3D geostatistical porosity modelling: A case study at the Saint-Flavien CO 2 storage project

3D geostatistical porosity modelling: A case study at the Saint-Flavien CO 2 storage project Maxime Claprood Institut national de la recherche scientifique, Québec, Canada Earth Modelling 2013 October 21, 2013

Thanks to our partners : Thanks to co-authors and collaborators : E. Gloaguen M.J. Duchesne D. Leavy M. Sauvageau E. Konstantinovskaya P. Doyen B. Giroux A. Achour R. Moyen M. Malo F. Badina

Thanks to for inviting me at this workshop and giving me the opportunity to present this work.

Objectives: Optimize the integration of well logs with 3D seismic cube to assess the porosity in the Saint-Flavien gas reservoir by geostatistical simulations. Adapt the Bayesian simulations workflow to deal with the lowporosity / complex geological environment of the Saint-Flavien reservoir. Evaluate the CO 2 storage potential of the Saint-Flavien reservoir under geological uncertainty.

Outline of presentation 1. What s special at the Saint-Flavien reservoir? 2. What kind of geophysical data is available? 3. What is the methodology to assess the porosity in the reservoir model? 4. Results: Porosity distribution and its uncertainty; Connectivity analysis; CO 2 storage potential at Saint-Flavien.

What s so special at Saint-Flavien? Québec City Montréal Saint-Flavien

What s so special at Saint-Flavien? NW Saint-Flavien reservoir SE 10 km from Castonguay et al. (2006)

What s so special at Saint-Flavien? Gas reservoir within a fold-thrust belt in the middle unit of Lower Ordovician Beekmantown Group, at an average depth of 1500m. Main reservoir in zone B1, mostly dolomitic. Porosity controlled by fractures. Other porous zones are known to exist, notably in zone C. Model porosity in zones A - B - C.

Geophysical data available 3D seismic amplitude cube : 4.9 x 3.9 km 2 3D deterministic Acoustic Impedance (AI) cube : 3.7 x 2.7 km 2 Total of 19 wells in Saint-Flavien. 11 wells with AI & porosity logs in the region to model. Wells logs are converted in TWT using Time-Depth Conversion algorithm of SKUA.

Geophysical data available Well logs are upscaled at the grid resolution using the Upscaling functions in SKUA. N

Geophysical data available Modeling is completed on 3D grid, but results will be presented on 2D profiles for visualization purpose: 3D seismic amplitude cube (a, b) 3D deterministic AI cube (c, d)

Methodology to model the porosity Methodology used is the Sequential Gaussian Simulations with a Bayesian Approach (BSS). Geostatistical method to estimate porosity, using AI and porosity logs and 3D AI cube inverted from seismic amplitude data. BSS uses the statistical relationship between AI and porosity, well defined in most sandstone reservoirs of moderate to high porosity. Potential reservoirs for CO 2 injection in Québec have low average porosity, with localised fractured zones of higher porosity: we are at the limits of resolution of the statistical relation between AI and porosity.

Methodology to model the porosity Porosity is known at 11 well logs. Porosity is simulated sequentially at 777 177 grid cells of the Saint- Flavien reservoir model. Cells size is: 20m x 20m x 2ms. Porosity value is drawn at each cell of the 3D grid from an a posteriori distribution, considering: a priori information from well logs and previously simulated points; the AI value read from the seismic derived AI cube and; the identified relation between porosity and AI.

BSS - Workflow BSS scheme as applied in Saint- Flavien.

BSS Step 1. at cell n, read the AI value from the seismic grid. (AI n = 15890 m s -1 g cm -3 )

BSS Step 1. Important principle behind BSS: AI values evaluated on seismic cube agree well with AI values computed on well logs. Lower vertical resolution of deterministic AI cube. This has a smoothing effect on AI values, inducing an important bias.

BSS Step 1. Histograms of AI AI from well logs AI from Det. AI cube Red lines are mean AI σ 1from well logs.

BSS Step 1. 3 petrophysical families could be identified from well logs and 2D PDF (AI vs Phi). We assign a family to all cells of the AI cube with respect to their AI value. Family 1: clean limestone with minor dolomite content. AI from well logs AI from Det. AI cube Red lines are mean AI σ 1from well logs.

BSS Step 1. 3 petrophysical families could be identified from well logs and 2D PDF (AI vs Phi). We assign a family to all cells of the AI cube with respect to their AI value. Family 1: clean limestone with minor dolomite content. AI from well logs AI from Det. AI cube Family 2: high dolomite content. Red lines are mean AI σ 1from well logs.

BSS Step 1. 3 petrophysical families could be identified from well logs and 2D PDF (AI vs Phi). We assign a family to all cells of the AI cube with respect to their AI value. Family 1: clean limestone with minor dolomite content. AI from well logs AI from Det. AI cube Family 2: high dolomite content. Family 3: high shale content Red lines are mean AI σ 1from well logs.

BSS Step 1 (Stochastic Seismic Inversion) Objective of SSI: Increase the vertical resolution of AI by generating numerous high-frequency AI cubes honouring: Seismic amplitude traces, Low-frequency initial AI cube (Deterministic AI cube), AI well logs. Inversions are completed on stratigraphic grid, using GeoSI (an application developed by CGG Veritas which runs on the GOCAD/SKUA platform). Horizons limiting the top and bottom of reservoir are used to focus the inversion on the reservoir level. SSI algorithm based on sequential Gaussian simulations.

