on borehole resistivity measurements acquired in the presence of OBM and WBM. Simulations confirm that the flow rate of OBM-filtrate invasion remains controlled by the initial mud-cake permeability and formation petrophysical properties, specifically capillary pressure and relative permeability. Moreover, WBM causes radial lengths of invasion 15%–40% larger than those associated with OBM as observed on the radial distributions of electrical resistivity. It is found also that, in general, flow rates of WBM-filtrate invasion are higher than those of OBM-filtrate invasion caused by viscosity contrasts between OBM filtrate and native fluids, which slow down the process of invasion. Such a conclusion is validated by the marginal variability of array-induction resistivity measurements observed in simulations of OBM invasion compared with those of WBM invasion.

Estimation of Dry-Rock Elastic Moduli Based on the Simulation of Mud-Filtrate Invasion Effects on Borehole Acoustic Logs

2009 ◽  
Vol 12 (06) ◽  
pp. 898-911 ◽  
Author(s):  
Tobiloluwa B. Odumosu ◽  
Carlos Torres-Verdín ◽  
Jesús M. Salazar ◽  
Jun Ma ◽  
Benjamin Voss ◽  
...  
Keyword(s):  
Bulk Modulus ◽  
Shear Wave ◽  
Elastic Properties ◽  
Elastic Moduli ◽  
Compressional Wave ◽  
Shear Rigidity ◽  
Spatial Distributions ◽  
Wave Velocities ◽  
Shear Wave Velocities ◽  
Mud Filtrate

Summary Reliable estimates of dry-rock elastic properties are critical to the accurate interpretation of the seismic response of hydrocarbon reservoirs. We describe a new method for estimating elastic moduli of rocks in-situ based on the simulation of mud-filtrate invasion effects on resistivity and acoustic logs. Simulations of mud-filtrate invasion account for the dynamic process of fluid displacement and mixing between mud-filtrate and hydrocarbons. The calculated spatial distributions of electrical resistivity are matched against resistivity logs by adjusting the underlying petrophysical properties. We then perform Biot-Gassmann fluid substitution on the 2D spatial distributions of fluid saturation with initial estimates of dry-bulk (kdry) modulus and shear rigidity (µdry) and a constraint of Poisson's ratio (?d) typical of the formation. This process generates 2D spatial distributions of compressional and shear-wave velocities and density. Subsequently, sonic waveforms are simulated to calculate shear-wave slowness. Initial estimates of the dry-bulk modulus are progressively adjusted using a modified Gregory-Pickett (1963) solution of Biot's (1956) equation to estimate a shear rigidity that converges to the well-log value of shear-wave slowness. The constraint on dynamic Poisson's ratio is then removed and a refined estimate of the dry-bulk modulus is obtained by both simulating the acoustic log (monopole) and matching the log-derived compressional-wave slowness. This technique leads to reliable estimates of dry-bulk moduli and shear rigidity that compare well to laboratory core measurements. Resulting dry-rock elastic properties can be used to calculate seismic compressional-wave and shear-wave velocities devoid of mud-filtrate invasion effects for further seismic-driven reservoir-characterization studies.

Fluid sensitivity study of elastic parameters in low-medium porosity and permeability reservoir rocks

2010 ◽  
Vol 7 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Fa-Gen Pei ◽  
Chang-Chun Zou ◽  
Tao He ◽  
Ge Shi ◽  
Gen-Gen Qiu ◽  
...  
Keyword(s):  
Sensitivity Study ◽  
Elastic Parameters ◽  
Reservoir Rocks ◽  
Porosity And Permeability ◽  
Medium Porosity

Streamline-based integration of time-lapse seismic and production data into petroleum reservoir models

Geophysics ◽  
2012 ◽  
Vol 77 (6) ◽  
pp. M73-M87 ◽  
Author(s):  
Alvaro Rey ◽  
Eric Bhark ◽  
Kai Gao ◽  
Akhil Datta-Gupta ◽  
Richard Gibson
Keyword(s):  
High Resolution ◽  
Finite Difference ◽  
Seismic Data ◽  
Time Lapse ◽  
Seismic Inversion ◽  
Absolute Permeability ◽  
Production Data ◽  
Petroleum Reservoir ◽  
Seismic Surveys ◽  
Fluid Saturation

We have developed an efficient approach of petroleum reservoir model calibration that integrates 4D seismic surveys together with well-production data. The approach is particularly well-suited for the calibration of high-resolution reservoir properties (permeability) because the field-scale seismic data are areally dense, whereas the production data are effectively averaged over interwell spacing. The joint calibration procedure is performed using streamline-based sensitivities derived from finite-difference flow simulation. The inverted seismic data (i.e., changes in elastic impedance or fluid saturations) are distributed as a 3D high-resolution grid cell property. The sensitivities of the seismic and production surveillance data to perturbations in absolute permeability at individual grid cells are efficiently computed via semianalytical streamline techniques. We generalize previous formulations of streamline-based seismic inversion to incorporate realistic field situations such as changing boundary conditions due to infill drilling, pattern conversion, etc. A commercial finite-difference flow simulator is used for reservoir simulation and to generate the time-dependent velocity fields through which streamlines are traced and the sensitivity coefficients are computed. The commercial simulator allows us to incorporate detailed physical processes including compressibility and nonconvective forces, e.g., capillary pressure effects, while the streamline trajectories provide a rapid evaluation of the sensitivities. The efficacy of our proposed approach was tested with synthetic and field applications. The synthetic example was the Society of Petroleum Engineers benchmark Brugge field case. The field example involves waterflooding of a North Sea reservoir with multiple seismic surveys. In both cases, the advantages of incorporating the time-lapse variations were clearly demonstrated through improved estimation of the permeability heterogeneity, fluid saturation evolution, and swept and drained volumes. The value of the seismic data integration was in particular proven through the identification of the continuity in reservoir sands and barriers, and by the preservation of geologic realism in the calibrated model.

scholarly journals On the consistency of scale among experiments, theory, and simulation

2017 ◽  
Vol 21 (2) ◽  
pp. 1063-1076 ◽  
Author(s):  
James E. McClure ◽  
Amanda L. Dye ◽  
Cass T. Miller ◽  
William G. Gray
Keyword(s):  
Capillary Pressure ◽  
Fluid Phase ◽  
Interfacial Area ◽  
Simulation Method ◽  
Flow In Porous Media ◽  
State Function ◽  
State Equations ◽  
Fluid Saturation ◽  
Phase Saturation ◽  
Two Fluid

Abstract. As a tool for addressing problems of scale, we consider an evolving approach known as the thermodynamically constrained averaging theory (TCAT), which has broad applicability to hydrology. We consider the case of modeling of two-fluid-phase flow in porous media, and we focus on issues of scale as they relate to various measures of pressure, capillary pressure, and state equations needed to produce solvable models. We apply TCAT to perform physics-based data assimilation to understand how the internal behavior influences the macroscale state of two-fluid porous medium systems. A microfluidic experimental method and a lattice Boltzmann simulation method are used to examine a key deficiency associated with standard approaches. In a hydrologic process such as evaporation, the water content will ultimately be reduced below the irreducible wetting-phase saturation determined from experiments. This is problematic since the derived closure relationships cannot predict the associated capillary pressures for these states. We demonstrate that the irreducible wetting-phase saturation is an artifact of the experimental design, caused by the fact that the boundary pressure difference does not approximate the true capillary pressure. Using averaging methods, we compute the true capillary pressure for fluid configurations at and below the irreducible wetting-phase saturation. Results of our analysis include a state function for the capillary pressure expressed as a function of fluid saturation and interfacial area.

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