Previous Part(s)

Part 1 - Overview

Objective

– Describe the simulation model and economic model that we will use for the waterflood performance evaluation of the reservoir cross section.

Introduction

In this post, we will briefly describe the simulation model that we will use for the waterflood performance evaluation.

The reservoir simulation model described here represents a base case. We will make adjustments to this base case model (e.g., the change the Kv/Kh ratio, tilt the reservoir, etc) to illustrate the effect of different factors (e.g., vertical communication between layers, gravity, etc.) on the waterflood performance.

Simulation Model

A simple cross-section (X-Z) simulation model is used to describe fluid flow in the reservoir cross-section. The simulation model is constructed mainly using the cross-section reservoir properties including permeability, porosity, and initial water saturation. We have made assumptions for the other parameters required to build a simulation model (e.g., relative permeability curves, well data, well controls, fluid and rock-fluid properties). These assumptions will be described later.

Cross-section Data

The cross-section data contains 20 layers. Relevant rock and rock-fluid properties, e.g., layer thickness, permeability, porosity and initial water saturation vary for each layer. Figure 1 shows the permeability vs. depth profile of the cross-section data.

Figure 1: Logarithm of permeability vs. depth for the cross-section.

Simulation Grid

The simulation model is consistent with the cross section data. The simulation grid contains 20 layers, each layer corresponding to a layer in the cross-section.

For our base case simulation model, we will assume a simulation grid of 100 x 1 x 20 cells. The dimension of each grid cell in the X-direction is 100ft and for the Y-direction, it is 500ft. The thickness (height) of each grid cell varies and is equal to the thickness of the corresponding layer in the cross-section. The dimension of the simulation grid is 10,000ft by 500ft by 439ft (this is the sum of all layer heights).

Figure 2 shows the simulation grid with the X-direction permeability property displayed. The highest permeabilities (approximately 900md) are found in layers 9 and 10 indicated by the red colored layers.

Figure 2: Simulation grid showing the X-direction permeability values (md).

The base case simulation model is horizontal. In later series, we will tilt the reservoir to investigate gravity effects.

Relative Permeability

The cross-section data contains different initial water saturation (Swi) values for each layer. We have assumed that the oil phase makes up the rest of the saturation, i.e., Soi = 1- Swi. As a result, our simulation model will contain only two phases, oil and water.

Corey relative permeability model was used to generate a base relative permeability curve. This base curve is then end-point adjusted for each layer to obtain the relative permeability curve for each layer. The adjustment ensures that the water phase is initially immobile in each layer. The relative permeability curves for the 20 layers is shown in Figure 3.

Figure 3: Relative permeability curves for the different layers

Wells

We assume that all wells are simple, fully-penetrating vertical wells, i.e., the wells are completed in all the layers of the simulation model. A well location is specified as (I, J, K1-K2) where I and J are the grid block indices in the X- and Y-directions respectively, and K1 and K2 represent the start and end layers where the wells are completed. Also, the well control type and control values specified for each well remains constant throughout the production period.

For the simulations, we will assume reservoir voidage controls for simplicity, and the total reservoir injection rate from the injector(s) is set equal to the total reservoir voidage rate from the producer.

Waterflooding well configuration

The base simulation model contains only two wells, a water injection well (injector) and an oil production well (producer).

Figure 3 shows the well configuration for waterflooding the cross-section. In Figure 3, L = 10,000 ft, W = 500 ft and H = 439 ft as described in the simulation grid section. The injector is located at the left end of the simulation model, completed in grid blocks (1,1,1-20), and the producer at the right end of the model and completed in grid blocks (100,1,1-20).

Figure 3: Well configuration for waterflooding.

Water is injected from the surface (indicated by blue arrow(s)) into the reservoir (via the injector’s wellbore). Water in the reservoir then displaces the oil (indicated by green arrows) towards the producer. Fluids in the producer then flows subsequently to the surface. In this setup, water is normally referred to as the displacing phase and oil as the displaced phase.

The fluids produced in the producer depends on the stage of the waterflood. Before water breakthrough (i.e., before the water reaches the producer), only oil is produced in the producer. After water breakthrough (water has reached the producer), both oil and water are produced with the oil rate decreasing and the water rate increasing with time.

