Anaerobic digestion process depends on substrate composition, load, digester type, mixing of substrate, quality of methanogens and other parameters, but also to a great extent on temperature. You didn't specify at what temperature your process has been carried out. For example, thermophilic digestion operates in temperatures above 50°C and can be much (up to ten times) faster than mesophilic process, for which optimum temperature is in range 35-40°C.

mesophilic about 40 C, total solids 10% , cow dung mixed with rice straw, C:N ratio close to 30:1

It happens some time when inoculum and your substrate are same. This also happens because of the release of some dissolve methane.  Also CO2  and H2 production starts in one week. You might also be lucky enough to get some good microbes and proper condition. Some more details are needed to reach exact conclusion like which gas in biogas were produced? Did it decrease later? What was the inoculum used? Was it active? etc

It can be explained in several ways. First, several factors including substrate type (biodegradability), organic loading, source of inoculum, temperature, pH, mixing, physical parameters of the reactor (geometry) and the activity of methanogens predominantly determine the biogas potential of an anaerobic digester. If you think all these parameters are quite normal to previous works, then, source of inoculum or the activity of methanogens could play a major role during the start up of this digester. For example, if you take seed sludge from a similar bioreactor with high methanogenic activity, then you should see a quicker adaptation than the normal. To understand it clearly, perform a SMA test (specific methanogenic activity test) with acetate or acetate + propionic+butyric as a substrates. Most importantly, did you check the composition of the biogas? During start up, you can even observe hydrogen (during acetogenesis step) and also carbon dioxide.

The reactor will start producing biogas almost instantly, but before you can use it you need to empty the first batch of gas completely (from fixed containers or domes), otherwise the gas contains oxigen from the air; this is an explosive mix.

Not enough information on the system. But I know when I did pilot tests long ago on   continuous stirred tank reactor (CSTR) anaerobic digesters under mesophilic conditions with different types of domestic sludge from wastewater plants, and freshly started up, gas did get produced within 7 days. Depend on the waste, conditions and reactor type and so on as others have also pointed out. See some links below:

http://www.scielo.br/scielo.php?pid=S1516-35982012001100013&script=sci_arttext

https://www.wisconsin.edu/waste-research/download/2014_student_reports/14%20OSH%20Bartell%20&%20Hands.pdf

http://www.ncbi.nlm.nih.gov/pubmed/17558773

https://www.ncsu.edu/bioresources/BioRes_09/BioRes_09_2_3323_AlJuhaimi_HAOAA_Biogar_Prodn_Anaerobic_Digestion_Date_Palm_Waste_5339.pdf

http://theorganicfarmer.org/Articles/choose-type-biogas-system-you-need

Also came across this innovative renewable biogas system marketed from Kenya - claims  biogas production in 7-10 days. See link below:

http://ssc.undp.org/content/dam/ssc/documents/Expo/2013/solutionforum/Solution%20Forum%204%20-%20IFAD/Flexi%20Biogas%20III.pdf

Couple more links I had indicating biogas production in 7 days:

http://www.hindawi.com/journals/isrn/2012/136959/

https://www.wpi.edu/Pubs/E-project/Available/E-project-030311-115831/unrestricted/English_Biogas_Brochure.pdf

With 10% inoculum it is not surprising that you start producing gas in one week (sometimes it is within 2-4 days). The purpose of the inoculum is to kick start  digestion immediately and 10% is substantial quantity to do that.

The lag phase depends on several factors. Among these, include the acclimation of the inoculum. If digestate from mature digesters treating rice straw is taken, you can expect a shorter lag phase. Another factor is the substrates used. Since you are using rice straw, which is highly lignocellulosic, biogas production may take some time to start since the sugars to be eventually degraded into methane are trapped by the lignin. If you want faster and more biogas production, you may consider pre-treating the rice straw by physical, physico-chemical or chemical techniques.

The anaerobic decomposition of organic matter occurs in a four-step process:-

1-     Hydrolysis: This first stage is usually the slowest of the four degradation steps. The bacteria trans form complex organic materials into liquefied monomers and polymers.

2-     Acidogenesis: In the second stage, acidogenic bacteria convert the soluble organic monomers of sugars and amino acids to ethanol and acids.

3-     Acetogenesis: In this third stage both long chain fatty acids and volatile fatty acids and alcohols are transformed by acetogenic bacteria into hydrogen, carbon dioxide and acetic acid.

4-     Methanogenesis: During this final stage, methanogenic bacteria convert the hydrogen and acetic acid to methane gas and carbon dioxide. Methanogenesis is affected by conditions in the reactor such as temperature, feed composition and organic loading rate.

10% inoculum...V/V = 90% substrate . I think your process is overload.  Try with 90% inoculum and 5-10% substrate or less.  This process is sensitive of overload of substrate.  It's not the same approach than with conventionnal fermentation.  By the way you can characterized your substrate in term of COD and adjust the load for the beginning to be not higher tha 5kg COD/m3.j (2 or 3 could be the best for start-up).

Yann      

Based on my experience for cow dung biogas, It need 7-21 days to produce first biogas. It is depend on the environment conditions and raw material type/composition which is used.

Biogas production depends on the composition of your feedstock. You didn't specify what substrate you used. Its organic components affect the rate of biogas produced and it's overall composition. Temperature and pH are also important factors to take note of. Most bioreactors run under mesophilic condition with neutral pH. This can also affect the rate of biogas production during the reaction's initiation and maintenance.

Retention time (also known as Hydraulic retention Time, HRT) is the average period that a given quantity of input remains in the digester to be acted upon by the methanogens. The theoretical retention time is calculated by dividing the average slurry holding volume of the digester by the volume of daily added substrate added daily.

Depending on the vessel geometry, the means of mixing, etc., the effective retention time may vary widely for the individual substrate constituents. Selection of a suitable retention time thus depends not only on the process temperature, but also on the type of substrate used.

In general the optimum retention time can vary between 30 and 100 days. For a night soil biogas digesters the retention time is extended with another 10 days so that the pathogens present in human faeces are largely destroyed.

In my experiment with a 20L digester, food Waste and dung substrate, gas production started from day 4.

It is not surprising if you use 10% of seed sludge from existing working digester and get biogas in a week.

You also need to maintain pH, temperature, alkalinity etc for proper reaction to get the result immediately..

Dear Ashrf Abdel Galil Anwer

I have spent more than a couple of years studying on Biogas and Anaerobic digestion. The bio-digestion process generates biogas since the 4th day, but in fact the initial volume of the produced biogas is quite low. As the retention time increases, the biogas generation rate speeds up as well and reaches to 80% of its maximum level in the 14th day (e.g. for poultry manure) and the 21th day (e.g. for cattle manure).

Regards