Experimental Evaluation of the Methane Number Measurement Procedure for Gaseous Fuel Rating

Abstract

Methane Number (MN) is a fuel rating technique for gaseous fuels analogous to Octane Number. This study establishes and shares a repeatable and reproducible method for MN determination of a gaseous fuel using a modified Cooperative Fuel Research Engine (CFR). Adaptations required to convert a CFR engine for use in the MN test procedure are identified. The investigation includes allowable environmental parameters and operating variation limits. An essential aspect of the MN method involves identifying and quantifying Knock Intensity (KI) during engine operation. CFR engines, originally designed for gasoline testing, come equipped with their own knock measurement systems utilizing a capacitive detonation sensor. The original system is compared with a Fast Fourier Transform (FFT) approach that uses a piezoelectric pressure transducer. Quantification of methane number requires an accurate assessment of the reference fuel blend (CH₄ + H₂). A comparison is carried out between dynamic blending using mass flow meters and bracketing using certified gas bottles containing various CH₄/H₂ blends from a gas supplier.

1. Introduction

End Gas Auto Ignition (EGAI) refers to the spontaneous combustion of unburned fuel molecules in an engine combustion chamber. This phenomenon occurs after the initial spark-induced ignition event, exposing the yet-to-burn mixture to a higher energy environment during the propagation of the flame front throughout the cylinder [1]. If the temperature is sufficient, and the required energy to propagate a flame is low enough, a secondary ignition site is formed, leading to a secondary flame front and subsequent pressure wave advancing outward in the yet-to-burn mixture. When the primary and secondary pressure waves meet, they cause a disturbance, which results in pressure fluctuations that produce the distinctive “knock” or “ringing” associated with auto-ignition events [2]. EGAI encompasses various classifications that delineate its nature and origin. The term “knock” refers to both the audible noise and high-frequency vibrations stemming from EGAI, often serving as a simplified reference for the phenomenon.

Methane Number serves as an experimentally derived parameter for assessing the susceptibility of gaseous fuels to EGAI. Originating from pioneering work by Leiker et al. [3] in Graz, Austria, beginning in 1963 and continuing through 1969, Methane Numbers emerged as a viable alternative to conventional gasoline rating methodologies, primarily due to constraints on maximum attainable values without resorting to extrapolative techniques. Leiker et al. investigated the influence of gas composition on fuel knock resistance, presenting ternary diagrams of Methane Number outcomes. However, they did not disclose their precise methodologies or the uncertainty of fuel samples utilized in establishing these relationships. Motoren Werke Mannheim AG (MWM) leveraged the ternary diagrams published by Leiker et al., created empirical data, and developed a method to calculate a methane number. Utilizing MWM’s efforts, the American Society of Testing Materials (ASTM) created software to determine a calculated Methane Number (MN_C) based on gaseous fuel composition and standardized it in ASTM D8221 [4]. In the years following the work by Leiker et al., various engine manufacturers have developed their own methods for determining natural gas knock resistance, with specific details regarding testing procedures and/or calculation methods remaining confidential.

Unlike liquid fuels and octane numbers, there is currently no standard test method for measuring the methane number of a gaseous fuel (e.g., natural gas) used in spark-ignition engines. With the anticipation of hydrogen blending into natural gas and its subsequent use in automotive applications, it is even more important that the limited data taken over fifty years ago [3] be revalidated in a defined and standardized manner. The purpose of this research was to create a repeatable and reproducible method for determining the Methane Number of gaseous fuels utilizing a modified Cooperative Fuel Research Engine.

The Methane Number is analogous to the octane number, which uses isooctane and n-heptane as reference fuels. The methane number method employs a mixture of methane (CH₄) as the Primary Reference Fuel (PRF) and hydrogen (H₂) or carbon dioxide (CO₂) as a Secondary Reference Fuel (SRF). In this method, the knock characteristics of a test fuel were compared to a mixture of methane and hydrogen. The mixture includes 100% methane (assigned a methane number of 100) and 100% hydrogen (assigned a methane number of 0). For example, a mixture of 80% methane and 20% hydrogen would correspond to a methane number of 80. To assign methane numbers greater than 100, the SRF is substituted for carbon dioxide (CO₂), which acts as a knock inhibiter along with methane, allowing methane numbers equaling 100 plus the percentage of carbon dioxide added to the blend. For example, a fuel blend consisting of 75% CH₄ and 25% CO₂ would correspond to a MN of 125. Fuel composition significantly influences gaseous fuel auto-ignition characteristics, with higher methane numbers indicating lower susceptibility to auto-ignition. This study investigated a typical natural gas fuel composition that had a methane number of 85, resembling the typical gaseous fuel available to consumers from utility providers.

2. Materials and Methods

2.1. Materials

The engine testing for this research utilized a modified Cooperative Fuel Research (CFR) F-2 Engine, originally manufactured in 1957 by the Waukesha Motor Company. These engines remain commercially available through CFR Engines Inc., Pewaukee, WI, USA, and are extensively utilized by petroleum refineries and state fuel analysis laboratories. Designed to facilitate comprehensive testing for compliance with knock resistance standards, CFR engines are an indispensable tool for fuel testing standards. A distinguishing feature of CFR engines is their capability to dynamically adjust the Compression Ratio (CR) without altering other operational parameters. This functionality is enabled by the design of the cylinder head and cylinder sleeve, which allows movement relative to the piston, rotating assembly, and lower casing. The upper and lower sections can adjust relative to each other by up to 31.4 mm, facilitating a CR range of 4:1 to 18:1.

The CFR engine utilized at the Colorado State University Powerhouse Energy Campus has undergone numerous modifications to align with a wide range of research objectives (pictured in Figure 1). Modifications made directly influencing the testing of Methane numbers are as follows:

• Knock Measurement System
  • In-cylinder water-cooled, piezoelectric pressure transducer (Kistler 6061A, Kistler Instrument Corp., Novi, MI, USA).
• Engine Control and Monitoring System
  • LabVIEW^TM (Austin, TX, USA) Virtual Instrumentation (VI) Panel
• Crank Position Measurement
  • Optical Engine Encoder (BEI L25, Sensata Technologies, Attleboro, MA, USA)
• Fuel Delivery System
  • Dynamic Fuel blending capability
  • Four needle valves for precise fuel flow control
  • Omega mass flow meters (FMA-1700, Omega Engineering Inc., Norwalk, CT, USA)
  • Coriolis flow meter
  • Fuel actuator valve (MCM-050AB, Hanbay Inc., Pointe-Claire, QC, Canada)
• Intake Manifold
  • High-speed Kistler piezo-resistive (Type 4007D) pressure transducer
  • Thermocouples sense air before and after the heater
  • 2-ft3 Plenum volume
  • Steel pressure relief burst disk
• Exhaust Manifold
  • High-speed Kistler piezo-resistive (Type 4007D) pressure transducer
  • Thermocouple sensing exhaust temperature
  • Steel pressure relief burst disk
  • Manual restriction valve
• Ignition Timing Control
  • Woodward Large Engine Control Module (LECM), Woodward Inc., Fort Collins, CO, USA
• Engine Speed and Load Control
  • 3.5 kW synchronous motor generator with the required gearing to produce AC power
  • Yaskawa regenerative Variable Frequency Drive (VFD), Yaskawa Global, Kitakyushu, Japan
• Air/Fuel Mixture Monitoring
  • Motorsports Technology Lambda Meter, MoTeC^TM, Research Center, Croydon South, Victoria, Australia
• Intake Air Conditioning/Dehumidification
  • 5000 BTU/hr. residential air conditioning unit
• Intake Manifold Pressurization
  • Industrial Air Compressor
  • Omega Air Flow Meter
  • Actuated butterfly valve

In Figure 2, A simplified diagram depicts the dynamic fuel blending system, the intake air pressure system, and the exhaust manifold.

