Construction and Validation of a Numerical Model of a Reservoir Consisting of Meandering Channels
- W. van Vark (Shell Intl. Petroleum Mij. B.V.) | A.H.M. Paardekam (Shell Research B.V.) | J.F. Brint (Shell Research B.V.) | J.B. van Lieshout (Shell Research B.V.) | P.M. George (Shell Intl. Petroleum Mij. B.V.)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Engineering
- Publication Date
- February 1994
- Document Type
- Journal Paper
- 9 - 14
- 1994. Society of Petroleum Engineers
- 5.1 Reservoir Characterisation, 5.4.1 Waterflooding, 5.1.3 Sedimentology, 5.1.2 Faults and Fracture Characterisation, 5.5.8 History Matching, 5.6.1 Open hole/cased hole log analysis, 5.6.3 Deterministic Methods, 5.1.5 Geologic Modeling, 2.4.3 Sand/Solids Control, 5.7.4 Probabilistic Methods, 1.14 Casing and Cementing, 1.6 Drilling Operations, 4.1.9 Tanks and storage systems, 1.2.3 Rock properties
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This paper discusses the modeling of a fluvial reservoir system. Construction of a detailed reservoir model was followed by a coarser numerical simulation model. During the history matching of the latter, we found that fluid transmissibilities had to be reduced significantly to reproduce the observed pressure differentials. Fault-related features are thought to be the reason that the sand continuity is so much lower than that predicted with sedimentological considerations only.
The reservoir examined is a 200-m-thick fluvial sequence with an overall net pay fraction of ˜30%. Core data show that the net pay consists of a system of meandering channels and crevasse splays. Fig. 1 shows the log response of a typical sequence. The channel thicknesses range from ˜3 to 15 m, whereas the crevasse splays are much thinner (0.8 to 3.5 m). Porosities are ˜13%, and permeabilities are ˜0.1 µm2, with good agreement between core data and results from drawdown/buildup tests. The buildup tests frequently indicated linear-flow regimes and thus support the channel model. Initial pressures indicated a uniform-pressure regime and a single, fieldwide oil/water contact.
The study was performed when almost 2 years of production history was available. Reconciliation of pressure and production data with volumetric estimates of stock-tank oil initially in place suggested that depletion drive (i.e., water influx), if any, is small. Significant differential depletions indicated restricted communication between the sand units. This was confirmed by interference tests, which failed to demonstrate communication over lateral distances of ˜700 m in most cases.
A waterdrive was proposed because recovery from a depletion drive is low and crude properties (0.82 g/cm3) are favorable for waterflooding. An extensive modeling program was begun because the reservoir system appeared to be complex.
The first step was construction of a detailed geologic model where probabilistic techniques were used to complete the model beyond elements that could be mapped confidently with deterministic procedures. This probabilistic method, which is intrinsically 3D, allows inclusion of more geologic information in a structured way than can be done with conventional 2D techniques. Note that, at any stage, the results of this more elaborate modeling procedure can be translated into a set of 2D property maps by vertically averaging a (representative) realization. Refs. 1 through 3 give more general descriptions and further discussions of stochastic modeling procedures and their merits.
The geologic model was converted into a numerical model that allowed evaluation of alternative development scenarios (e.g., pattern vs. line drive, well spacing, and completion strategy) after it had been matched with field observations. Scaling up was required because the numerical model was coarser than the geologic model. Numerous averaging procedures exist that are geared to particular permeability configurations.4,5
This paper discusses model construction, scaling up from a detailed geologic to a practical simulation model, and calibration of the simulation model to field performance.
Fig. 2 shows the representative reservoir sector selected. Areal dimensions were 2.40×1.35 km. Five wells had been drilled in the area at the time of the study, two of which had been in production for almost 2 years. Fig. 3 shows that the pressure profiles contain a great deal of character; therefore, comparison with simulated performance is meaningful. However, the drawback of using an element model is that not all its boundaries are barriers to flow. Material-balance considerations indicate a net influx into the element, but this crossflow is not constant with time because of variations in off-take. Consequently, quantitative history matching is not possible and comparisons between field and model must be qualitative.
Detailed Geologic Model
Geologic models were constructed with a modeling program that combines actual field data with general geologic knowledge.6,7 The program uses a matrix of discrete cells, "voxels," to model the sand distribution and properties. Voxel sizes were selected on the basis of estimates of channel and crevasse dimensions, which are measured in meters vertically and in hundreds of meters areally. This resulted in 75×75×1-m voxels, giving a 127,872-voxel model. Log data were used to generate detailed correlations that subsequently were used to generate a series of models by means of the following five-step approach.
Step 1 - Modeling of Correlated Sand Bodies.
Maps were generated of the isopach thicknesses and tops of all correlated sands from well data with an anisotropy ratio that reflects the degree of sandbody elongation. The correlations indicated a fieldwide dominant north-northwest to south-southeast channel orientation. All channels in the model (correlated and noncorrelated) were mapped to agree with that trend.
Step 2 - Modeling of Noncorrelated Sand Bodies at Wells.
Once a model is established for the correlated sand bodies, noncorrelated sand bodies are modeled under the following rules.
1. The sand-body thickness observed at the well is taken as the sand-body thickness throughout.
2. Lateral sand-body extent is derived from statistical geometry data.
3. Channel sand bodies are modeled as rectangular bars, and crevasse splays are modeled as disks.
4. Sand-body orientation is sampled from the general distribution of orientations.
Step 3 - Modeling of Sand Bodies Between Wells.
After Step 2, the volumetric proportions of the different genetic-unit types are still lower than those inferred from well data because sand bodies not penetrated by any well still need to be generated. For the sand bodies in the interwell area, the modeling rules are the same as for sand bodies generated in Step 2 except for sand-body thickness, which is sampled from a distribution that is based on sand-body thicknesses observed at the wells. The sand bodies generated in this way will not intersect an existing well or any of the correlated shales. This process is continued until the overall volume fractions of the sands in the model are equal to the distribution observed at the wells.
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