Micro-Structural Rock Modeling: Methodology and Application

in Formation Evaluation

Guodong Jin1, Chun Lan1, Wei Shao1, and Songhua Chen1, 2

1Baker Hughes Incorporated, Houston, Texas, USA

2 Now at Halliburton, Houston, Texas, USA

ABSTRACT

We present an integrated micro-structural rock modeling approach from the first principles to reconstruct a representative rock model of an earth formation for each depth of interest. The reconstructed model is constrained by formation parameters derived from logging measurements and is used to determine rock macroscopic properties that are not measured directly from well logs. Our modeling approach simulates the way the clastic rock formed over millions of years, with periods of grain sedimentation, compaction and diagenesis. The input parameters including the density, porosity, grain mineralogy, grain size distribution, cement and clay content, are derived directly or indirectly from downhole logging measurements and/or geological data. For illustrations, we apply this technique to reservoir core samples and one field well data. The predicted rock permeability is compared with laboratory measurements. The proposed methodology is robust and inexpensive, which can be used routinely to make quantitative predictions of petrophysical properties of reservoir rocks. In addition, this approach can be used by geoscientists to explain log responses and their sensitivity to various controlling factors.

Keywords: Rock model, microstructure, sedimentation, compaction, diagenesis, absolute permeability, formation evaluation, log measurement

INTRODUCTION

The microstructure of a reservoir rock and the physical characteristics of the solid and the fluids occupying the pore space jointly determine its transport, electric, and mechanical properties. The relation between rock geometric microstructure and macroscopic properties is an open fundamental problem whose solution is important to many applications ranging from oil and gas production to polymer physics and material science [1].

Theoretically, macroscopic properties can be derived by numerically solving the governing differential equations, such as Stokes’ or Laplace’s equation, directly on an accurate three-dimensional (3D) representation of the

rock microstructure. There are several ways in which a 3D description of rock pore space can be obtained. Interested readers are referred to papers [2-4] and the references therein for the details of these approaches. Here, we briefly describe two methods of reconstructing the rock microstructure: direct imaging technique and micro-structural rock modeling (or pore-scale modeling) method.

Direct 3D imaging techniques now enable one to accurately describe the complex microstructure of reservoir rocks via X-ray micro-computed tomography (micro-CT) [5, 6]. It consists of a large number of 2D tomographic slices that are collected together to create a 3D representation of real rock. Although there is a growing interest in using these techniques from the oil/gas industry, complications still exist to prevent them from routine use: The technology is still not readily available and it requires rock samples, which are not always available for each well and/or each depth due to the slow and expensive operation of downhole coring. Imaging the samples is also time-consuming and expensive. In practice, the main drawback of such techniques is not so much technical as temporal.

As an alternative, micro-structural rock modeling approaches, which create numerical rock models via simulation of various geologic processes involved in forming the rock (sedimentation, compaction, cementation, etc), have become increasingly attractive. These simulation techniques have the advantages of low cost and high speed, as well as their ability to overcome the present resolution constraints of experiments [1, 3, 7]. However, the necessary input data required for the modeling processes, such as the porosity, grain size distribution, mineralogy, and diagenetic features, are usually derived from core/thin section analysis or from detailed knowledge of the geologic history of each particular formation. Such requirements make it impossible to apply the modeling approaches practically and applicably on a continuous scale, such as downhole logging interpretation.

This paper presents an integrated modeling technique to reconstruct a relevant pore geometric model of rock at each depth of interest. Similar to other modeling techniques [1, 3, 7], this approach simulates the way the

clastic rock formed over millions of years, with periods of grain sedimentation, compaction and diagenesis. However, all input parameters including the density, porosity, grain mineralogy, grain size distribution, cement and clay content, are obtained directly or indirectly from logging measurements and/or geological information. This will eventually reduce or eliminate the need for cutting cores. In addition, efficient algorithms are developed to reduce the computational cost, thus making this technique practical and applicable for downhole logging interpretation. In the following, we first describe the methodology of reconstructing the clastic rock model. Then, we give two examples to illustrate its application in formation evaluation. The computed permeabilities of modeled rocks are compared to laboratory measurements performed on the corresponding core samples.