2.2. Methods

2.2.1. Knock Measurement Systems

The two methods used for knock quantification within the scope of this project were the CSU-developed Fast Fourier Transform of a Bandpass Signal system and the Knock Measurement System that was provided with the original CFR engine. Other potential methods of knock quantification are described by Bayliff [5] and Wise [1].

2.2.2. CSU FFT Bandpass Knock Measurement

The method involves a Fast Fourier Transform (FFT) analysis of cylinder pressure readings to assess pressure trace dynamics in the frequency domain, aligning with methodologies by Brunt [2] and Elmqvist [6]. It quantifies auto-ignition events by correlating pre-detonation points with cylinder geometry, factoring in the time for a pressure wave to travel twice the cylinder diameter at the local speed of sound.

The anticipated knock frequency, based on the local speed of sound of the CFR engine cylinder (82.55 mm bore), is 5850 Hz. LabVIEW^TM, used for the combustion logger program, employs an FFT Power Spectrum function to analyze real-time cylinder pressure signals. A bandpass filter eliminates operating frequency, revealing pressure distortions indicative of knocking. The CFR-F2 engine operates at 900 rpm (15 Hz), which is used in ASTM D2700, a Motor Octane Number (MON) method [7]. Figure 3 depicts light and heavy engine knock conditions, with multiple oscillations in pressure occurring after the peak pressure and subsequent peak on the FFT plot with a frequency near 6 kHz corresponding to the anticipated value. The bandpass filter removes low and high-frequency noise tailored to the CFR engine cylinder geometry. Knock Intensity is the measure of the amplitude of the FFT of an individual pressure trace. The Knock Integral represents the sum of maximum FFT spike magnitudes over successive combustion cycles. The equation for the Knock Integral is given in Equation (1).

$$\mathrm{K}\mathrm{I}=\mathrm{A}\mathrm{r}\mathrm{e}{\mathrm{a}}_{\mathrm{b}\mathrm{o}\mathrm{u}\mathrm{n}\mathrm{d}\mathrm{e}\mathrm{d}}={\displaystyle {\sum }_{\mathrm{i}=1}^{\mathrm{n}}}\left\{\left(\mathrm{i}+1\right)-\mathrm{i}\right\}\left\{\mathrm{K}\mathrm{L}\left(\mathrm{i}+1\right)+\mathrm{K}\mathrm{L}\left(\mathrm{i}\right)\right\}/2$$

(1)

In Figure 4, FFT magnitude variations over 1400 cycles at different knock levels are plotted demonstrating the typical variation over the course of 3 min of operation at 900 rpm. Knock Integral is used because it quantifies knock severity and persistence and is displayed to the operator as a rolling 200-cycle value. This was performed to allow the operator to better match knock intensities between samples and allow for a greater difference between similar knocking conditions.

2.2.3. CFR Knock Measurement System

The CSU CFR engine was manufactured in 1957 and came equipped with a Knock Measurement System, which was available until 2009 when the manufacturer switched to a digital system. The system serves as an analog method for gauging the intensity of engine knock during operation and is the standard for the testing of gasoline knock resistance. For normal operational use of the CFR engine, this system provides a means to measure the relative changes in knock intensity, requiring operators to determine the onset of knock and change sensitivity impacting the Knock Meter reading in “divisions”. The analog detonation meter isolates relative knock amplitude through signal averaging and filtering, transmitting it to the detonation meter, which displays the relative intensity on a comparative scale. One of the focuses of this research was to determine the viability of the CFR Knock Measurement System for the Methane Number test procedure and compare the results to the CSU FFT Bandpass system.

2.2.4. Methane Number Test Methods

Three methods to determine the Methane Number of a gaseous fuel were evaluated during this research project.

(1)

Matching KI Value-which was the method used by Leiker [3] and most researchers [8,9] who have reported methane numbers.

(2)

KI Bracketing-which is the method developed by CSU using the methodology described by ASTM’s RON [10] and MON [7,11] test methods.

(2a)

Dynamic Blending

(2b)

Pre-Mixed Blending

2.2.5. Matching KI Value

Originally pioneered by Leiker et al. [3] and used by Wise [1] for the testing of Methane Numbers, the procedure relies on matching the knock intensity of the test sample fuel and a reference fuel blend. Using this method requires finite control of the changing methane/hydrogen reference fuel composition, and the means of accurately measuring their flow rates determine the MN value. The following method utilized the CSU FFT Bandpass Knock Measurement system.

• Start the CFR engine, allowing ample time to reach steady state operating conditions with set Intake Mixture Temperature, mixture ratio, and Ignition timing.
• Gradually increase the compression ratio by increments of 0.5, allowing intervals for the engine to stabilize and reach the knock intensity state. Continue raising the compression ratio until the onset of audible knock is detected. Maintain a constant compression ratio for the remainder of the test.
• Record a 1000-cycle interval of operating conditions and pressure trace data, focusing on the Knock Integral to designate the Target KI.
• Terminate the test sample fuel flow, allowing time for the fuel mixture to leave the CFR engine intake system while the engine continues motoring.
• Activate the methane flow for the primary reference fuel (PRF) and let the engine stabilize to measure the Current KI.
  • Note: For test fuels with low KI resistance, the Current KI can be close to zero
• Choose the Secondary Reference Fuel (SRF) based on the Current KI relative to the Target KI.
  • If Current KI < Target KI: SRF = Hydrogen (H₂)
  • If Current KI > Target KI: SRF = Carbon Dioxide (CO₂)
• Make gradual increases and changes to the SRF flow until Current KI = Target KI
• Record 1000-cycle intervals of operating conditions and pressure trace data.
• The MN test is now complete. Turn off the PRF and SRF fuel flows and stop the engine.