Production Schedule

We have assumed a total production time of 15 years in the base model. As described earlier, the well controls are fixed and constant throughout the production period. Later, we will remove this limitation and allow the well control to vary within fixed time intervals.

Economic model

We will use an economic model to evaluate different production scenarios, e.g., primary depletion, waterflooding. A simple economic model is used to compute net present value (NPV). NPV is an important economic criterion for evaluating and comparing different projects. Projects with higher NPV values are (generally) better. There are other important economic indicators, e.g., discounted cash flow rate of return (ROR, DCFROR), development cost, pay out time, etc. However for simplicity, we will focus more on NPV.

The economic model we use accounts for well drilling and completion costs, royalty rate, tax rate, and operating expense related to production and injection of oil and water phases. The parameter values assumed in the economic model are shown in Table 1.

All wells are pre-drilled and are fully operational prior to start of production. Hence, the well drilling and completion costs are incurred in the first year of production.

In the economic model, the operating expenses and fluid prices and costs are assumed to be fixed throughout the production period. For the rest of the series, we will assume these economic parameters for computing NPV.

Simulation Model Assumptions

Other assumptions in the simulation model include:

• all grid cells have a net-to-gross (NTG) of 1.0.

• all grid cells in the model are active.

• rock properties (PERMX, PERMY, PERMZ, PORO, …) are constant for each layer.

• each grid cell’s X-direction permeability (PERMX) is set equal to corresponding layer value from the cross-section. Porosity and initial water saturation are defined similarly.

• permeability in the X (PERMX) and Y (PERMY) directions are equal, while the permeability in the Z-direction (PERMZ) is 10% of PERMX.

• relative permeability curves are generated using Corey model, then end-point adjusted for each layer.

• dead oil PVT model, i.e., no gas is dissolved in the oil phase. There is no gas in the simulation model.

• no artificial lift curves and hence pressure losses in the tubing are not modeled.

• constant well controls throughout production period.

Conclusion

In this post, we have described the (base) simulation model that we will use for the waterflood performance evaluation of the cross-section. The description is at a high-level and does not include details of the simulation deck. We have chosen this approach because there are different reservoir simulators with different requirements, file formats/layouts, and also not to burden non reservoir engineers with too much technical details. However, if there is enough interest, we will make a separate post showing how the different components are put together to obtain the simulation deck.

While the simulation model can be built by hand, we use an automatic workflow tool for generating (and running) the simulation models. There are many simulation cases (hence simulation models) that we will consider in the tutorial series, so it will be too time consuming to build each simulation model, submit the simulations, and post-process the results manually. These tasks (and others) are performed automatically by the tool.

What’s Next

Having described the simulation model, we can now make simulation runs to model fluid flow in the cross sections. In our next post, we will consider different production scenarios and compare the benefits of waterflooding over primary depletion. We will use cumulative oil produced (COP) and net present value as metrics for our comparisons.

Do not hesitate to contact me with feedbacks and comments.

Nomenclature

- COP          = Cumulative oil produced (m3 or STB)
- DCFROR, ROR  = Discounted cash flow rate of return, Rate of Return
- Kv/Kh        = Vertical to horizontal permeability ratio, Fraction
- md           = milliDarcy, unit of permeability measurement
- NPV          = Net Present Value, $
- NTG          = Net-to-gross ratio, Fraction
- PORO         = Grid cell porosity, Fraction
- PERMX        = X-direction grid cell permeability, md
- PERMY        = Y-direction grid cell permeability, md
- PERMZ        = Z-direction grid cell permeability, md
- PVT          = Pressure volume temperature
- Swi          = Initial water saturation, Fraction.
- Soi          = Initial oil satuation, Fraction.

References

Here is a (contnuously updated) list of some useful references for additional reading or for understanding concepts described here.

• Willhite, G.P. Waterflooding, SPE Textbook Series Volume 3, (1986), Society of Petroleum Engineers, Richardson, TX. ISBN 978-1-55563-005-8

• Oystein Pettersen Basics of Reservoir Simulation the Eclipse Reervoir Simulator, Lecture Notes (2006), Department of Mathematics, University of Bergen. http://folk.uib.no/fciop/index_htm_files/ResSimNotes.pdf

• Petrowiki Relative Permeability Models