SIMULATION METHODOLOGY

Sedimentary rock is formed as a result of several complex processes: source rock fragmentation, sediment transport and erosion, sedimentation, compaction, and diagenesis. When the energy of a transporting medium becomes too low, sediments deposit [8]. Once deposited, the sediments are compacted. Later, water flows through the deposited sedimentary bed dissolving, nucleating, and growing solid materials by the processes summarily called diagenesis [9]. Diagenetic alteration usually cements the discrete grains of a sediment into a solid rock. It is extremely difficult, if not impossible, to simulate these dynamic rock-forming processes in detail. Instead, we only model the end result of these processes. Sedimentation

Sedimentation is the process of deposition of rock grains (or sediments) transported by air, water, wind, etc. Deposition occurs when the forces responsible for sediment transportation are no longer sufficient to overcome the forces of grain weight and friction, creating a resistance to motion. The end-result of sedimentation is an initial sediment (or grain packing) of clastic rocks.

We developed an efficient algorithm to generate the initial sediment of clastic rocks with spherical grains and variable size distribution. Spherical grain packings are usually used to represent the granular media and/or provide a basis for the reconstruction of sedimentary rock. The algorithm simulates the ‘dynamic’ process of grain sedimentation under gravity at a very slow settling velocity. First, grains are generated according to a given grain size distribution, which can be obtained or estimated from the laboratory test, geological setting, or nuclear-magnetic-resonance (NMR) log measurement

[10]. Figure 1 shows an example of (a) NMR T2

distribution obtained from downhole measurements at the depth of 1205.25 ft for the Johnson City Stribling #3 well (shown later), and (b) the corresponding grain size distribution derived from T2 distribution. To mimic the stochastic nature of grain deposition, the generated grains are then randomly selected and deposited (one at a time) from random locations above an existing bed of grains. They are allowed to settle down, roll over, or penetrate through the bed until they reach a stable location.

(a) NMR T2 distribution

(b) Grain size distribution

Figure 1: (a) Measured NMR T2 distribution at the depth of 1205.25 ft of Johnson City Stribling #3 well (shown later); (b) Grain size distribution derived from NMR T2 distribution shown in (a).

Note that this scheme ignores the translations and rotations of rock grains and the dynamic interaction among these grains. Also, it does not involve physical forces explicitly. However, this approach is very computationally efficient (less than a minute) compared with the complicated distinct-element-based algorithm (~hours), which explicitly takes into account the grain shapes, along with the forces and their moments [1, 11]. Figure 2 shows the computer-generated initial sediment

(or grain packing) from the grain size distribution shown in Figure 1 for the formation at the depth of 1205.25 ft. It comprises of 25.3% quartz and 60.6% K-feldspar (as mass percentages in total solid material), which are derived from FLeXTM downhole measurements. The packing dimension is 0.65 mm × 0.65 mm × 0.65 mm and the number of grains is 11451. The packing porosity is about 34.5%. The time of generating the packing is 57 seconds on a computer whose configuration is Intel(®) Core(TM) 2 Duo CPU, T7250 @ 2.00 GHZ, 1.99GHZ, 2.00 GB of RAM.

Figure 2: Computer-generated initial grain packing for the formation at the depth of 1205.25 ft of Johnson City Stribling #3 well. Colors denote the grain mineralogy

Compaction

Compaction reduces rock bulk volume in response to the applied stress and is an important agent of porosity reduction in sandstones undergoing burial. Compaction forces grains to move closer together, thereby reducing pore space and pressing out some of the contained air and water.