Calculating the MN value from methane and hydrogen flow rates determined by flow meters requires converting from a mass flowrate ($\frac{\mathrm{g}}{\mathrm{m}\mathrm{i}\mathrm{n}}$) to a molar flowrate ($\frac{\mathrm{m}\mathrm{o}\mathrm{l}}{\mathrm{m}\mathrm{i}\mathrm{n}})$. Converting from average molar flow rates to MN values involves Equation (2) if the SRF is H₂ and Equation (3) when CO₂ is used as the SRF.

$$\mathrm{IF} \mathrm{SRF}={\mathrm{H}}_2: \mathrm{M}\mathrm{N}=\frac{\mathrm{a}\mathrm{v}\mathrm{g}.\mathrm{C}{\mathrm{H}}_4\mathrm{m}\mathrm{o}\mathrm{l} \mathrm{f}\mathrm{l}\mathrm{o}\mathrm{w}}{\mathrm{a}\mathrm{v}\mathrm{g}.\mathrm{C}{\mathrm{H}}_4\mathrm{m}\mathrm{o}\mathrm{l} \mathrm{f}\mathrm{l}\mathrm{o}\mathrm{w}+{\mathrm{a}\mathrm{v}\mathrm{g}.\mathrm{H}}_2\mathrm{m}\mathrm{o}\mathrm{l} \mathrm{f}\mathrm{l}\mathrm{o}\mathrm{w}}\ast 100$$

(2)

$$\mathrm{IF} \mathrm{SRF}={\mathrm{CO}}_2: \mathrm{M}\mathrm{N}=\left(\frac{\mathrm{a}\mathrm{v}\mathrm{g}.\mathrm{C}{\mathrm{O}}_2\mathrm{m}\mathrm{o}\mathrm{l} \mathrm{f}\mathrm{l}\mathrm{o}\mathrm{w}}{\mathrm{a}\mathrm{v}\mathrm{g}.\mathrm{C}{\mathrm{H}}_4\mathrm{m}\mathrm{o}\mathrm{l} \mathrm{f}\mathrm{l}\mathrm{o}\mathrm{w}+\mathrm{a}\mathrm{v}\mathrm{g}.{\mathrm{C}\mathrm{O}}_2\mathrm{m}\mathrm{o}\mathrm{l} \mathrm{f}\mathrm{l}\mathrm{o}\mathrm{w}}+1\right)\ast 100$$

(3)

2.3. KI Bracketing

2.3.1. Approach #1: Dynamic Blending

The stable operation of an engine undergoing EGAI is complex, with many variables that need to be simultaneously controlled at constant values. Combining the complicated nature of engine operation and inconsistencies of EGAI, matching knock intensity between a test fuel and a reference fuel blend is challenging. During MN testing, the intention is to vary the hydrogen and methane blend ratio to match the KI, but it is difficult to determine how close it is enough, especially with intake temperature, ignition timing, and intake pressure affecting the development of knock. To reduce the time spent matching knock intensity to a higher level of precision and to develop a relationship between MN and KI for given operating parameters, a new method for testing MN was devised. This method eliminates the need to accurately control the reference fuel blend to match specific KI values, which are intrinsically unstable. To establish a direct relationship between KI and MN, an adapted MN method was developed and included below as a step-by-step procedure.

• Select the Compression Ratio (CR), Intake Mixture Temperature, and Ignition timing values specified by the MN testing procedure.
• Start the CFR engine and allow enough time to reach Steady State Operating Conditions.
• Switch to the test sample fuel and set the fuel flow solenoid position to achieve stoichiometric operating conditions (λ = 1.000).
• Gradually increase the compression ratio by increments of 0.5, allowing the engine to stabilize and reach the knock intensity state at each interval. Continue increasing the compression ratio until audible knock onset is detected, then maintain a constant compression ratio for the remainder of the test.
  • If audible knock is not achieved before reaching maximum CR, lower the CR and retard the ignition timing in one-degree increments and repeat step 4 until audible knock is achieved.
• Record three (3) 1000-cycle intervals of operating conditions and pressure trace data. Focus on Knock Integral and take note of the average value. This is Target KI.
• Terminate the test sample fuel flow, allowing time for the fuel mixture to leave the CFR engine intake system while the engine continues motoring.
• Activate the methane flow for the primary reference fuel (PRF) and let the engine stabilize to measure the Current KI.
• Select the secondary reference fuel (SRF) based on the relation between the Current KI and the Target KI.
  • If Current KI < Target KI: SRF = Hydrogen (H₂)
  • If Current KI > Target KI: SRF = Carbon Dioxide (CO₂)
• Make gradual increases in SRF until Current KI = ~1.2 x Target KI (TKI-high) and record 1000-cycle intervals while keeping SRF flow constant.
• Make gradual increases in SRF until Current KI = ~1.0 x Target KI (TKI-Med) and record 1000-cycle intervals while keeping SRF flow constant.
• Make gradual increases in SRF until Current KI = ~ 0.8 x Target KI (TKI-Low) and record 1000-cycle interval while keeping SRF flow constant.
• The MN test is now complete. T turns off the PRF and SRF fuel flows and stops the engine.

2.3.2. Post-Processing Procedure

• The Knock Intensity of each power stroke is measured and averaged over each 1000-cycle data collection period.

  1a.

  TKI-High

  1b.

  TKI-Med

  1c.

  TKI-Low

• Calculate the Methane Number using Equation (2) or Equation (3).
• Plot MN vs. Avg. KI for the Reference fuel blends used.
• Generate a linear regression equation using these 3 TKI-MN points, evaluating the validity of the three tests based on the R² value achieved.
• Using the average KI from the test fuel blend, calculate the MN.

Utilizing the Methane Number (MN) of the three reference fuel blends enables the establishment of a linear relationship between MN and knock intensity, facilitating direct calculation of MN based on the test fuel knock intensity. Although the relationship between MN and knock intensity is inherently exponential, linear regression offers a viable approximation within a constrained range of MN values without the addition of unnecessary complexity. The coefficient of determination (R²) between the linear regression and reference fuel blends serves as an indicator of confidence in the MN value determined by this method.

An example of the Dynamic Blending Bracketing KI method is illustrated with the labeled values from Figure 5. In the example case, the average KI for the test sample fuel was 2.60 kPa²/s². The test sample fuel was replaced with pure methane, and then the hydrogen flow rate was increased until the knock intensity surpassed the target KI, and a 1000-cycle data set was collected. This blend, deemed “TKI-High”, corresponded to an average methane percentage of 85.57 and an average KI of 3.54 kPa²/s². The flow of H₂ was decreased until the Current KI was near the value of the Target KI, and a 1000-cycle data set was collected. This blend deemed “TKI-Med” corresponded to an average methane percentage of 87.88 and an average KI of 2.81 kPa²/s². The flow of H₂ was further reduced until the Current KI was less than the Target KI, and a 1000-cycle data set was collected. This blend deemed “TKI-Low” corresponded to an average methane percentage of 91.62 and an average KI of 1.65 kPa²/s². Using these three reference fuel blend data points, a linear regression trendline is fit with the form:

$$\mathrm{K}\mathrm{I}\left(\mathrm{M}\mathrm{N}\right)=\mathrm{a}\left(\mathrm{M}\mathrm{N}\right)+\mathrm{b}$$

Using the coefficients from the linear regression trendline and the average KI of test fuel 1000 cycle test, the methane number of the fuel blend can be calculated:

$$\mathrm{M}\mathrm{N}\left(\mathrm{T}\mathrm{e}\mathrm{s}\mathrm{t} \mathrm{F}\mathrm{u}\mathrm{e}\mathrm{l}\right)=\frac{\left(\mathrm{A}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{g}\mathrm{e} \mathrm{K}\mathrm{I}\right)-\mathrm{b}}{\mathrm{a}}=\frac{2.60-30.347}{-0.3133}=88.56$$

(4)

Determining an acceptable R² interval involves balancing test accuracy with the stability of the Knock Intensity (KI) parameter and the Methane Number (MN). Leiker et al. [3] stated that the MN they determined has a confidence interval of ±1 MN, which represents a significant uncertainty. Over the course of testing and data analysis, results from tests with an R² exceeding 0.95 are considered to be adequate for use. Tests with R² below 0.95 should constitute a re-test to improve the use of the linear regression.

