Upscaling of Single- and Two-Phase Flow in Reservoir Engineering

Hans Bruining

• Verlag: CRC Press
• Jahr: 2021
• ISBN:
  9781000463309
• Auflage: 1
• Thema: Tecnologia e ingegneria
• Thema: Ingegneria chimica e biochimica

This book describes fundamental upscaling aspects of single-phase/two-phase porous media flow for application in petroleum and environmental engineering. Many standard texts have been written about this subject. What distinguishes this work from other available books is that it covers fundamental issues that are frequently ignored but are relevant for developing new directions to extend the traditional approach, but with an eye on application.

Our dependence on fossil energy is 80–90% and is only slowly decreasing. Of the estimated 37 (~40) Gton/year, anthropogenic emissions of about 13 Gton/year of carbon dioxide remain in the atmosphere. An Exergy Return on Exergy Invested analysis shows how to obtain an unbiased quantification of the exergy budget and the carbon footprint. Thus, the intended audience of the book learns to quantify his method of optimization of recovery efficiencies supported by spreadsheet calculations.

As to single-phase-one component fluid transport, it is shown how to deal with inertia, anisotropy, heterogeneity and slip. Upscaling requires numerical methods. The main application of transient flow is to find the reasons for reservoir impairment. The analysis benefits from solving the porous media flow equations using (numerical) Laplace transforms. The multiphase flow requires the definition of capillary pressure and relative permeabilities. When capillary forces dominate, we have dispersed (Buckley-Leverett flow). When gravity forces dominate, we obtain segregated flow (interface models). Miscible flow is described by a convection-dispersion equation. We give a simple proof that the dispersion coefficient can be approximated by Gelhar's relation, i.e., the product of the interstitial velocity, the variance of the logarithm of the permeability field and a correlation length.

The book will appeal mostly to students and researchers of porous media flow in connection with environmental engineering and petroleum engineering.

1 Dutch and Worldwide Energy Recovery; Exergy Return on Exergy Invested

DOI: 10.1201/9781003168386-1

OBJECTIVE OF THIS CHAPTER

To give the course participant, based on generally available data, a background in the problems associated with replacing fossil fuels¹ by something else [159].

• It is useful to construct a figure like Figure 1.3 with your preferred energy strategy,
• make a division of the national and worldwide energy supply in terms of the present requirement of gas, oil, coal, renewable and nuclear,
• make also a division of the energy consumption of various sectors, such as industry, agricultural services, traffic, household, electricity /heat, refineries and others,
• make a division [159] of your liking for distributing between “renewable” sources [159] such as wind (2.0 MW /km² (on shore) - 3.0 MW /km² (off shore), solar PV panels (5 MW/km²), concentrating solar power (15 MW/km², tidal pools (3 MW/km², tidal streams (6 MW/km², biofuel (0.5 MW/km²), energy saving, clean zero carbon footprint fossil fuel using CO₂ storage, etc., on the one hand and fossil fuel (gas oil/coal) and nuclear on the other hand,
• to show that renewables suffer from an extremely low energy density. For wind, it is typically the power of a bicycle lamp per square meter.

We adopt the approach of MacKay [159] in suggesting that a proposed alternative strategy must be based on arithmetics. Here we keep in mind that for the Dutch situation, we use 110 GW and worldwide we use 15000 GW-18000 GW. Possibly, such amounts are not necessary or can be partly replaced by renewables, but the ideas to decrease them must “add up” and be backed up by arithmetics.

Introduction

The introduction of an energy recovery process poses four questions. (a) What is the impact on the total energy budget? (b) Is there a net gain, i.e., is the energy required to recover the energy less than the energy produced? (c) What is the net carbon footprint? (d) Is there a gap between the optimum recovery and the current state of the art?

Conversion to renewable energy is a challenge. Moreover, renewable energy sources are sparse [242]; for instance, on shore wind energy delivers 2.0 MW/km² [159], meaning that the entire surface area 40,000 km² of the Netherlands is required to supply its total energy by wind energy. Moreover, renewable energy sources are intermittent due to differences between day and night, seasonal fluctuations and weather effects, which implies that efficient storage methods have to be implemented [74]. It is convenient to express the energy in terms of exergy, i.e., the energy that can be converted into work as otherwise energies of different quality are put on a single heap. A crude Exergy Return on Exergy Invested (ERoEI) analysis is not difficult and is of great help to show whether the use of the selected exergy source is a viable option. The ERoEI analysis [87, 90, 114] calculates the recovered exergy and compares it to the exergy costs that need to be sacrificed (drilling costs, fluid circulation costs, etc.) to make the recovery process possible. Such an analysis will also provide an estimate of the carbon footprint. Another advantage of this analysis is that it shows where the improvement of the recovery process is useful. We have also added some facts, which the reader may find useful, to put the exergy recovery process in a more general perspective. For fossil fuel recovery, it is important to know how much the worldwide temperature increases with increasing carbon dioxide in the atmosphere. Information regarding drilling costs is provided such that the reader can easily carry out his own approximate ERoEI analysis and possibly find inspiration to introduce renewable energy sources much faster than the current trends suggest.

¹ to reduce carbon dioxide emission.

1.1 Fraction Fossil in Current Energy Mix

Figure 1.1 shows the fraction of fossil fuel in the Dutch and worldwide energy mix. Indeed, according to [100], in 2015, the Netherlands (world) uses 38.7 (4331.3) Mtoe² oil, 28.6 (3135.2) Mtoe natural gas, 10.6 (3839.9) Mtoe coal, 0.9 (583.1) nuclear energy, 0.0 (892.9) Mtoe hydroelectricity, and 2.7 (364.9) Mtoe renewable energy. The primary energy consumption in the Netherlands in 2015 was 81.6 (13147.3) Mtoe. This means that in 2015, 95.5% of the primary energy consumption in the Netherlands is fossil fuel-based, compared to 86.0% worldwide [100]. These unfavorable numbers in the Netherlands reflect the availability of methane in a huge gas field. The World Bank quotes 91.36% as opposed to 95.5% for the Netherlands,³ showing typical discrepancies of global energy-related data in the literature. If one studies this subject more closely, one finds that the large uncertainties stem from all kinds of reasons. It is outside the scope of the introduction into this matter to sta...