The company, which uses technology developed by Aberdeen University spin-out Data2Text, said the agreement is initially on a month-by-month basis starting from January.
Arria's natural language generation (NLG) engine is being used to monitor machinery on an oil platform in the Gulf of Mexico operated by the US-based Shell Exploration and Production Company.
NLG is a field of artificial intelligence which involves computer programmes being set up to analyse complex sets of data.
Those numbers are then translated into readable reports for human consumption.
AIM-listed Arria indicated the new contract with Shell may be superceded in the coming months.
Arria said: "The terms of the extension include Shell's continued usage of the Arria NLG Engine in the Gulf of Mexico and for ongoing support work.
"Arria and Shell are also discussing the project definition to be included in longer term agreements for Shell's usage of the Arria NLG Engine and associated services, on terms and conditions to be determined."
No financial details of the contract were revealed.
Data2Text was founded four years ago in Aberdeen by Professor Ehud Reiter, Dr Somayajulu Sripada, Ian Davy and John Perry.
London-based Arria took a minority stake in Data2Text in May 2012 before more recently acquiring the whole company.
That saw the Data2Text founders all given stakes in Arria and they remain among the largest shareholders.
Prof Reiter, Dr Sripada and Mr Davy each have around 5.3 million shares with Mr Perry thought to hold about half that.
Aberdeen University has a stake of 4.8 million shares which is equivalent to more than 4.7% of the issued share capital.
Shares have been as high as 282.5p since its flotation and closed yesterday up 9p, or 7% at 140p.
At that valuation the stakes of Prof Reiter, Dr Sripada and Mr Davy are worth around £7.4m but all have lock-in periods.