2.3.3. Approach #2: Pre-Mixed Blends

When calculating the MN, the measurement of flow rate is crucial for the accuracy of the method. Inherently, flow meters are a source of error and a possible reason to discredit results. The flowmeters require frequent calibrations and calibration checks. In the liquid fuel methods, isooctane and n-heptane are blended in exact quantities before being added to the carburetor, eliminating the need for real-time blending. To resemble the Research Octane Number (RON) [10] and Motor Octane Number (MON) [7,11] test methods more closely, Certified Pre-mixed Reference Fuel (CPRF) blends of methane and hydrogen were purchased in 4 concentrations ranging from 75–90% methane corresponding to the expected range of MN for natural gas. To establish a relationship between KI and MN, an adapted method was developed and is included below as a step-by-step procedure.

• Select the desired Compression Ratio (CR), Intake Mixture Temperature, and Ignition timing values.
• Start the CFR engine and allow it to reach steady state operating conditions.
• Activate test fuel flow and allow the engine to reach stable operating conditions.
• Make gradual increases in compression ratio (+0.5), allowing the engine to reach a steady state. Continue gradual increases in compression ratio until the onset of audible knock. The compression ratio will remain constant for the rest of the test.
  • If audible knock is not achieved before reaching maximum CR, lower CR retard ignition time and repeat step 4 until audible knock is achieved.
• Record (3)1000-cycle intervals of operating conditions and pressure trace data.
• Select 3 CPRF blends that bracket the test fuel in anticipated MN.
  • If GC data is unavailable, begin with CPRF 1 = 85–15 and select PRF 2 and 3 based on KI.
• Terminate the test fuel flow, allowing time for fuel mixture volumes to return to atmospheric pressure while the engine continues motoring.
• Activate the CPRF-1 flow and let the engine stabilize before recording a 1000-cycle interval.
• Terminate the CPRF-1 fuel flow, allowing time for the fuel mixture to leave the CFR engine intake system while the engine continues motoring.
  NOTE: If CPRF-2 and 3 have not been selected, determine the closer two blends that will bracket the fuel. Examples are provided below:
  • Test KI = 500, PRF 1(85 MN) = 700, PRF 2:(80–0), and PRF 3:(90–10)
  • Test KI = 500, PRF 1(85 – 15) = 100, PRF 2:(80–20), PRF 3(75–25)
• Activate CPRF-2 and let the engine stabilize before recording a 1000-cycle interval.
• Repeat steps 9 & 10 with CPRF-3
• MN test is complete. Turn off the fuel flow and stop the engine.

2.4. Post-Processing Procedure

• The KI of each power stroke is averaged over 1000 cycles.

  1a.

  CPRF-High: Blend with Higher KI than Target KI

  1b.

  CPRF-Med: Blend with Similar KI to Target KI

  1c.

  CPRF-Low: Blend with Lower KI than Target KI

• The MN of each blend is included in the blend certifications.
• Plot MN vs. Avg. KI for TKI-High, TKI-Med, and TKI-Low Blends.
• Generate an exponential regression equation using these 3 TKI-MN points.
• Using the average KI from the test fuel blend, calculate the MN.

Removing the uncertainty and complication associated with fuel flowrate measurement simplifies the MN measurement allowing for a streamlined process. From the perspective of the operator, this method reduces the overall complexity and makes it much easier to have generate an approximation for MN when operating the engine. Also utilizing pre-mixed fuel blends enables the testing of a wider range of fuel samples with one calibration procedure.

An example of the Premixed Blends Bracketing KI method is illustrated with the labeled values from Figure 6. In the test, the Target KI for the test fuel was determined as 3.61 kPa²/s². Subsequently, the test fuel was substituted with an 80-20 (CH₄-H₂) CPRF, allowing the engine to attain steady knocking conditions, and a 1000-cycle data set was collected. This CPRF yielded an average KI of 16.9 kPa²/s², designated as CPRF-High. The process was replicated with two additional CPRFs featuring higher methane concentrations bracketing the Target KI. The 85-15 CPRF resulted in an average KI of 5.45 kPa²/s², denoted as CPRF-Med, while the 90-10 CPRF returned an average KI of 0.84 kPa²/s², earning the designation CPRF-Low. Using these (3)-reference fuel blend data points, an exponential regression trendline is fit with the form:

$$f\left(MN\right)=a \ast \mathrm{e}\mathrm{x}\mathrm{p}\left(b \ast MN\right)$$

Using the coefficients from the linear regression trendline and the average KI of test fuel, the methane number of the fuel blend can be calculated:

$$MN\left(Test Fuel\right)=\frac{\ln \left(\frac{\left(Average KI\right)}{a}\right)}{b}=\frac{\ln \left(\frac{3.61}{4.181\ast {10}^9}\right)}{-0.2414}=86.45$$

The number of CPRF blends afforded to this project fell outside of that which would be desired to effectively utilize the linear regression technique. Comparing exponential to linear regression techniques for determining MN, Figure 7 illustrates the difference in MN values between the linear and exponential regression curves when the three pre-mixed reference blends are used for the linear and exponential calculation. For this example, the exponential has a much higher degree of accuracy, while the linear regression technique tended to overpredict the MN. Figure 8 illustrates the use of the 85 MN and 90 MN CPRF blends bracketing the test sample fuel, and, in this situation, the linear regression more closely predicts MN, but a valid R² value is still not achieved. It is recommended that three pre-mixed reference blends be used to determine the methane number. If only two are used, they should not be different by more than 5 MN.

Impact of Control Parameter Setpoints and Variation on the Test Method

The testing environment is an important consideration when measuring the knock resistance of a fuel. There are multiple parameters that have varying levels of impact on the knock tendencies and repeatability of an MN test. For the purposes of this research, the impact of certain operating conditions and parameters was investigated. The impact of each parameter on the MN was evaluated, and parameters including Intake Mixture Temperature (IMT), ignition timing, Intake Manifold Pressure (IMP), and air/fuel mixture were identified as significant and therefore were addressed.

