## 4 Conclusions  
The following conclusions can be drawn from the above study:  
* In the biogas-DME hybrid dual-fuel engine, CO was generated at the beginning of the combustion process and concentrated mainly in the burnt mixture, behind the flame front. The formation of \(\mathrm{NO_{x}}\) mainly occurred in the reaction region with T \(>\) 1250 \({}^{\circ}\)K and reached the maximum value at approximatively the same position with the peak of temperature. Soot concentration appeared at the beginning of diesel combustion. It reached the first peak at the same crank position of complete combustion of diesel and the second peak at the same position of the maximum temperature.
* At any biogas composition, when DME content increased, \(\mathrm{W_{i}}\) and \(\mathrm{NO_{x}}\) increased while CO and soot volume fraction decreased. The effects of DME on \(\mathrm{W_{i}}\) and soot volume fraction were more significant with poor biogas than with rich biogas, contrary to its effect tendency on CO and \(\mathrm{NO_{x}}\) concentrations.
* With a given operating condition, equivalence ratio, and DME content, the biogas compositions only slightly affected the performance and emission of a hybrid dual-fuel engine. With a fixed 20% DME addition, as shifting from biogas M6C4 to biogas M8C2, the indicative engine cycle work increased by 3%, the maximum gas temperatures rose by 50 \({}^{\circ}\)K, the concentration of CO in the exhaust gas decreased by 20%, the \(\mathrm{NO_{x}}\) concentration went up by 50%, while the soot volume fraction was practically unchanged.
* At a fixed global equivalence ratio \(\phi\) when \(\phi_{\mathrm{gas}}\) increased (i.e., \(\phi_{\mathrm{die}}\) decreased), \(\mathrm{W_{i}}\) and \(\mathrm{NO_{x}}\) concentration increased while CO concentration and soot volume fraction decreased. The effects of DME content on the combustion properties and pollutant emissions were more significant at high \(\phi_{\mathrm{gas}}\).
* At the same operating conditions and global equivalence ratio, biogas-DME PCCI mode was more advantageous than biogas-DME hybrid dual-mode both in engine performance and pollutant emissions except for \(\mathrm{NO_{x}}\). With the same global equivalence ratio \(\phi\) = 0.97, as it shifted from biogas fueling mode to biogas-40% DME fueling mode, \(\mathrm{W_{i}}\) increased by 6% and by 11%, CO emission was reduced by 15% and by 25% while the \(\mathrm{NO_{x}}\) concentration increased by 15% and by 30% for the biogas-DME hybrid dual-fuel engine and for the biogas-DME PCCI engine, respectively. The soot volume fraction decreased sharply with the increase in \(\phi_{\mathrm{gas}}\) in the hybrid dual-fuel engine, and it practically vanished in the PCCI engine.
* Biogas-DME PCCI combustion mode without diesel pilot injection is ideal, but the control of ignition timing and heat release characteristics is a challenge. Thus, the substitution of diesel pilot ignition by DME pilot ignition in a biogas-DME hybrid dual engine is the optimal solution both for performance improvement and pollution emissions reduction.  
[PERSON] was in charge of conceptualization, methodology, formal analysis, writing--review and editing, and project administration. [PERSON] is the corresponding author of this research work. He was in charge of conceptual generation, software, validation, formal analysis, writing--original draft preparation, writing--review, and editing. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Ministry of Education and Training of Vietnam, research grant number CTB2018-DNA.01.  
The authors wish to express their appreciation to Vietnam-German University (VGU) for the supports of facilities in numerical modeling.  
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.