Considering the practical requirement of computation speed in log interpretation, we model the result of compaction using a linear process similar to that described in Ref [7]. The vertical coordinate of every sand grain is shifted downwards according to the formula

( )zzz λ−= 10 (1)

where z is the new vertical position and z0 is the original

one. The compaction factor zλ is determined by

2

0

01 cc c

z +−

=φ

φφλ (2)

Here, 1c and 2c are constants; 0φ is the initial

porosity of the grain packing; cφ is the porosity after

compaction that can be estimated indirectly from a given

depth and pore pressure. In addition, the value of cφ

must be constrained by the condition: the pore space after compaction must be large enough to hold all diagenetic cements and clays including the micro pore space among them. In the modeling, we assume that rock early porosity loss is completely caused by compaction only. Diagenesis Diagenesis turns an unconsolidated loose sediment into a rock. It involves all physical, chemical and biochemical processes that affect sediments between the time of deposition and metamorphism. Diagenesis mainly includes two types of processes: cementation and authigenesis [12]. Depending on minerals and specific geological settings, various styles of cementation patterns occurs in nature. Figure 3 shows several major diagenetic features considering in the modeling, such as cement overgrowth, pore-filling, pore-lining, and pore-bridging [13].

Figure 3: Schematic diagram of different diagenetic patterns occurring in nature [13].

In the simulation, cement overgrowth is modeled using the algorithm described in Ref [1], which accounts for the effect of grain size and pore space restriction on the rate of cement growth. Pore-lining or -bridging clays are simulated by randomly and uniformly precipitating them on the exposed grain surfaces. Pore-filling cement or clays are modeled by completely filling randomly selected pores within the rock. Note that the solid volume of clay/cement is derived from downhole mineral tool measurement, and the amount of microporosity is estimated from NMR tool measurement. In addition, it is critical to separate diagenetic clays from detrital (structural) clays. Otherwise, microporosity might be overestimated. Figure 4 shows part of the simulated rock sample after different cements/clays are deposited within the rock pore space for the formation at the depth of 1205.25 ft of Johnson City Stribling #3 well. It comprises 25.3% quartz and 60.6% K-feldspar, 4.2% siderite, and 9.9% chlorite (as mass percentages in total solid material),

which are derived from FLeX downhole measurements. The porosity of the simulated sample is 10.19% while the measured NMR porosity is 10.21%.

Figure 4: Digital image of the modeled rock sample for the formation at the depth of 1205.25 ft of Johnson City Striling #3 well. Colors denote different mineralogy for grains, cement and clay.

APPLICATION

In this section, we apply our numerical simulation methods to reconstruct rock models for two different application cases: 34 sandstone core samples from a diversity of geologic settings, and one field well data. The absolute permeability of the rock models is computed using the lattice-Boltzmann-based flow simulation algorithm [4, 14]. Simulation results are compared to laboratory measurements performed on the corresponding core samples.

Core samples

The proposed methodology is first tested on clastic core samples from a diversity of geologic settings. We selected 34 sandstone samples from our Shell Catalog database. Laboratory study was previously conducted in detail on these samples to determine their compositional, textural and petrophyiscal properties. The measured properties include grain size distribution, mineralogy, porosity, permeability, and so on. Figure 5 shows the quartz, feldspar, and cement/clay weight percentage in the ternary diagram for all 34 selected samples. Using the measured grain size distribution and X-ray diffraction mineralogy, both of which by analog can be directly or indirectly determined from downhole measurements, we reconstruct numerical rocks and calculate their permeability. Two different schemes are used to account for the effect of clay minerals and cements on rock models and their petrophysical properties:

1. Pore Network Model (PNM): the void space of a grain packing is first approximated by a network of spherical pores connected by cylindrical flow channels. The effect of clay and cement is then taken into account in the computation of rock flow properties. Note that in PNM clay/cement is not ‘physically’ introduced in the pore space of rock models.