For these investigations, the CSU in-cylinder pressure transducer and the Bandpass FFT method were utilized. This was performed to ensure consistent KI values without influence from the operator and the objective onset of the knock. Throughout this investigation, there were no changes made to the in-cylinder pressure transducer, signal processing, or the method used for knock quantification. Utilizing each of these tests, an acceptable parameter setpoint is determined and an acceptable variation range as determined.

3. Results of Control Parameter Studies

3.1. Intake Mixture Temperature

The intake air temperature (IAT) requirements for other researcher tests assessing fuel knock resistance vary. The RON [10] method specifies an IAT value of 52 °C ± 1 °C (125 °F ± 2 °F), while the MON method [7] specifies 38 °C ± 2.8 °C (100 °F ± 5°F). This parameter is different (upstream) than the temperature of the air–fuel mixture in the intake manifold, which is cited in the MON method as intake mixture temperature (IMT) and is specified at 149 °C ± 1 °C (300 °F ± 2 °F). Considering the limited literature citations, the value cited by Leiker et al. [3] of 20 °C (68 °F) was used for the IMT, which is the temperature of the mixture in the intake manifold before the combustion chamber. Leiker et al. did not specifically mention ambient air temperature, but it could be assumed to be the temperature of the test cell. Leiker et al. concluded knock tendency was influenced by intake temperature, with lower MN fuels exhibiting a larger change in KI when tested at higher temperatures.

The first step in analyzing the effects of IMT on MN is determining the relationship between CR and IMT on KI. The two independent variables in this study were CR and IMT. The objective of this study was to better understand the effect these two independent variables had on the onset and intensity of knock. For this study, testing was conducted with the same natural gas fuel sample and constant engine operating conditions, aside from the compression ratio, which was varied. Figure 9 displays the data highlighting the high correlation between the exponential trend lines and the experimental data. For higher IMTs, the KI increased at a greater rate, indicating knock was more sensitive at similar knock values. This was further demonstrated by comparing the slope at a given KI for each of the three IMT values tested.

The next stage of the IMT investigation was to determine the effect of small variations in IMT on the KI experienced by the CFR engine. To isolate IMT as the independent variable, the engine was operated with as little variation as possible to other parameters, including fuel composition, ignition timing, mixture, air pressure, oil, and coolant temperatures. The engine was allowed ample time to reach a steady state before testing began to reduce any possible effects of thermal conditions outside the intake manifold. In selecting the set point for the IMT fluctuation tests, 70 °C was chosen. At this temperature range, the current supplied to the mixture heater could be accurately measured while reducing the risk of backfires in the intake manifold. In practice, with an IMT of 70 °C, ignition timing of 15° (before Top Dead Center) bTDC, 85 kPa atmospheric pressure, and a constant CR of 14:1, the CFR engine was able to maintain consistent KI. The test included five Intake Manifold Heater Current (IMHC) levels ranging from 1.2 to 1.4 amps, which correlated with a variation in IMT of ~4 °C. Over the small temperature range of 4 °C, there was a significant change in KI. The result of the Intake Mixture Temperature Sensitivity study is plotted in Figure 10. The plot displays a linear curve fit with a strong correlation. The interaction of each point from the linear curve fit with the ±1 σ error bars strengthens the validity of the correlation.

Notably, in the 1.35A condition, two temperature points exhibit significant KI variation (0.346 kPa²/s²) despite minimal temperature difference (0.023 °C), illustrating expected KI variation under consistent conditions. The temperature fluctuation during each test, excluding outliers, was restricted to 0.25 °C over 5 min of data collection, despite a notable KI change. To establish an acceptable IMT variation that prevents a significant KI shift surpassing the observed difference between similar temperature results, it was determined that a 1.7 °C change in IMT would yield a change in KI of 0.346 kPa²/s^2, which was considered to be acceptable.

To determine the effect IMT had on the MN value, several different IMT values were considered, spanning the typical temperatures seen in typical engine applications. When operating using low IMT values (<30 °C), even with the use of a chiller (or very low ambient air temperature), heat from the engine transferred through the intake manifold and subsequently raised the IMT. Conversely, when using high IMT values reaching 149 °C (300 °F), there is a very real possibility of ignition in the intake manifold (backfire). Such an event is very possible when utilizing reference fuel blends with high concentrations of hydrogen.

To reduce the effects of uncontrolled variables such as ambient temperature, MN test results are only compared within tests conducted on the same day. Additionally, the engine was given sufficient time to stabilize before testing commenced, mitigating any potential impact from transient thermal effects. Figure 11 shows results from 2 different days of testing, with the maximum variation occurring over temperature values tested of ±1.5 MN. For each day of testing, there was a linear trendline fit to the data to investigate the relationship between IMT setpoint and MN. Using the trendlines from the two days of testing displayed in Figure 11 and the expected variation in KI, the following relationship can be formed:

$$\frac{dMN}{d\left(IMT\right)}=-0.0066 MN \mathrm{u}\mathrm{n}\mathrm{i}\mathrm{t}\mathrm{s}/°\mathrm{C}$$

3.2. Ignition Timing

The objective of this study is to explore the effect varying ignition timing has on the MN of a given test. Autoignition is affected by ignition timing, and generally, the earlier the initiation of the spark, the greater the KI will be registered. Ignition timing is a set parameter with the Woodward LECM; therefore, the Variation study was not conducted.

Considering other methods of knock resistance testing, the MON method [7,11] utilizes a technique with ignition timing dependent on CR. At higher CRs, the spark is retarded to reduce the knock tendency, effectively increasing the resolution that can be achieved by only adjusting CR. The ignition timing range utilized by the MON method is between 14–26° bTDC. The RON method [10] utilizes a constant 13° bTDC ignition timing value. Leiker et al. [3] employed a consistent 15° bTDC ignition timing, with no mention of alternative values in their MN test results, thus leaving the effect of ignition timing on MN unpublished.

Studying the variability of fuel with ignition timing required increasing CR until the onset of knock and then advancing ignition timing and measuring the effect on KI. The data developed was from a single day of testing with consistent fuel composition, and all test parameters were held constant. The Ignition timing variability study utilizing 70 °C IMT and ignition timing ranged from 15° to 25° bTDC while the two test cases differed only in the fixed compression ratio, 15:1 and 15.5:1. Figure 12 shows the results, and both CRs tested showed similar trends. For both cases, there was a positive linear relationship between KI and ignition timing for timing values 17–23° and then a slight negative relationship after 23° bTDC.