BSS Step 1 (Stochastic Seismic Inversion) Complete several global realisations of high-frequency AI cube.

BSS Step 1 (Stochastic Seismic Inversion) AI from well logs AI from Det. cube AI from SSI cube Family 1 + Family 2 + Family 3 Red lines are mean AI σ 1from well logs.

BSS Step 1. at cell n, read the AI value from the seismic grid. (AI n = 15890 m s -1 g cm -3 )

BSS Step 2. In this low-porosity environment, it is hard to imagine how we could identify these 3 petrophysical families from this graph only!!

BSS Step 2. By completing a normal-score transform on the porosity data, we could better define the petrophysical families on the 2D PDF. NS

BSS Step 2. In this low-porosity environment, it is hard to imagine how we could identify these 3 petrophysical families from this graph only!!

BSS Step 3. Probability to draw values of porosity from kriging mean and kriging variance, using initial porosity data from well logs, and previously simulated cells. Variograms are computed in the Spatial Data Analysis application of SKUA. Porosity well logs 0% 5%

BSS Step 3. Porosity well logs 0% high

BSS Step 4. Probability to draw all possible values of porosity with respect to AI = 15 890 read from AI cube at cell n.

BSS Step 5. A posteriori distribution is a compromise between kriging and likelihood. Distribution from kriging at Step 3. Likelihood computed at Step 4.

BSS Step 6. We go back to step 1, we start over at cell n+1 for all 777 177 cells of the Saint-Flavien s model. And we ran the whole algorithm 250 times to get multiple realisations of the porosity field in Saint-Flavien.

Results - Porosity Distribution 3 realisations of the porosity field of the Saint-Flavien reservoir

Results - Porosity Distribution (a-b) Probability of exceeding 2% cut-off porosity. (c-d) Probability of exceeding 1% cut-off porosity. (e-f) Probability of exceeding 1% cut-off porosity and belonging to Family 3 less than 50%.

Results Connectivity Analysis Porous and connected pockets computed on realizations of porosity A B C. Connected porous pockets of porosity higher than 1% and cells not belonging to Family 3. Computed using the Reservoir Data Analysis workflow from SKUA. Surface connectivity considered here other options exist (edge, volume).

Results - CO 2 Storage Potential Using the connected pore volume computed for realizations A B C shown in previous slide, we compute the CO 2 storage potential and efficiency factor of the Saint-Flavien reservoir. We follow the standard of The 2012 North American Carbon Storage Atlas. G = V F (1 S ) r CO2 - w E G CO2 = total mass of CO 2 possible to inject; V ϕ = connected pore volume; S w = water saturation; ρ = CO 2 density at reservoir level and; E = CO 2 storage efficiency factor (connected pore volume divided by the total pore volume of each realization). Computations are made for the limits of the 3D numerical model of the Saint- Flavien reservoir and should not be extrapolated.

Results - CO 2 Storage Potential Model Total Mass of CO 2 (G CO2 Mt ) Storage Efficiency Factor (E - %) Average porosity in Connected Pore Volume ( Φ - % ) A 1.03 26.8 1.40 B 1.65 31.0 1.44 C 2.50 36.2 1.39

Conclusions The BSS algorithm could effectively be adapted to evaluate the porosity distribution in the low porosity / complex geology environment of the Saint- Flavien reservoir. The use of SKUA was very efficient to generate the 3D grid, and integrate all kinds of geophysical data (3D seismic cube, 3D AI cubes obtained by SSI, AI and porosity well logs). The uncertainty and variability of the porosity field can be appreciated by comparing different realizations, and computing probability of exceeding different cut-off porosities. Connectivity analysis and CO 2 storage potential are completed on each realization separately, giving minimum, maximum, and mean expected value on the potential of CO 2 storage in Saint-Flavien.

SSI BSS - Methodology Step 1 (Stochastic Seismic Inversion) 1.1 Define a random path to visit all surface nodes (x,y) of the seismic grid. node (x,y)

BSS Step 1 (Stochastic Seismic Inversion) 1.2 At every surface node, generate several local realisations of high-frequency AI traces by SGS. Initial low-frequency AI cube (Det AI), and a priori geostatistical model from AI logs and previously simulated AI traces guide the inversion with their own level of confidence.

BSS Step 1 (Stochastic Seismic Inversion) 1.2 At every surface node, generate several local realisations of high-frequency AI traces by SGS. Initial low-frequency AI cube (Det AI), and a priori geostatistical model from AI logs and previously simulated AI traces guide the inversion with their own level of confidence. Initial Det. AI trace at node (x,y) 5 realisations of high-frequency AI trace at node (x,y)

BSS Step 1 (Stochastic Seismic Inversion) 1.3 Convolve local high-frequency AI traces with seismic wavelet to obtain highfrequency seismic traces. * =

BSS Step 1 (Stochastic Seismic Inversion) 1.4 Keep best high-frequency seismic trace which becomes conditioning data for the next surface node to invert. Go back to Step 2 for next node, until all nodes are visited. Initial seismic trace at node (x,y) 5 realisations of highfrequency seismic trace at node (x,y) We keep best fitting trace at node (x,y).