2. Clastic Rock Model, Sphere (CRMS): clay/cement is directly deposited on the pore space. Figure 4 shows such an example. The flow simulation is performed directly on the rock model without any approximation.

Figure 5: Quartz, feldspar, and cement/clay weight percentages for all 34 selected clastic rock samples from Shell Catalog database.

Figure 6: Computed average permeability of simulated rock samples vs. the measurements on core samples.

Figure 6 shows the comparison between the computed average permeability of rock models with the measurements on the corresponding core samples. The average permeability is defined as the mean value of the permeabilities in the x-, y- and z-directions. Generally the PNM scheme overestimates the absolute permeability,

while the computed permeability from CRMS is in good agreement with the laboratory measurements. A possible explanation of the overestimation of PNM scheme is that the pore space geometry of the rock model is not exactly replicated by PNM. An efficient approach, which generates the PNM to represent the real geometry and topology of the pore space, is needed to make genuine predictions.

Field well data

In this section, we apply the micro-structural rock modeling technique to a field well data from the Johnson City Stribling #3 well. The well was drilled through well consolidated formations using a 6 11/16-in. bit size. The borehole transverses various clean to very shaly sands comprising fresh water aquifer zones. The well has been extensively cored during the drilling. Laboratory measurements on cores provide the permeability for comparison. The well logging data including the density, NMR response and mineralogy was described in Ref [15]. In the modeling, we first derive the grain size distribution from NMR log data for each depth of the formation where core data was provided, and then reconstruct a representative numerical rock model for that formation. Figure 7 displays the portion of downhole NMR measurements and the corresponding grain size distribution derived from T2 distributions.

Figure 7: NMR T2 relaxation spectrum (track 1) from downhole measurements and the corresponding grain size distribution derived from T2 distributions (track 2).

The generated rock model at each depth is further used to calculate its absolute permeability. Figure 8 shows the comparison of the permeability calculated from the reconstructed rock models with the corresponding core

measurements. Track 1 shows the NMR porosity (red crosses) and core porosity (blue circles). The difference can be observed between these two values. NMR porosity is used as input in the modeling. Track 2 displays the comparison of the computed permeability of rock models and the measured permeability of corresponding core samples. Track 3 lists the ratio of computed permeability to the measurements. Two solid black lines give the same order of magnitude of permeability. Here, we arbitrarily define predictions of the permeability of target rock samples as accurate if they fall within the same order of magnitude as the measured permeability of core sample from the same depth. One observes that our simulation result generally agrees well with the laboratory measurements considering the downhole tool responses usually representing a larger scale (~feet). In addition, the porosity difference may also contribute to the permeability difference since the porosities are relatively small. Currently we are still working on improving the modeling technique and data extraction from tool measurements.

Figure 8: Comparison of porosity and permeability between the generated rock models and the corresponding core samples from the same depth of Johnson City well.

CONCLUIONS

We have presented an integrated micro-structural rock modeling technique to reconstruct a relevant pore geometric model of rock at each depth with a low-cost computation. All input parameters are obtained directly or indirectly from downhole logging measurements and/or geological information, which could eventually eliminate the need for cutting cores. Initial sediment packings are generated from the grain mineralogy and the grain size distribution that is obtained from the knowledge of depositional environment, core sample analysis, or NMR log measurement. Sediment compaction is then modeled based on the depth and pore

pressure information; Depending on minerals and specific geological settings, various styles of cementation patterns are simulated such as cement overgrowth, pore-filling, pore-lining, and pore-bridging. Such rock models, which are further constrained by formation parameters derived from logging data, are used to determine petrophysical properties.

In addition to enhancing petrophysical parameter prediction, this technique can be used by geoscientists to explain log responses and their sensitivity to various controlling factors. Combined with the techniques of logging while drilling, this technology can be readily adapted to predict formation petrophysical properties while drilling, which enables decisions on drilling, completion and production in a timely and cost-effective manner.

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