The effect of varying ignition timing on MN was also explored. The procedure involved testing the MN of a natural gas test sample using ignition timing ranging from 12° to 21° bTDC. Figure 13 presents results for the 5 MN tests using different ignition timing. The very low slope of the linear regression and R² value indicates the MN is not greatly affected by the ignition timing. Another point of significance is that the tolerance of ±1 MN was maintained with multiple tests occurring with similar operating parameters. Using the slope of the linear regression, a relationship between MN and Ignition timing can be formed:

$$\frac{dMN}{d\left(IgnitionTime\right)}=0.03 MN \mathrm{u}\mathrm{n}\mathrm{i}\mathrm{t}\mathrm{s}/°\mathrm{b}\mathrm{T}\mathrm{D}\mathrm{C}$$

3.3. Intake Manifold Pressure

The objective of this section is to explore the effect intake manifold pressure (IMP) has on the measured MN of a sample gaseous fuel. For this study, the IMP was regulated via the facility’s compressed air system, while the exhaust manifold pressure (EMP) was altered using a manual exhaust restriction valve. However, lowering the EMP beyond ambient conditions was not feasible. The lab systems can simulate elevated pressure conditions in the CFR engine but introduce fluctuations in the intake pressure system of ±5 kPa. These variations occur every few seconds but still allow the average KI value, which encompasses 1000 cycles, to be used as the IMP remains constant during that time. Analyzing the feasibility of the MN method at CSU in Fort Collins, Colorado, which lies at ~5000 ft above sea level, will serve as the lowest possible IMP encompassing most natural gas testing facilities in the country (excluding facilities in southern Wyoming).

The first step in analyzing the impact of IMP was to determine the effects of CR and IMP on KI. The two independent variables in this study are CR and IMP. For this study, the same NG sample, IMT, and ignition timing values were utilized. In Figure 14, the results of the KI Variability study are shown and allow comparison for the different IMP values tested. All IMPs tested have very similar trends and indicate there is little difference between the onset of EGAI based on IMP. The spacing between the pressure cases remains consistent, indicating a linear relationship between KI and IMP.

This section determined the amount of IMP can vary without generating noticeable differences in KI, which would affect the MN results. The test was conducted with a consistent CR of 12.8:1, ignition timing of 15° bTDC, and IMT of 74° ± 0.25 °C. Other testing parameters, such as coolant and oil temperature, remained constant at nominal values. In Figure 15, the results of the IMP sensitivity sweep are shown. The individual data points correspond to the average KI for a given average IMP over 1000 cycle tests. The plot includes a linear curve fit and shows a strong correlation of IMP to KI. Using the same value for KI variation as used in the IMT case. It was determined that a 0.615 kPa change in IMP would yield a change in KI of 0.346 kPa²/s², which was considered to be acceptable.

In the calculation for allowable variation of IMP, there is an exponential relationship between increasing pressure and KI. For heavy knock conditions, small intake manifold pressure changes have a larger impact on average KI, but the knock parameter has more variability associated with it.

To accurately replicate operation at lower elevations, both the IMP and EMP were changed and targeted to the same value. Fluctuations in IMP, maintained within ±5 kPa, posed challenges in consistency, particularly with λ. The recorded fluctuations remained consistent at ±5 kPa and resulted in a larger fluctuation in λ of ±0.01. Fortunately, these fluctuations remained consistent across the testing range and were assumed independent of results. The test procedure included the repetition of measurements with the same test sample gas and consistent operating conditions on different days to minimize differences in responses to the tests. Results from three days of testing, depicted in Figure 16, illustrate the effect of IMP on MN.

Variations within the expected ambient pressure range of 85–105 kPa were smaller than the registered variation between test days at identical operating conditions. Exploring elevated pressure conditions (115–200 kPa) revealed a negative relationship between MN and IMP. Results between the days of testing all registered a similar negative correlation with an improved correlation with a wider range of IMPs tested. Using the average linear regression between the different days of testing, the relationship between MN and IMP is as follows:

$$\frac{dMN}{dIMP}=-0.0487 MN \mathrm{u}\mathrm{n}\mathrm{i}\mathrm{t}\mathrm{s}/\mathrm{k}\mathrm{P}\mathrm{a}$$

3.4. Air/Fuel Mixture Ratio

The air–fuel mixture (λ) ratio is a crucial parameter and influences many engine performance characteristics. Utilizing natural gas as a fuel presents a challenge in determining the correct mixture of fuel to air as natural gas has unknown concentrations of different hydrocarbons. In the other knock rating techniques, the peak knocking condition is utilized. For gaseous fuels like methane or propane, where accurate chemical compositions are known, fuel flow rates can be calculated to ensure chemically correct operation, adjusting for air pressure. Given the varied fuel composition of natural gas, an O₂ sensor was placed in the exhaust. Measure λ removed uncertainty regarding the fuel mixture. For this system, a MoTeC^TM, Professional Lambda Meter (PLM) was used in conjunction with a Bosch O₂ sensor.

The testing for the comparison between CR and KI with different λ values involved incrementally increasing CR and recording operating conditions. The results of this study are included in Figure 17. Among the λ values tested, there was a notably stronger correlation for λ = 1 compared to the others. KI values were less consistent outside the 0.95–1.05 range, and misfires occurred beyond the 0.8–1.2 range, making an average KI figure impractical. The results from this study indicate a significant connection between stoichiometric operating conditions and predictable knock characteristics.

The next sets of tests were conducted with a consistent CR of 14:1, the ignition timing of 15° bTDC, IMP, and EMP at ambient conditions, and an IMT of 70° ± 0.25 °C. Other testing parameters, such as coolant and oil temperature, remained constant at nominal values. In Figure 18, the results of the fuel reactivity sweep are shown, which indicates there is a piecewise linear relationship between λ and average KI. The absolute value of the trendline slopes on either side of the peak value occurring at λ = 1.000 are about the same. This is a helpful relationship because it allows for a symmetric tolerance band to be applied to λ. To determine an average fluctuation of KI, the 1000-cycle test was split into five sections consisting of 200 cycles. The difference between the average of each of these sections and the 1000-cycle dataset determines a typical, expected variation amount with consistent operating parameters. The average difference between the 200-cycle and 1000-cycle periods was 0.363, and using the equation for the line of best fit for the piece-wise function on the rich side, it was determined that a 0.0065 change in λ would yield a change in KI of 0.363 kPa²/s². Applying the same relationship to the lean condition, a change in λ of 0.0074 would yield a change in KI of 0.363 kPa²/s². Considering the air–fuel ratio system only registers 0.001 λ, the maximum allowable variation in λ was determined to be ± 0.007.

The MN measurement requires reproducing knock intensity between a test and reference fuel. Multiple MN tests were performed with different λ values to determine if there was a correlation in the results. The test range was limited to a range of 0.9–1.2 because the KI was found to be highly unstable outside this range. Figure 19 shows the results from 2 days of testing, which support the conclusion of a significant relationship between MN and λ. Following this observation, a second test was conducted spanning a larger range of λ values to validate the results from the first test. The second test supported the findings of the first with a larger variation between lean and rich operating conditions. Within the bounds of the test, it was observed that the λ value had a significant effect on the MN.

$$\frac{dMN}{d\mathsf{\lambda }}=20.9 MN \mathrm{u}\mathrm{n}\mathrm{i}\mathrm{t}\mathrm{s}/\mathsf{\lambda }$$

3.5. Recommended Environmental and Testing Parameters

The operation of an internal combustion engine is a dynamic activity with the requirement of keeping many variables within a given range. Through this research, a better understanding of these values was determined. When measuring the MN of natural gas and other gaseous fuels, the recommended set points and subsequent allowable variation are provided in

Table 1. Research Determined Methane Number Test Parameter Set Points and Variation.

Parameter	Set Point	Allowable Variation (±)
Ignition Timing	12°–21° bTDC	0°
Intake Manifold Temperature	70 °C	1.7 °C
Intake Manifold Pressure	Atmospheric	0.62 kPa (0.09 psig)
Exhaust Manifold Pressure	Atmospheric	2.5 kPa (0.36 psig)
Mixture Ratio	Stoichiometric (λ = 1.000)	0.007 λ

. The values presented in Table 1 only account for a small portion of the environmental and testing parameters present in the operation of an engine. The additional parameters listed in

Table 2. Additional Environmental and Testing Parameters are listed by the MON method [7] and Leiker et al. [3].

Parameter	Set Point	Allowable Variation (±)
Engine RPM	900 RPM	9 RPM
Humidity	0.00534 kg H2O per kg (37.5 grains of H2O per lb.) Dry Air	0.0018 kg (12.5 grains)
Coolant Temperature	100 °C (212 °F)	1.5 °C (3 °F)
Coolant Level (HOT)	“LEVEL HOT” mark	1 cm (0.4 in.)
Coolant Level (COLD)	Just visible in sight glass	1 cm (0.4 in.)
Oil Temperature	57 °C (135 °F)	8 °C (15 °F)
Oil Level (Running & Hot)	Mid-Level in sight glass	0.5 cm (0.2 in.)
Oil Level (Stopped & Cold)	Top of sight glass	0.5 cm (0.2 in.)
Oil Pressure	190 kPa (27.5 psig)	17 kPa (2.5 psig)
Crankcase Internal Pressure	Atmospheric	−2.5 kPa (−0.36 psig)

were based on the requirements listed by the MON method [7]. In the case of coolant level, oil pressure, and oil level, these parameters are unique to the CFR engine system for continued lubrication and cooling. The relationship between the parameters listed in Table 2 and knock intensity was not investigated during this research.

3.6. Dynamic Blending KI Bracketing Method Validation

In evaluating the significance of Methane Number (MN) in characterizing a fuel’s propensity for autoignition, it becomes imperative to validate measurement results by comparing them to a fuel with a known MN. To ensure the robustness of the Bracketing KI Method, validation was undertaken using a certified blend of CH₄/H₂ as the “unknown” sample. The outcome of this validation test utilizing an 85–15 CH₄-H₂ blend is depicted in Figure 20. The certificate of gas analysis from the supplier for the 85–15 CH₄-H₂ “unknown” test fuels had an actual measured value of methane of 85.09 ± 2 mol %. According to the definition of MN, this mixture should have resulted in an MN of exactly 85.09, but achieving an average MN of 84.7 is well within the range of expected error. This verifies the Dynamic Blending Bracketing KI technique produced an accurate MN value for a known blend of methane and hydrogen.

3.7. Comparison between Dynamic and Premixed KI Bracketing Methods

A comparison between these two methods was made between two different techniques for relating the knock intensity of test fuels to reference blends and determining MN. Figure 6 presents the plots for the certified pre-mixed blends under identical operating conditions, while Figure 21 depicts the dynamic blending technique. Under identical operating conditions aside from the compression ratio used, the dynamic blending technique yielded an MN outcome of 86.15, whereas the premixed blends produced an MN of 86.5. This outcome confirms the viability of both techniques to replicate results and provides additional validation for the calibration of the flow meters used in dynamic blending.

As part of the work, it was noted that the MN values of 86.15 or 86.5 differed from the MN calculated by ASTM D8221 [4], which is 79 MNc. Uncertainties in the current method alone cannot explain a significant portion of the difference. Many details of the method used by Leiker et al. [3], as well as experimental data of ternary gaseous fuel compositions, have never been published. Leiker et al. presented experimental data as ternary mixture diagrams, which were used by the method to estimate a methane number (MNc). These diagrams were later digitized by MWM and used in a computer software program for the calculation. Leiker et al. may have had sparse experimental data in this region of low blends of higher hydrocarbon (C4–C6) fuel compositions and may have relied on extrapolation and interpolation, resulting in an over-accounting for these components.

3.8. Comparison between CSU FFT Bandpass and CFR Knock Measurement Systems

Direct comparisons between the CSU FFT Bandpass system and the CFR engine knock meter system are limited by the subjective nature of the CFR system. However, the objective of this study was to determine a method for adjusting the settings of the CFR Detonation Meter to output readings similar to the CSU FFT Bandpass method.

The CFR engine design is such that there is one port in the cylinder head for a pressure transducer or the CFR detonation meter. This means only one knock measurement system can be tested at a time, and hence, differences in knock intensity must be recreated at two different times. There are many adjustments available on the original CFR knock measurement system for precise tuning of knock measurement. Through trial and error, a method for setting the CFR “METER READING” and “SPREAD” values to match the CSU FFT Bandpass system was developed. The method is as follows:

• With the CFR engine off, adjust the screw on the meter face to the threshold of needle movement.
• Bring the engine to steady operating conditions using natural gas.
• Change fuel to known Reference Blend (90–10).
• Increase CR until an audible knock is detected.
• Adjust METER READING dials to achieve 50 KI.
• Increase METER READING coarse dial 1 division.
• Record ΔKI
• Change SPREAD and repeat steps 4–6 until ΔKI = 10 divisions.
  Note: the SPREAD setting was exceedingly low to match the CSU System (0.7)
• Change METER READING to match audible knock level from CSU FFT Bandpass System (3–5 Knock Divisions)
  Note: The Meter Reading setting was required to be very high (8.9) because of the low SPREAD setting.

Figure 22 shows the results from tests investigating the relationship between each method with similar operating conditions using the 90-10 CPRF blend. The results for the comparison between the two methods were not scaled in any way, but rather, the initial CFR KI value was set to a low value using the SPREAD dial. When referencing the CFR system, the unit used is the Knock Meter Reading (KMR), and the CSU system used the average KI.

3.9. Methane Number Measurement Uncertainty

Directly calculating the total uncertainty associated with the Methane Number test procedure is a challenging ordeal, with many different variables adding variation to the measurement. To estimate the total uncertainty associated with the Methane Number, multiple tests were conducted over a 6-month period and plotted in Figure 23. For tests investigating the uncertainty, the following testing parameters were followed: ambient intake/exhaust pressure, stoichiometric mixture, 70 °C intake mixture temperature, and 15° bTDC ignition timing. All results included in the uncertainty analysis had an R² > 0.95, with an average value of 85.6 and a standard deviation of 0.608.

4. Discussion

IMT has a strong role in the propagation of EGAI for a fuel sample with higher temperatures, leading to an increase in both KI and sensitivity to CR. The effect of slight variations in IMT on the KI experienced by the engine has been shown. This was complicated by the unpredictable nature of EGAI and the ability for different knock levels to vary with consistent engine operating conditions. When operating an engine, as in any control system, constraining testing variables unnecessarily adds complications and inherent expenses. Thus, the objective of the IMT Variation study was to set the largest bound on IMT while not exceeding an expected change in KI between two tests with similar temperatures. Based on the data from this natural gas sample, the maximum allowable IMT variation over the course of a test should be ±1.7 °C (3.0 °F).

Ignition timing is a value that is set and does not vary over the operation of the engine, making for a variable that can be easily forgotten. The results of the investigation of ignition timing vs. MN revealed a very low correlation, indicating the value can be left to the user as long as it remains constant between the reference blend and test fuel. An interesting phenomenon occurred comparing 12° bTDC and 17° bTDC cases: hydrogen addition had a greater impact on KI for lower (closer to TDC) ignition timings, indicating greater EGAI sensitivity to fuels with a lower knock resistance.

The data showed that engines with elevated IMP demanded significantly more fuel while producing increased power, necessitating higher fuel manifold pressure to meet flow requirements and overcome IMP. Additionally, higher IAP levels resulted in substantially higher cylinder pressure compared to lower IAP cases despite similar knock intensity. The impact of hydrogen addition on KI varied with pressure, with higher IMP leading to a reduced effect of hydrogen percentage on knock intensity. Moreover, elevated IMP conditions were found to increase exhaust gas temperatures, indicating higher cylinder temperatures and potential engine wear. To prevent exceeding peak cylinder pressure when increasing CR, tests were conducted in both high-to-low and low-to-high pressure directions, confirming the influence of IMP on measured MN.

There is a significant impact of the air–fuel ratio, λ on KI and MN. Thus, ensuring a consistent method for fuel flow control and real-time λ control is crucial for the MN test method. When exhaust gas composition monitoring for λ is unavailable, peak KI conditions also correspond with λ = 1 and represent the most stable KI values.

The operating parameters involved in the Methane Number test procedure that were analyzed in this research are summarized in

Table 3. Parameter Variability and Sensitivity Results.

Variable	$\frac{\mathit{d}\mathit{K}\mathit{I}}{\mathit{d}\left(\mathit{V}\mathit{a}\mathit{r}\mathit{i}\mathit{a}\mathit{b}\mathit{l}\mathit{e}\right)}$	Allowable Variation (±)	$\frac{\mathit{d}\left(\mathit{M}\mathit{N}\right)}{\mathit{d}\left(\mathit{V}\mathit{a}\mathit{r}\mathit{i}\mathit{a}\mathit{b}\mathit{l}\mathit{e}\right)}$
Ignition Timing	Non-linear	Not Applicable *	0.029
Intake Manifold Temperature	0.286	1.66 °C	−0.004
Intake Manifold Pressure	0.562	0.615 kPa	−0.049
Mixture Ratio (λ)	52.2	0.007 λ Units	20.9

* Ignition timing is a parameter set using the digital encoder and is based on precise engine crank angle position. Thus, this parameter does not vary.

. For ignition timing and intake mixture temperature, MN outcomes show a weak correlation, allowing operators flexibility in selecting values for stability and ease of operation while minimizing variation. Conversely, intake manifold pressure and mixture ratio exhibit a stronger correlation with MN outcomes, necessitating operators to consider their impact on stability and compare results across testing conditions. Although consistency in each parameter throughout testing is essential, variations within the tolerance provided in Table 3 are expected and should be maintained.

Comparing the two methods of knock measurement, they each provide a benefit and inherit drawbacks depending on the application. The FFT Bandpass system provides consistent KI values without intervention from the operator and operational parameters. The system also provides insight into cylinder pressures and a detailed analysis of the engine operation. In a research environment, such insight is beneficial, but in a regulatory environment, such information would not be necessary. The drawback to the FFT Bandpass method is its real benefit, with the sensitivity of the method not being able to be adjusted to gain finer resolution between knocking conditions. The CFR Knock Meter method provides such adjustment in resolution and allows a definitive KI metric without the use of post-processing. Even with these differences between methods, both produce a KI parameter that can be used to accurately determine MN.

5. Conclusions

The purpose of this work was to develop a method for determining MN and evaluate the effect of environmental factors and test parameters on end gas auto-ignition on a spark-ignited gaseous fuel engine. This evaluation was completed using a Cooperative Fuel Research engine with modifications implemented to operate using gaseous fuels and control environment parameters. The noteworthy impacts that environment parameters and testing methods have on KI and MN are as follows:

• The ignition timing used for MN has a substantial impact on the KI for a given compression ratio, but this remains constant between the test fuel and reference fuels.
• The intake mixture temperature has minimal influence on MN results but does increase the intensity of EGAI. It was maintained at 70 °C (158 °F) ± 1.7 °C (3.1 °F) to facilitate EGAI while mitigating the risk of backfire.
• Intake manifold pressure significantly affects MN results and knock intensity. It was concluded that MN tests should occur at ambient atmospheric pressure, with fluctuations restricted to ±0.62 kPa. A 10 kPa increase in pressure yields a 0.5 MN variation, which is within the anticipated parameter fluctuation.
• The Air/Fuel ratio can vary significantly over the course of a test and has a significant impact on the KI. It was determined that a λ of 1.000 corresponded to the peak KI value and was the most stable condition. To minimize the effects of λ variations, the unit should be kept within a range of ±0.007.
• This study compared the CSU FFT Bandpass and CFR Knock Detection methods, each offering advantages and disadvantages. Both systems are considered viable for determining MN, with steps for matching sensitivity outlined in this paper.

MN test uncertainty was approximated by testing a consistent fuel sample multiple times over a 6-month period with consistent test parameters and different environmental conditions. The MN test results from these tests have a standard deviation of 0.61 MN units.

This work produced a viable test method for determining the methane number (MN) of a gaseous fuel using a CFR engine. The investigation defined environmental parameters and operating variation limits for the test method. Two methods were developed and validated to determine the MN. These two methods plus the original method are fundamentally the same but allow differences in how reference fuels are generated during the testing allowing a user a choice based on their operational constraints.

6. Future Work

Gaseous fuels with lower methane numbers exhibit reduced ignition delays and faster flame speeds, fostering conditions for low-temperature combustion chemistry and auto-ignition initiation. These gaseous fuels, e.g., hydrogen blended into natural gas, are becoming of commercial significance, and could be tested using this new method to determine the validity of historical data used in today’s methane number index calculators.

While the repeatability of the method has been shown, feedback from other researchers using the proposed method would assist in determining its reproducibility. Also, it would be useful to conduct more testing, to determine the level of bias, if any, between the Matching KI and Bracketing Reference Fuels methods.

Additional testing should be performed with different gaseous fuels offering a range of MN values in order to determine the causes for the differences between the MN values determined by this method and those predicted by the current MN prediction tools.

We propose that the ASTM D03 Gaseous Fuels Subcommittee in collaboration with engine researchers develop a new test method based on this work with the format similar to the existing MON standards [7,11].